%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET894+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:48:54 PM UTC 2026
% Result : Theorem 189.39s 27.09s
% Output : CNFRefutation 198.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 9718 ( 72 unt; 0 def)
% Number of atoms : 32454 (24030 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 30096 (7360 ~;22694 |; 37 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 10 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-3 aty)
% Number of variables : 59343 ( 0 sgn59327 !; 16 ?;59181 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f3,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f4,axiom,
! [X0,X1,X2] :
( X2 = cartesian_product2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4,X5] :
( X3 = ordered_pair(X4,X5)
& in(X5,X1)
& in(X4,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(f5,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f7,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f11,conjecture,
! [X0,X1] : cartesian_product2(singleton(X0),singleton(X1)) = singleton(ordered_pair(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_zfmisc_1) ).
fof(f12,negated_conjecture,
~ ! [X0,X1] : cartesian_product2(singleton(X0),singleton(X1)) = singleton(ordered_pair(X0,X1)),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f15,plain,
? [X0,X1] : cartesian_product2(singleton(X0),singleton(X1)) != singleton(ordered_pair(X0,X1)),
inference(ennf_transformation,[],[f12]) ).
fof(f16,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| X2 = X0 )
& ( X0 != X2
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f17,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(rectify,[],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ( ( in(sK0(X0,X1),X1)
| sK0(X0,X1) = X0 )
& ( ~ in(sK0(X0,X1),X1)
| sK0(X0,X1) != X0 ) )
| X1 = singleton(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ? [X4,X5] :
( X3 = ordered_pair(X4,X5)
& in(X5,X1)
& in(X4,X0) ) )
& ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X4,X5] :
( X3 = ordered_pair(X4,X5)
& in(X5,X1)
& in(X4,X0) ) )
& ( ~ in(X3,X2)
| ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) ) ) )
| X2 = cartesian_product2(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) != X2
| ! [X8] :
( ( ~ in(X8,X2)
| ? [X11,X12] :
( ordered_pair(X11,X12) = X8
& in(X12,X1)
& in(X11,X0) ) )
& ( ! [X9,X10] :
( ordered_pair(X9,X10) != X8
| ~ in(X10,X1)
| ~ in(X9,X0) )
| in(X8,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X6,X7] :
( ordered_pair(X6,X7) = X3
& in(X7,X1)
& in(X6,X0) ) )
& ( ~ in(X3,X2)
| ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) ) ) )
| X2 = cartesian_product2(X0,X1) ) ),
inference(rectify,[],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) != X2
| ! [X8] :
( ( ~ in(X8,X2)
| ( ordered_pair(sK4(X0,X1,X8),sK5(X0,X1,X8)) = X8
& in(sK5(X0,X1,X8),X1)
& in(sK4(X0,X1,X8),X0) ) )
& ( ! [X9,X10] :
( ordered_pair(X9,X10) != X8
| ~ in(X10,X1)
| ~ in(X9,X0) )
| in(X8,X2) ) ) )
& ( ( ( in(sK1(X0,X1,X2),X2)
| ( sK1(X0,X1,X2) = ordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2))
& in(sK3(X0,X1,X2),X1)
& in(sK2(X0,X1,X2),X0) ) )
& ( ~ in(sK1(X0,X1,X2),X2)
| ! [X4,X5] :
( ordered_pair(X4,X5) != sK1(X0,X1,X2)
| ~ in(X5,X1)
| ~ in(X4,X0) ) ) )
| X2 = cartesian_product2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5]),skolemize(X3,sK1(X0,X1,X2)),skolemize(X6,sK2(X0,X1,X2)),skolemize(X7,sK3(X0,X1,X2)),skolemize(X11,sK4(X0,X1,X8)),skolemize(X12,sK5(X0,X1,X8))],[f20]) ).
fof(f22,plain,
! [X0,X1,X2,X3] :
( ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ( in(X1,X3)
& in(X0,X2) ) )
& ( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f23,plain,
! [X0,X1,X2,X3] :
( ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ( in(X1,X3)
& in(X0,X2) ) )
& ( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f22]) ).
fof(f28,plain,
cartesian_product2(singleton(sK9),singleton(sK10)) != singleton(ordered_pair(sK9,sK10)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10]),skolemize(X0,sK9),skolemize(X1,sK10)],[f15]) ).
fof(f30,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f31,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| ~ in(X3,X1)
| X0 = X3 ),
inference(cnf_transformation,[],[f18]) ).
fof(f32,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| X0 != X3
| in(X3,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f35,plain,
! [X2,X0,X1,X8] :
( cartesian_product2(X0,X1) != X2
| ~ in(X8,X2)
| ordered_pair(sK4(X0,X1,X8),sK5(X0,X1,X8)) = X8 ),
inference(cnf_transformation,[],[f21]) ).
fof(f36,plain,
! [X2,X0,X1,X8] :
( cartesian_product2(X0,X1) != X2
| ~ in(X8,X2)
| in(sK5(X0,X1,X8),X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f37,plain,
! [X2,X0,X1,X8] :
( cartesian_product2(X0,X1) != X2
| ~ in(X8,X2)
| in(sK4(X0,X1,X8),X0) ),
inference(cnf_transformation,[],[f21]) ).
fof(f39,plain,
! [X2,X0,X1] :
( in(sK1(X0,X1,X2),X2)
| sK1(X0,X1,X2) = ordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2))
| cartesian_product2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f21]) ).
fof(f40,plain,
! [X2,X0,X1] :
( in(sK1(X0,X1,X2),X2)
| in(sK3(X0,X1,X2),X1)
| cartesian_product2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f21]) ).
fof(f41,plain,
! [X2,X0,X1] :
( in(sK1(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| cartesian_product2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f21]) ).
fof(f42,plain,
! [X2,X0,X1,X4,X5] :
( ~ in(sK1(X0,X1,X2),X2)
| ordered_pair(X4,X5) != sK1(X0,X1,X2)
| ~ in(X5,X1)
| ~ in(X4,X0)
| cartesian_product2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f21]) ).
fof(f43,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f5]) ).
fof(f45,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f23]) ).
fof(f46,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f47,plain,
! [X2,X3,X0,X1] :
( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f23]) ).
fof(f52,plain,
cartesian_product2(singleton(sK9),singleton(sK10)) != singleton(ordered_pair(sK9,sK10)),
inference(cnf_transformation,[],[f28]) ).
fof(f53,plain,
! [X2,X0,X1,X4,X5] :
( ~ in(sK1(X0,X1,X2),X2)
| sK1(X0,X1,X2) != unordered_pair(unordered_pair(X4,X5),singleton(X4))
| ~ in(X5,X1)
| ~ in(X4,X0)
| cartesian_product2(X0,X1) = X2 ),
inference(definition_unfolding,[],[f42,f43]) ).
fof(f54,plain,
! [X2,X0,X1] :
( in(sK1(X0,X1,X2),X2)
| sK1(X0,X1,X2) = unordered_pair(unordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),singleton(sK2(X0,X1,X2)))
| cartesian_product2(X0,X1) = X2 ),
inference(definition_unfolding,[],[f39,f43]) ).
fof(f56,plain,
! [X2,X0,X1,X8] :
( cartesian_product2(X0,X1) != X2
| ~ in(X8,X2)
| unordered_pair(unordered_pair(sK4(X0,X1,X8),sK5(X0,X1,X8)),singleton(sK4(X0,X1,X8))) = X8 ),
inference(definition_unfolding,[],[f35,f43]) ).
fof(f58,plain,
! [X2,X3,X0,X1] :
( ~ in(X1,X3)
| ~ in(X0,X2)
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f47,f43]) ).
fof(f59,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(definition_unfolding,[],[f46,f43]) ).
fof(f60,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(definition_unfolding,[],[f45,f43]) ).
fof(f61,plain,
cartesian_product2(singleton(sK9),singleton(sK10)) != singleton(unordered_pair(unordered_pair(sK9,sK10),singleton(sK9))),
inference(definition_unfolding,[],[f52,f43]) ).
fof(f62,plain,
! [X3,X1] :
( singleton(X3) != X1
| in(X3,X1) ),
inference(equality_resolution,[],[f32]) ).
fof(f63,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f62]) ).
fof(f64,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f31]) ).
fof(f67,plain,
! [X0,X1,X8] :
( ~ in(X8,cartesian_product2(X0,X1))
| in(sK4(X0,X1,X8),X0) ),
inference(equality_resolution,[],[f37]) ).
fof(f68,plain,
! [X0,X1,X8] :
( ~ in(X8,cartesian_product2(X0,X1))
| in(sK5(X0,X1,X8),X1) ),
inference(equality_resolution,[],[f36]) ).
fof(f69,plain,
! [X0,X1,X8] :
( ~ in(X8,cartesian_product2(X0,X1))
| unordered_pair(unordered_pair(sK4(X0,X1,X8),sK5(X0,X1,X8)),singleton(sK4(X0,X1,X8))) = X8 ),
inference(equality_resolution,[],[f56]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f30]) ).
tcf(c_53,plain,
! [X0: $i] : in(X0,singleton(X0)),
inference(cnf_transformation,[],[f63]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ~ in(X1,X3)
| ~ in(X0,X2)
| ~ in(sK1(X2,X3,X4),X4)
| ( unordered_pair(unordered_pair(X0,X1),singleton(X0)) != sK1(X2,X3,X4) ) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X0)
| in(sK1(X0,X1,X2),X2)
| ( cartesian_product2(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X1,X2),X1)
| in(sK1(X0,X1,X2),X2)
| ( cartesian_product2(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK1(X0,X1,X2),X2)
| ( cartesian_product2(X0,X1) = X2 )
| ( unordered_pair(unordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),singleton(sK2(X0,X1,X2))) = sK1(X0,X1,X2) ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(X1,X2,X0),X1)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(X1,X2,X0),X2)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK4(X1,X2,X0),sK5(X1,X2,X0)),singleton(sK4(X1,X2,X0))) = X0 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X2,X0),singleton(X2)),cartesian_product2(X3,X1))
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_71,negated_conjecture,
singleton(unordered_pair(unordered_pair(sK9,sK10),singleton(sK9))) != cartesian_product2(singleton(sK9),singleton(sK10)),
inference(cnf_transformation,[],[f61]) ).
tcf(c_784,plain,
singleton(unordered_pair(singleton(sK9),unordered_pair(sK9,sK10))) != cartesian_product2(singleton(sK9),singleton(sK10)),
inference(superposition,[status(thm)],[c_50,c_71]) ).
tcf(c_787,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK4(singleton(X1),X2,X0) = X1 )
| ~ in(X0,cartesian_product2(singleton(X1),X2)) ),
inference(superposition,[status(thm)],[c_60,c_54]) ).
tcf(c_789,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK5(X1,singleton(X2),X0) = X2 )
| ~ in(X0,cartesian_product2(X1,singleton(X2))) ),
inference(superposition,[status(thm)],[c_61,c_54]) ).
tcf(c_791,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3)) ),
inference(superposition,[status(thm)],[c_50,c_65]) ).
tcf(c_793,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X1)),cartesian_product2(X2,X3)) ),
inference(superposition,[status(thm)],[c_50,c_65]) ).
tcf(c_795,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X3)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3)) ),
inference(superposition,[status(thm)],[c_50,c_66]) ).
tcf(c_797,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X1)),cartesian_product2(X2,X3)) ),
inference(superposition,[status(thm)],[c_50,c_66]) ).
tcf(c_799,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK1(singleton(X0),X1,X2),X2)
| ( cartesian_product2(singleton(X0),X1) = X2 )
| ( sK2(singleton(X0),X1,X2) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_54]) ).
tcf(c_800,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,singleton(X2)),X0)
| ( cartesian_product2(X0,X1) = singleton(X2) )
| ( sK1(X0,X1,singleton(X2)) = X2 ) ),
inference(superposition,[status(thm)],[c_56,c_54]) ).
tcf(c_803,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK1(X0,singleton(X1),X2),X2)
| ( cartesian_product2(X0,singleton(X1)) = X2 )
| ( sK3(X0,singleton(X1),X2) = X1 ) ),
inference(superposition,[status(thm)],[c_57,c_54]) ).
tcf(c_804,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X1,singleton(X2)),X1)
| ( cartesian_product2(X0,X1) = singleton(X2) )
| ( sK1(X0,X1,singleton(X2)) = X2 ) ),
inference(superposition,[status(thm)],[c_57,c_54]) ).
tcf(c_807,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X2)),cartesian_product2(X1,X3))
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_50,c_64]) ).
tcf(c_809,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X2,X0),singleton(X0)),cartesian_product2(X1,X3))
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_50,c_64]) ).
tcf(c_813,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(X2,X3)) ),
inference(superposition,[status(thm)],[c_50,c_791]) ).
tcf(c_820,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X3)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(X2,X3)) ),
inference(superposition,[status(thm)],[c_50,c_795]) ).
tcf(c_831,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X2,X3,cartesian_product2(singleton(X0),X1)),X3)
| ( cartesian_product2(singleton(X0),X1) = cartesian_product2(X2,X3) )
| ( sK4(singleton(X0),X1,sK1(X2,X3,cartesian_product2(singleton(X0),X1))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_787]) ).
tcf(c_832,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,cartesian_product2(singleton(X0),X1)),X2)
| ( cartesian_product2(singleton(X0),X1) = cartesian_product2(X2,X3) )
| ( sK4(singleton(X0),X1,sK1(X2,X3,cartesian_product2(singleton(X0),X1))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_787]) ).
tcf(c_833,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK1(cartesian_product2(singleton(X0),X1),X2,X3),X3)
| ( cartesian_product2(cartesian_product2(singleton(X0),X1),X2) = X3 )
| ( sK4(singleton(X0),X1,sK2(cartesian_product2(singleton(X0),X1),X2,X3)) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_787]) ).
tcf(c_834,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK1(X2,cartesian_product2(singleton(X0),X1),X3),X3)
| ( cartesian_product2(X2,cartesian_product2(singleton(X0),X1)) = X3 )
| ( sK4(singleton(X0),X1,sK3(X2,cartesian_product2(singleton(X0),X1),X3)) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_787]) ).
tcf(c_835,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X1),X2,sK4(cartesian_product2(singleton(X1),X2),X3,X0)) = X1 )
| ~ in(X0,cartesian_product2(cartesian_product2(singleton(X1),X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_787]) ).
tcf(c_836,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),X0)) = X2 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(singleton(X2),X3))) ),
inference(superposition,[status(thm)],[c_61,c_787]) ).
tcf(c_837,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X1),X3,unordered_pair(unordered_pair(X0,X2),singleton(X0))) = X1 )
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_64,c_787]) ).
tcf(c_857,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X2,X3,cartesian_product2(X0,singleton(X1))),X3)
| ( cartesian_product2(X0,singleton(X1)) = cartesian_product2(X2,X3) )
| ( sK5(X0,singleton(X1),sK1(X2,X3,cartesian_product2(X0,singleton(X1)))) = X1 ) ),
inference(superposition,[status(thm)],[c_57,c_789]) ).
tcf(c_858,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,cartesian_product2(X0,singleton(X1))),X2)
| ( cartesian_product2(X0,singleton(X1)) = cartesian_product2(X2,X3) )
| ( sK5(X0,singleton(X1),sK1(X2,X3,cartesian_product2(X0,singleton(X1)))) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_789]) ).
tcf(c_859,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK1(cartesian_product2(X0,singleton(X1)),X2,X3),X3)
| ( cartesian_product2(cartesian_product2(X0,singleton(X1)),X2) = X3 )
| ( sK5(X0,singleton(X1),sK2(cartesian_product2(X0,singleton(X1)),X2,X3)) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_789]) ).
tcf(c_860,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK1(X2,cartesian_product2(X0,singleton(X1)),X3),X3)
| ( cartesian_product2(X2,cartesian_product2(X0,singleton(X1))) = X3 )
| ( sK5(X0,singleton(X1),sK3(X2,cartesian_product2(X0,singleton(X1)),X3)) = X1 ) ),
inference(superposition,[status(thm)],[c_57,c_789]) ).
tcf(c_861,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(X1,singleton(X2),sK4(cartesian_product2(X1,singleton(X2)),X3,X0)) = X2 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,singleton(X2)),X3)) ),
inference(superposition,[status(thm)],[c_60,c_789]) ).
tcf(c_862,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),X0)) = X3 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,singleton(X3)))) ),
inference(superposition,[status(thm)],[c_61,c_789]) ).
tcf(c_863,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(X3,singleton(X1),unordered_pair(unordered_pair(X2,X0),singleton(X2))) = X1 )
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_64,c_789]) ).
tcf(c_882,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X2,X0)),cartesian_product2(X1,X3))
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_50,c_807]) ).
tcf(c_888,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X1),X3,unordered_pair(singleton(X0),unordered_pair(X0,X2))) = X1 )
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_807,c_787]) ).
tcf(c_889,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(X3,singleton(X1),unordered_pair(singleton(X2),unordered_pair(X2,X0))) = X1 )
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_807,c_789]) ).
tcf(c_890,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(singleton(X2),unordered_pair(X0,X2)),cartesian_product2(X3,X1))
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_50,c_809]) ).
tcf(c_898,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X1),X3,unordered_pair(unordered_pair(X2,X0),singleton(X0))) = X1 )
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_809,c_787]) ).
tcf(c_899,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(X3,singleton(X1),unordered_pair(unordered_pair(X0,X2),singleton(X2))) = X1 )
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_809,c_789]) ).
tcf(c_900,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(singleton(X2),unordered_pair(X2,X0)),cartesian_product2(X3,X1))
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_50,c_882]) ).
tcf(c_906,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X1),X3,unordered_pair(singleton(X0),unordered_pair(X2,X0))) = X1 )
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_882,c_787]) ).
tcf(c_907,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(X3,singleton(X1),unordered_pair(singleton(X2),unordered_pair(X0,X2))) = X1 )
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_882,c_789]) ).
tcf(c_918,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X2,X3,cartesian_product2(X0,X1)),X3)
| ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( unordered_pair(unordered_pair(sK4(X0,X1,sK1(X2,X3,cartesian_product2(X0,X1))),sK5(X0,X1,sK1(X2,X3,cartesian_product2(X0,X1)))),singleton(sK4(X0,X1,sK1(X2,X3,cartesian_product2(X0,X1))))) = sK1(X2,X3,cartesian_product2(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_57,c_62]) ).
tcf(c_919,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,cartesian_product2(X0,X1)),X2)
| ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( unordered_pair(unordered_pair(sK4(X0,X1,sK1(X2,X3,cartesian_product2(X0,X1))),sK5(X0,X1,sK1(X2,X3,cartesian_product2(X0,X1)))),singleton(sK4(X0,X1,sK1(X2,X3,cartesian_product2(X0,X1))))) = sK1(X2,X3,cartesian_product2(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_56,c_62]) ).
tcf(c_920,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK1(cartesian_product2(X0,X1),X2,X3),X3)
| ( cartesian_product2(cartesian_product2(X0,X1),X2) = X3 )
| ( unordered_pair(unordered_pair(sK4(X0,X1,sK2(cartesian_product2(X0,X1),X2,X3)),sK5(X0,X1,sK2(cartesian_product2(X0,X1),X2,X3))),singleton(sK4(X0,X1,sK2(cartesian_product2(X0,X1),X2,X3)))) = sK2(cartesian_product2(X0,X1),X2,X3) ) ),
inference(superposition,[status(thm)],[c_56,c_62]) ).
tcf(c_921,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK1(X2,cartesian_product2(X0,X1),X3),X3)
| ( cartesian_product2(X2,cartesian_product2(X0,X1)) = X3 )
| ( unordered_pair(unordered_pair(sK4(X0,X1,sK3(X2,cartesian_product2(X0,X1),X3)),sK5(X0,X1,sK3(X2,cartesian_product2(X0,X1),X3))),singleton(sK4(X0,X1,sK3(X2,cartesian_product2(X0,X1),X3)))) = sK3(X2,cartesian_product2(X0,X1),X3) ) ),
inference(superposition,[status(thm)],[c_57,c_62]) ).
tcf(c_922,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0)),sK5(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0))),singleton(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0)))) = sK4(cartesian_product2(X1,X2),X3,X0) )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_62]) ).
tcf(c_923,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( unordered_pair(unordered_pair(sK4(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0)),sK5(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0))),singleton(sK4(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0)))) = sK5(X1,cartesian_product2(X2,X3),X0) )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_61,c_62]) ).
tcf(c_924,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2))),sK5(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2)))),singleton(sK4(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2))))) = unordered_pair(unordered_pair(X2,X0),singleton(X2)) )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_62]) ).
tcf(c_925,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2))),sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2)))),singleton(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2))))) = unordered_pair(singleton(X0),unordered_pair(X0,X2)) )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_62]) ).
tcf(c_926,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0))),sK5(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0)))),singleton(sK4(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0))))) = unordered_pair(unordered_pair(X2,X0),singleton(X0)) )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_62]) ).
tcf(c_927,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0))),sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0)))),singleton(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0))))) = unordered_pair(singleton(X0),unordered_pair(X2,X0)) )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_62]) ).
tcf(c_928,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2))),sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2)))),singleton(sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2))))) = unordered_pair(singleton(X2),unordered_pair(X0,X2)) )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_62]) ).
tcf(c_963,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cartesian_product2(X0,X1) = singleton(X2) )
| ( sK1(X0,X1,singleton(X2)) = X2 )
| ( unordered_pair(unordered_pair(sK2(X0,X1,singleton(X2)),sK3(X0,X1,singleton(X2))),singleton(sK2(X0,X1,singleton(X2)))) = sK1(X0,X1,singleton(X2)) ) ),
inference(superposition,[status(thm)],[c_58,c_54]) ).
tcf(c_964,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( unordered_pair(unordered_pair(sK2(X2,X3,cartesian_product2(X0,X1)),sK3(X2,X3,cartesian_product2(X0,X1))),singleton(sK2(X2,X3,cartesian_product2(X0,X1)))) = sK1(X2,X3,cartesian_product2(X0,X1)) )
| ( unordered_pair(unordered_pair(sK4(X0,X1,sK1(X2,X3,cartesian_product2(X0,X1))),sK5(X0,X1,sK1(X2,X3,cartesian_product2(X0,X1)))),singleton(sK4(X0,X1,sK1(X2,X3,cartesian_product2(X0,X1))))) = sK1(X2,X3,cartesian_product2(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_58,c_62]) ).
tcf(c_965,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X0,X1) )
| ( sK4(singleton(X2),X3,sK1(X0,X1,cartesian_product2(singleton(X2),X3))) = X2 )
| ( unordered_pair(unordered_pair(sK2(X0,X1,cartesian_product2(singleton(X2),X3)),sK3(X0,X1,cartesian_product2(singleton(X2),X3))),singleton(sK2(X0,X1,cartesian_product2(singleton(X2),X3)))) = sK1(X0,X1,cartesian_product2(singleton(X2),X3)) ) ),
inference(superposition,[status(thm)],[c_58,c_787]) ).
tcf(c_966,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X0,X1) )
| ( sK5(X2,singleton(X3),sK1(X0,X1,cartesian_product2(X2,singleton(X3)))) = X3 )
| ( unordered_pair(unordered_pair(sK2(X0,X1,cartesian_product2(X2,singleton(X3))),sK3(X0,X1,cartesian_product2(X2,singleton(X3)))),singleton(sK2(X0,X1,cartesian_product2(X2,singleton(X3))))) = sK1(X0,X1,cartesian_product2(X2,singleton(X3))) ) ),
inference(superposition,[status(thm)],[c_58,c_789]) ).
tcf(c_988,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ~ in(X1,X3)
| ~ in(X0,X2)
| ~ in(sK1(X2,X3,X4),X4)
| ( unordered_pair(singleton(X0),unordered_pair(X0,X1)) != sK1(X2,X3,X4) ) ),
inference(superposition,[status(thm)],[c_50,c_55]) ).
tcf(c_990,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ~ in(X1,X2)
| ~ in(X0,X3)
| ~ in(sK1(X2,X3,X4),X4)
| ( unordered_pair(unordered_pair(X0,X1),singleton(X1)) != sK1(X2,X3,X4) ) ),
inference(superposition,[status(thm)],[c_50,c_55]) ).
tcf(c_994,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0))),sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0)))),singleton(sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0))))) = unordered_pair(singleton(X2),unordered_pair(X2,X0)) )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_62]) ).
tcf(c_1009,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cartesian_product2(singleton(X0),X1) = singleton(X2) )
| ( sK2(singleton(X0),X1,singleton(X2)) = X0 )
| ( sK1(singleton(X0),X1,singleton(X2)) = X2 ) ),
inference(superposition,[status(thm)],[c_799,c_54]) ).
tcf(c_1010,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X0,X1) )
| ( sK2(singleton(X2),X3,cartesian_product2(X0,X1)) = X2 )
| ( unordered_pair(unordered_pair(sK4(X0,X1,sK1(singleton(X2),X3,cartesian_product2(X0,X1))),sK5(X0,X1,sK1(singleton(X2),X3,cartesian_product2(X0,X1)))),singleton(sK4(X0,X1,sK1(singleton(X2),X3,cartesian_product2(X0,X1))))) = sK1(singleton(X2),X3,cartesian_product2(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_799,c_62]) ).
tcf(c_1011,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(singleton(X0),X1) = cartesian_product2(singleton(X2),X3) )
| ( sK2(singleton(X2),X3,cartesian_product2(singleton(X0),X1)) = X2 )
| ( sK4(singleton(X0),X1,sK1(singleton(X2),X3,cartesian_product2(singleton(X0),X1))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_787]) ).
tcf(c_1012,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X0,singleton(X1)) )
| ( sK2(singleton(X2),X3,cartesian_product2(X0,singleton(X1))) = X2 )
| ( sK5(X0,singleton(X1),sK1(singleton(X2),X3,cartesian_product2(X0,singleton(X1)))) = X1 ) ),
inference(superposition,[status(thm)],[c_799,c_789]) ).
tcf(c_1018,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(cartesian_product2(X0,X1),X2) = singleton(X3) )
| ( sK1(cartesian_product2(X0,X1),X2,singleton(X3)) = X3 )
| ( unordered_pair(unordered_pair(sK4(X0,X1,sK2(cartesian_product2(X0,X1),X2,singleton(X3))),sK5(X0,X1,sK2(cartesian_product2(X0,X1),X2,singleton(X3)))),singleton(sK4(X0,X1,sK2(cartesian_product2(X0,X1),X2,singleton(X3))))) = sK2(cartesian_product2(X0,X1),X2,singleton(X3)) ) ),
inference(superposition,[status(thm)],[c_800,c_62]) ).
tcf(c_1019,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X0),X1),X2) = singleton(X3) )
| ( sK1(cartesian_product2(singleton(X0),X1),X2,singleton(X3)) = X3 )
| ( sK4(singleton(X0),X1,sK2(cartesian_product2(singleton(X0),X1),X2,singleton(X3))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_787]) ).
tcf(c_1020,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(cartesian_product2(X0,singleton(X1)),X2) = singleton(X3) )
| ( sK1(cartesian_product2(X0,singleton(X1)),X2,singleton(X3)) = X3 )
| ( sK5(X0,singleton(X1),sK2(cartesian_product2(X0,singleton(X1)),X2,singleton(X3))) = X1 ) ),
inference(superposition,[status(thm)],[c_800,c_789]) ).
tcf(c_1032,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cartesian_product2(X0,singleton(X1)) = singleton(X2) )
| ( sK3(X0,singleton(X1),singleton(X2)) = X1 )
| ( sK1(X0,singleton(X1),singleton(X2)) = X2 ) ),
inference(superposition,[status(thm)],[c_803,c_54]) ).
tcf(c_1033,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X0,X1) )
| ( sK3(X2,singleton(X3),cartesian_product2(X0,X1)) = X3 )
| ( unordered_pair(unordered_pair(sK4(X0,X1,sK1(X2,singleton(X3),cartesian_product2(X0,X1))),sK5(X0,X1,sK1(X2,singleton(X3),cartesian_product2(X0,X1)))),singleton(sK4(X0,X1,sK1(X2,singleton(X3),cartesian_product2(X0,X1))))) = sK1(X2,singleton(X3),cartesian_product2(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_803,c_62]) ).
tcf(c_1034,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(singleton(X0),X1) = cartesian_product2(X2,singleton(X3)) )
| ( sK3(X2,singleton(X3),cartesian_product2(singleton(X0),X1)) = X3 )
| ( sK4(singleton(X0),X1,sK1(X2,singleton(X3),cartesian_product2(singleton(X0),X1))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_787]) ).
tcf(c_1035,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X0,singleton(X1)) = cartesian_product2(X2,singleton(X3)) )
| ( sK3(X2,singleton(X3),cartesian_product2(X0,singleton(X1))) = X3 )
| ( sK5(X0,singleton(X1),sK1(X2,singleton(X3),cartesian_product2(X0,singleton(X1)))) = X1 ) ),
inference(superposition,[status(thm)],[c_803,c_789]) ).
tcf(c_1054,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X2,cartesian_product2(X0,X1)) = singleton(X3) )
| ( sK1(X2,cartesian_product2(X0,X1),singleton(X3)) = X3 )
| ( unordered_pair(unordered_pair(sK4(X0,X1,sK3(X2,cartesian_product2(X0,X1),singleton(X3))),sK5(X0,X1,sK3(X2,cartesian_product2(X0,X1),singleton(X3)))),singleton(sK4(X0,X1,sK3(X2,cartesian_product2(X0,X1),singleton(X3))))) = sK3(X2,cartesian_product2(X0,X1),singleton(X3)) ) ),
inference(superposition,[status(thm)],[c_804,c_62]) ).
tcf(c_1055,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X2,cartesian_product2(singleton(X0),X1)) = singleton(X3) )
| ( sK1(X2,cartesian_product2(singleton(X0),X1),singleton(X3)) = X3 )
| ( sK4(singleton(X0),X1,sK3(X2,cartesian_product2(singleton(X0),X1),singleton(X3))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_787]) ).
tcf(c_1056,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X2,cartesian_product2(X0,singleton(X1))) = singleton(X3) )
| ( sK1(X2,cartesian_product2(X0,singleton(X1)),singleton(X3)) = X3 )
| ( sK5(X0,singleton(X1),sK3(X2,cartesian_product2(X0,singleton(X1)),singleton(X3))) = X1 ) ),
inference(superposition,[status(thm)],[c_804,c_789]) ).
tcf(c_1060,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,X0),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_837]) ).
tcf(c_1061,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK4(singleton(X4),X1,unordered_pair(unordered_pair(sK1(X2,X3,singleton(X4)),X0),singleton(sK1(X2,X3,singleton(X4))))) = X4 )
| ( unordered_pair(unordered_pair(sK2(X2,X3,singleton(X4)),sK3(X2,X3,singleton(X4))),singleton(sK2(X2,X3,singleton(X4)))) = sK1(X2,X3,singleton(X4)) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_837]) ).
tcf(c_1062,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,singleton(X2)),X4)
| ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,singleton(X2)),X0),singleton(sK1(X3,X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_837]) ).
tcf(c_1063,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,singleton(X2)),X3)
| ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,singleton(X2)),X0),singleton(sK1(X3,X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_837]) ).
tcf(c_1064,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(singleton(X2),X3,X4),X4)
| ( cartesian_product2(singleton(X2),X3) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK2(singleton(X2),X3,X4),X0),singleton(sK2(singleton(X2),X3,X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_837]) ).
tcf(c_1065,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,singleton(X2),X4),X4)
| ( cartesian_product2(X3,singleton(X2)) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK3(X3,singleton(X2),X4),X0),singleton(sK3(X3,singleton(X2),X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_837]) ).
tcf(c_1066,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X1),X4,unordered_pair(unordered_pair(sK4(singleton(X1),X2,X0),X3),singleton(sK4(singleton(X1),X2,X0)))) = X1 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(singleton(X1),X2)) ),
inference(superposition,[status(thm)],[c_60,c_837]) ).
tcf(c_1067,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X2),X4,unordered_pair(unordered_pair(sK5(X1,singleton(X2),X0),X3),singleton(sK5(X1,singleton(X2),X0)))) = X2 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,singleton(X2))) ),
inference(superposition,[status(thm)],[c_61,c_837]) ).
tcf(c_1068,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = singleton(X2) )
| ( sK2(singleton(X3),X4,singleton(X2)) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK1(singleton(X3),X4,singleton(X2)),X0),singleton(sK1(singleton(X3),X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_837]) ).
tcf(c_1069,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X2),X3) = singleton(X4) )
| ( sK1(singleton(X2),X3,singleton(X4)) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK2(singleton(X2),X3,singleton(X4)),X0),singleton(sK2(singleton(X2),X3,singleton(X4))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_837]) ).
tcf(c_1070,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = singleton(X2) )
| ( sK3(X3,singleton(X4),singleton(X2)) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,singleton(X4),singleton(X2)),X0),singleton(sK1(X3,singleton(X4),singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_837]) ).
tcf(c_1071,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X2)) = singleton(X4) )
| ( sK1(X3,singleton(X2),singleton(X4)) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK3(X3,singleton(X2),singleton(X4)),X0),singleton(sK3(X3,singleton(X2),singleton(X4))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_837]) ).
tcf(c_1143,plain,
! [X0: $i,X1: $i] : sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,X1),singleton(X0))) = X0,
inference(superposition,[status(thm)],[c_53,c_1060]) ).
tcf(c_1144,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X0,X1) = X2 )
| ( sK4(singleton(X3),X2,unordered_pair(unordered_pair(X3,sK1(X0,X1,X2)),singleton(X3))) = X3 )
| ( unordered_pair(unordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),singleton(sK2(X0,X1,X2))) = sK1(X0,X1,X2) ) ),
inference(superposition,[status(thm)],[c_58,c_1060]) ).
tcf(c_1145,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X2,X3,X1),X3)
| ( cartesian_product2(X2,X3) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK1(X2,X3,X1)),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_1060]) ).
tcf(c_1146,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,X1),X2)
| ( cartesian_product2(X2,X3) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK1(X2,X3,X1)),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_1060]) ).
tcf(c_1147,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK1(X1,X2,X3),X3)
| ( cartesian_product2(X1,X2) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK2(X1,X2,X3)),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_1060]) ).
tcf(c_1148,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK1(X2,X1,X3),X3)
| ( cartesian_product2(X2,X1) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK3(X2,X1,X3)),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_1060]) ).
tcf(c_1149,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X3),X1,unordered_pair(unordered_pair(X3,sK4(X1,X2,X0)),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_1060]) ).
tcf(c_1150,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X3),X2,unordered_pair(unordered_pair(X3,sK5(X1,X2,X0)),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_1060]) ).
tcf(c_1151,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_1060]) ).
tcf(c_1152,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_1060]) ).
tcf(c_1153,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_1060]) ).
tcf(c_1154,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_1060]) ).
tcf(c_1155,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_1060]) ).
tcf(c_1156,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_1060]) ).
tcf(c_1157,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(singleton(X2),X3) = X1 )
| ( sK2(singleton(X2),X3,X1) = X2 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK1(singleton(X2),X3,X1)),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_1060]) ).
tcf(c_1158,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X1,X2) = singleton(X3) )
| ( sK1(X1,X2,singleton(X3)) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK2(X1,X2,singleton(X3))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_1060]) ).
tcf(c_1159,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X2,singleton(X3)) = X1 )
| ( sK3(X2,singleton(X3),X1) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK1(X2,singleton(X3),X1)),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_1060]) ).
tcf(c_1160,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X2,X1) = singleton(X3) )
| ( sK1(X2,X1,singleton(X3)) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK3(X2,X1,singleton(X3))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_1060]) ).
tcf(c_1250,plain,
! [X0: $i,X1: $i] : sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,X1))) = X0,
inference(superposition,[status(thm)],[c_50,c_1143]) ).
tcf(c_1252,plain,
! [X0: $i,X1: $i] : sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X1,X0),singleton(X0))) = X0,
inference(superposition,[status(thm)],[c_50,c_1143]) ).
tcf(c_1264,plain,
! [X0: $i,X1: $i] : sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X1,X0))) = X0,
inference(superposition,[status(thm)],[c_50,c_1250]) ).
tcf(c_1296,plain,
! [X0: $i,X1: $i] :
( in(X1,singleton(X1))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X1)),cartesian_product2(singleton(X1),singleton(X0))) ),
inference(superposition,[status(thm)],[c_1252,c_60]) ).
tcf(c_1306,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,X2),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_863]) ).
tcf(c_1307,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK5(X1,singleton(X4),unordered_pair(unordered_pair(X0,sK1(X2,X3,singleton(X4))),singleton(X0))) = X4 )
| ( unordered_pair(unordered_pair(sK2(X2,X3,singleton(X4)),sK3(X2,X3,singleton(X4))),singleton(sK2(X2,X3,singleton(X4)))) = sK1(X2,X3,singleton(X4)) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_863]) ).
tcf(c_1308,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,singleton(X2)),X4)
| ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK1(X3,X4,singleton(X2))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_863]) ).
tcf(c_1309,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,singleton(X2)),X3)
| ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK1(X3,X4,singleton(X2))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_863]) ).
tcf(c_1310,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(singleton(X2),X3,X4),X4)
| ( cartesian_product2(singleton(X2),X3) = X4 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK2(singleton(X2),X3,X4)),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_863]) ).
tcf(c_1311,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,singleton(X2),X4),X4)
| ( cartesian_product2(X3,singleton(X2)) = X4 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK3(X3,singleton(X2),X4)),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_863]) ).
tcf(c_1312,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X4,singleton(X1),unordered_pair(unordered_pair(X3,sK4(singleton(X1),X2,X0)),singleton(X3))) = X1 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(singleton(X1),X2)) ),
inference(superposition,[status(thm)],[c_60,c_863]) ).
tcf(c_1313,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X4,singleton(X2),unordered_pair(unordered_pair(X3,sK5(X1,singleton(X2),X0)),singleton(X3))) = X2 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,singleton(X2))) ),
inference(superposition,[status(thm)],[c_61,c_863]) ).
tcf(c_1314,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = singleton(X2) )
| ( sK2(singleton(X3),X4,singleton(X2)) = X3 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK1(singleton(X3),X4,singleton(X2))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_863]) ).
tcf(c_1315,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X2),X3) = singleton(X4) )
| ( sK1(singleton(X2),X3,singleton(X4)) = X4 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK2(singleton(X2),X3,singleton(X4))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_863]) ).
tcf(c_1316,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = singleton(X2) )
| ( sK3(X3,singleton(X4),singleton(X2)) = X4 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK1(X3,singleton(X4),singleton(X2))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_863]) ).
tcf(c_1317,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X2)) = singleton(X4) )
| ( sK1(X3,singleton(X2),singleton(X4)) = X4 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK3(X3,singleton(X2),singleton(X4))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_863]) ).
tcf(c_1382,plain,
! [X0: $i,X1: $i] : sK5(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,X1),singleton(X0))) = X1,
inference(superposition,[status(thm)],[c_53,c_1306]) ).
tcf(c_1383,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( unordered_pair(unordered_pair(sK2(X2,X3,X0),sK3(X2,X3,X0)),singleton(sK2(X2,X3,X0))) = sK1(X2,X3,X0) )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(X2,X3,X0),X1),singleton(sK1(X2,X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_58,c_1306]) ).
tcf(c_1384,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X2,X3,X0),X3)
| ( cartesian_product2(X2,X3) = X0 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(X2,X3,X0),X1),singleton(sK1(X2,X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_57,c_1306]) ).
tcf(c_1385,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,X0),X2)
| ( cartesian_product2(X2,X3) = X0 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(X2,X3,X0),X1),singleton(sK1(X2,X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_1306]) ).
tcf(c_1386,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK1(X0,X2,X3),X3)
| ( cartesian_product2(X0,X2) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK2(X0,X2,X3),X1),singleton(sK2(X0,X2,X3)))) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_1306]) ).
tcf(c_1387,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK1(X2,X0,X3),X3)
| ( cartesian_product2(X2,X0) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK3(X2,X0,X3),X1),singleton(sK3(X2,X0,X3)))) = X1 ) ),
inference(superposition,[status(thm)],[c_57,c_1306]) ).
tcf(c_1388,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(X1,singleton(X3),unordered_pair(unordered_pair(sK4(X1,X2,X0),X3),singleton(sK4(X1,X2,X0)))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_1306]) ).
tcf(c_1389,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK5(X1,X2,X0),X3),singleton(sK5(X1,X2,X0)))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_1306]) ).
tcf(c_1390,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(cartesian_product2(X3,X1),singleton(X4),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X4),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_1306]) ).
tcf(c_1391,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(cartesian_product2(X1,X3),singleton(X4),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X4),singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_1306]) ).
tcf(c_1392,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(cartesian_product2(X1,X3),singleton(X4),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X4),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_1306]) ).
tcf(c_1393,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(cartesian_product2(X1,X3),singleton(X4),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X4),singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_1306]) ).
tcf(c_1394,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(cartesian_product2(X3,X1),singleton(X4),unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X4),singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_1306]) ).
tcf(c_1395,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(cartesian_product2(X3,X1),singleton(X4),unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X4),singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_1306]) ).
tcf(c_1396,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(singleton(X2),X3) = X0 )
| ( sK2(singleton(X2),X3,X0) = X2 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(singleton(X2),X3,X0),X1),singleton(sK1(singleton(X2),X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_799,c_1306]) ).
tcf(c_1397,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X0,X2) = singleton(X3) )
| ( sK1(X0,X2,singleton(X3)) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK2(X0,X2,singleton(X3)),X1),singleton(sK2(X0,X2,singleton(X3))))) = X1 ) ),
inference(superposition,[status(thm)],[c_800,c_1306]) ).
tcf(c_1398,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X2,singleton(X3)) = X0 )
| ( sK3(X2,singleton(X3),X0) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(X2,singleton(X3),X0),X1),singleton(sK1(X2,singleton(X3),X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_803,c_1306]) ).
tcf(c_1399,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X2,X0) = singleton(X3) )
| ( sK1(X2,X0,singleton(X3)) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK3(X2,X0,singleton(X3)),X1),singleton(sK3(X2,X0,singleton(X3))))) = X1 ) ),
inference(superposition,[status(thm)],[c_804,c_1306]) ).
tcf(c_1453,plain,
! [X0: $i,X1: $i] : sK5(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,X1))) = X1,
inference(superposition,[status(thm)],[c_50,c_1382]) ).
tcf(c_1455,plain,
! [X0: $i,X1: $i] : sK5(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X1,X0),singleton(X0))) = X1,
inference(superposition,[status(thm)],[c_50,c_1382]) ).
tcf(c_1457,plain,
! [X0: $i,X1: $i] :
( in(X1,singleton(X1))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(singleton(X0),singleton(X1))) ),
inference(superposition,[status(thm)],[c_1382,c_61]) ).
tcf(c_1475,plain,
! [X0: $i,X1: $i] : sK5(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X1,X0))) = X1,
inference(superposition,[status(thm)],[c_50,c_1453]) ).
tcf(c_1477,plain,
! [X0: $i,X1: $i] :
( in(X1,singleton(X1))
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(singleton(X0),singleton(X1))) ),
inference(superposition,[status(thm)],[c_1453,c_61]) ).
tcf(c_1505,plain,
! [X0: $i,X1: $i] :
( in(X1,singleton(X1))
| ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(singleton(X0),singleton(X1))) ),
inference(superposition,[status(thm)],[c_1475,c_61]) ).
tcf(c_1524,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_888]) ).
tcf(c_1525,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK4(singleton(X4),X1,unordered_pair(singleton(sK1(X2,X3,singleton(X4))),unordered_pair(sK1(X2,X3,singleton(X4)),X0))) = X4 )
| ( unordered_pair(unordered_pair(sK2(X2,X3,singleton(X4)),sK3(X2,X3,singleton(X4))),singleton(sK2(X2,X3,singleton(X4)))) = sK1(X2,X3,singleton(X4)) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_888]) ).
tcf(c_1526,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,singleton(X2)),X4)
| ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK1(X3,X4,singleton(X2))),unordered_pair(sK1(X3,X4,singleton(X2)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_888]) ).
tcf(c_1527,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,singleton(X2)),X3)
| ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK1(X3,X4,singleton(X2))),unordered_pair(sK1(X3,X4,singleton(X2)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_888]) ).
tcf(c_1528,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(singleton(X2),X3,X4),X4)
| ( cartesian_product2(singleton(X2),X3) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK2(singleton(X2),X3,X4)),unordered_pair(sK2(singleton(X2),X3,X4),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_888]) ).
tcf(c_1529,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,singleton(X2),X4),X4)
| ( cartesian_product2(X3,singleton(X2)) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK3(X3,singleton(X2),X4)),unordered_pair(sK3(X3,singleton(X2),X4),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_888]) ).
tcf(c_1530,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X1),X4,unordered_pair(singleton(sK4(singleton(X1),X2,X0)),unordered_pair(sK4(singleton(X1),X2,X0),X3))) = X1 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(singleton(X1),X2)) ),
inference(superposition,[status(thm)],[c_60,c_888]) ).
tcf(c_1531,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X2),X4,unordered_pair(singleton(sK5(X1,singleton(X2),X0)),unordered_pair(sK5(X1,singleton(X2),X0),X3))) = X2 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,singleton(X2))) ),
inference(superposition,[status(thm)],[c_61,c_888]) ).
tcf(c_1532,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = singleton(X2) )
| ( sK2(singleton(X3),X4,singleton(X2)) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK1(singleton(X3),X4,singleton(X2))),unordered_pair(sK1(singleton(X3),X4,singleton(X2)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_888]) ).
tcf(c_1533,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X2),X3) = singleton(X4) )
| ( sK1(singleton(X2),X3,singleton(X4)) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK2(singleton(X2),X3,singleton(X4))),unordered_pair(sK2(singleton(X2),X3,singleton(X4)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_888]) ).
tcf(c_1534,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = singleton(X2) )
| ( sK3(X3,singleton(X4),singleton(X2)) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK1(X3,singleton(X4),singleton(X2))),unordered_pair(sK1(X3,singleton(X4),singleton(X2)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_888]) ).
tcf(c_1535,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X2)) = singleton(X4) )
| ( sK1(X3,singleton(X2),singleton(X4)) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK3(X3,singleton(X2),singleton(X4))),unordered_pair(sK3(X3,singleton(X2),singleton(X4)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_888]) ).
tcf(c_1563,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X0,X1) = X2 )
| ( sK4(singleton(X3),X2,unordered_pair(singleton(X3),unordered_pair(X3,sK1(X0,X1,X2)))) = X3 )
| ( unordered_pair(unordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),singleton(sK2(X0,X1,X2))) = sK1(X0,X1,X2) ) ),
inference(superposition,[status(thm)],[c_58,c_1524]) ).
tcf(c_1564,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X2,X3,X1),X3)
| ( cartesian_product2(X2,X3) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X2,X3,X1)))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_1524]) ).
tcf(c_1565,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,X1),X2)
| ( cartesian_product2(X2,X3) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X2,X3,X1)))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_1524]) ).
tcf(c_1566,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK1(X1,X2,X3),X3)
| ( cartesian_product2(X1,X2) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X1,X2,X3)))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_1524]) ).
tcf(c_1567,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK1(X2,X1,X3),X3)
| ( cartesian_product2(X2,X1) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X2,X1,X3)))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_1524]) ).
tcf(c_1568,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X3),X1,unordered_pair(singleton(X3),unordered_pair(X3,sK4(X1,X2,X0)))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_1524]) ).
tcf(c_1569,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X3),X2,unordered_pair(singleton(X3),unordered_pair(X3,sK5(X1,X2,X0)))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_1524]) ).
tcf(c_1570,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_1524]) ).
tcf(c_1571,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_1524]) ).
tcf(c_1572,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_1524]) ).
tcf(c_1573,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_1524]) ).
tcf(c_1574,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_1524]) ).
tcf(c_1575,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_1524]) ).
tcf(c_1576,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(singleton(X2),X3) = X1 )
| ( sK2(singleton(X2),X3,X1) = X2 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK1(singleton(X2),X3,X1)))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_1524]) ).
tcf(c_1577,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X1,X2) = singleton(X3) )
| ( sK1(X1,X2,singleton(X3)) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X1,X2,singleton(X3))))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_1524]) ).
tcf(c_1578,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X2,singleton(X3)) = X1 )
| ( sK3(X2,singleton(X3),X1) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X2,singleton(X3),X1)))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_1524]) ).
tcf(c_1579,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X2,X1) = singleton(X3) )
| ( sK1(X2,X1,singleton(X3)) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X2,X1,singleton(X3))))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_1524]) ).
tcf(c_1643,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_889]) ).
tcf(c_1644,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK5(X1,singleton(X4),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X2,X3,singleton(X4))))) = X4 )
| ( unordered_pair(unordered_pair(sK2(X2,X3,singleton(X4)),sK3(X2,X3,singleton(X4))),singleton(sK2(X2,X3,singleton(X4)))) = sK1(X2,X3,singleton(X4)) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_889]) ).
tcf(c_1645,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,singleton(X2)),X4)
| ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X3,X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_889]) ).
tcf(c_1646,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,singleton(X2)),X3)
| ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X3,X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_889]) ).
tcf(c_1647,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(singleton(X2),X3,X4),X4)
| ( cartesian_product2(singleton(X2),X3) = X4 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK2(singleton(X2),X3,X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_889]) ).
tcf(c_1648,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,singleton(X2),X4),X4)
| ( cartesian_product2(X3,singleton(X2)) = X4 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK3(X3,singleton(X2),X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_889]) ).
tcf(c_1649,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X4,singleton(X1),unordered_pair(singleton(X3),unordered_pair(X3,sK4(singleton(X1),X2,X0)))) = X1 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(singleton(X1),X2)) ),
inference(superposition,[status(thm)],[c_60,c_889]) ).
tcf(c_1650,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X4,singleton(X2),unordered_pair(singleton(X3),unordered_pair(X3,sK5(X1,singleton(X2),X0)))) = X2 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,singleton(X2))) ),
inference(superposition,[status(thm)],[c_61,c_889]) ).
tcf(c_1651,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = singleton(X2) )
| ( sK2(singleton(X3),X4,singleton(X2)) = X3 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK1(singleton(X3),X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_889]) ).
tcf(c_1652,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X2),X3) = singleton(X4) )
| ( sK1(singleton(X2),X3,singleton(X4)) = X4 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK2(singleton(X2),X3,singleton(X4))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_889]) ).
tcf(c_1653,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = singleton(X2) )
| ( sK3(X3,singleton(X4),singleton(X2)) = X4 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X3,singleton(X4),singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_889]) ).
tcf(c_1654,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X2)) = singleton(X4) )
| ( sK1(X3,singleton(X2),singleton(X4)) = X4 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK3(X3,singleton(X2),singleton(X4))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_889]) ).
tcf(c_1697,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( unordered_pair(unordered_pair(sK2(X2,X3,X0),sK3(X2,X3,X0)),singleton(sK2(X2,X3,X0))) = sK1(X2,X3,X0) )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,X3,X0)),unordered_pair(sK1(X2,X3,X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_58,c_1643]) ).
tcf(c_1698,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X2,X3,X0),X3)
| ( cartesian_product2(X2,X3) = X0 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,X3,X0)),unordered_pair(sK1(X2,X3,X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_57,c_1643]) ).
tcf(c_1699,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,X0),X2)
| ( cartesian_product2(X2,X3) = X0 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,X3,X0)),unordered_pair(sK1(X2,X3,X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_1643]) ).
tcf(c_1700,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK1(X0,X2,X3),X3)
| ( cartesian_product2(X0,X2) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK2(X0,X2,X3)),unordered_pair(sK2(X0,X2,X3),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_1643]) ).
tcf(c_1701,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK1(X2,X0,X3),X3)
| ( cartesian_product2(X2,X0) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK3(X2,X0,X3)),unordered_pair(sK3(X2,X0,X3),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_57,c_1643]) ).
tcf(c_1702,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(X1,singleton(X3),unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(sK4(X1,X2,X0),X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_1643]) ).
tcf(c_1703,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(X2,singleton(X3),unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(sK5(X1,X2,X0),X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_1643]) ).
tcf(c_1704,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(cartesian_product2(X3,X1),singleton(X4),unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_1643]) ).
tcf(c_1705,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(cartesian_product2(X1,X3),singleton(X4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_1643]) ).
tcf(c_1706,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(cartesian_product2(X1,X3),singleton(X4),unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_1643]) ).
tcf(c_1707,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(cartesian_product2(X1,X3),singleton(X4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_1643]) ).
tcf(c_1708,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(cartesian_product2(X3,X1),singleton(X4),unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_1643]) ).
tcf(c_1709,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(cartesian_product2(X3,X1),singleton(X4),unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_1643]) ).
tcf(c_1710,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(singleton(X2),X3) = X0 )
| ( sK2(singleton(X2),X3,X0) = X2 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(singleton(X2),X3,X0)),unordered_pair(sK1(singleton(X2),X3,X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_799,c_1643]) ).
tcf(c_1711,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X0,X2) = singleton(X3) )
| ( sK1(X0,X2,singleton(X3)) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK2(X0,X2,singleton(X3))),unordered_pair(sK2(X0,X2,singleton(X3)),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_800,c_1643]) ).
tcf(c_1712,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X2,singleton(X3)) = X0 )
| ( sK3(X2,singleton(X3),X0) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,singleton(X3),X0)),unordered_pair(sK1(X2,singleton(X3),X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_803,c_1643]) ).
tcf(c_1713,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X2,X0) = singleton(X3) )
| ( sK1(X2,X0,singleton(X3)) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK3(X2,X0,singleton(X3))),unordered_pair(sK3(X2,X0,singleton(X3)),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_804,c_1643]) ).
tcf(c_1823,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X0,X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_898]) ).
tcf(c_1824,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK4(singleton(X4),X1,unordered_pair(unordered_pair(X0,sK1(X2,X3,singleton(X4))),singleton(sK1(X2,X3,singleton(X4))))) = X4 )
| ( unordered_pair(unordered_pair(sK2(X2,X3,singleton(X4)),sK3(X2,X3,singleton(X4))),singleton(sK2(X2,X3,singleton(X4)))) = sK1(X2,X3,singleton(X4)) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_898]) ).
tcf(c_1825,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,singleton(X2)),X4)
| ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X0,sK1(X3,X4,singleton(X2))),singleton(sK1(X3,X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_898]) ).
tcf(c_1826,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,singleton(X2)),X3)
| ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X0,sK1(X3,X4,singleton(X2))),singleton(sK1(X3,X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_898]) ).
tcf(c_1827,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(singleton(X2),X3,X4),X4)
| ( cartesian_product2(singleton(X2),X3) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X0,sK2(singleton(X2),X3,X4)),singleton(sK2(singleton(X2),X3,X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_898]) ).
tcf(c_1828,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,singleton(X2),X4),X4)
| ( cartesian_product2(X3,singleton(X2)) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X0,sK3(X3,singleton(X2),X4)),singleton(sK3(X3,singleton(X2),X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_898]) ).
tcf(c_1829,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X1),X4,unordered_pair(unordered_pair(X3,sK4(singleton(X1),X2,X0)),singleton(sK4(singleton(X1),X2,X0)))) = X1 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(singleton(X1),X2)) ),
inference(superposition,[status(thm)],[c_60,c_898]) ).
tcf(c_1830,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X2),X4,unordered_pair(unordered_pair(X3,sK5(X1,singleton(X2),X0)),singleton(sK5(X1,singleton(X2),X0)))) = X2 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,singleton(X2))) ),
inference(superposition,[status(thm)],[c_61,c_898]) ).
tcf(c_1831,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = singleton(X2) )
| ( sK2(singleton(X3),X4,singleton(X2)) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X0,sK1(singleton(X3),X4,singleton(X2))),singleton(sK1(singleton(X3),X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_898]) ).
tcf(c_1832,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X2),X3) = singleton(X4) )
| ( sK1(singleton(X2),X3,singleton(X4)) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X0,sK2(singleton(X2),X3,singleton(X4))),singleton(sK2(singleton(X2),X3,singleton(X4))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_898]) ).
tcf(c_1833,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = singleton(X2) )
| ( sK3(X3,singleton(X4),singleton(X2)) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X0,sK1(X3,singleton(X4),singleton(X2))),singleton(sK1(X3,singleton(X4),singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_898]) ).
tcf(c_1834,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X2)) = singleton(X4) )
| ( sK1(X3,singleton(X2),singleton(X4)) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X0,sK3(X3,singleton(X2),singleton(X4))),singleton(sK3(X3,singleton(X2),singleton(X4))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_898]) ).
tcf(c_1851,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X0,X1) = X2 )
| ( sK4(singleton(X3),X2,unordered_pair(unordered_pair(sK1(X0,X1,X2),X3),singleton(X3))) = X3 )
| ( unordered_pair(unordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),singleton(sK2(X0,X1,X2))) = sK1(X0,X1,X2) ) ),
inference(superposition,[status(thm)],[c_58,c_1823]) ).
tcf(c_1852,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X2,X3,X1),X3)
| ( cartesian_product2(X2,X3) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK1(X2,X3,X1),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_1823]) ).
tcf(c_1853,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,X1),X2)
| ( cartesian_product2(X2,X3) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK1(X2,X3,X1),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_1823]) ).
tcf(c_1854,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK1(X1,X2,X3),X3)
| ( cartesian_product2(X1,X2) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK2(X1,X2,X3),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_1823]) ).
tcf(c_1855,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK1(X2,X1,X3),X3)
| ( cartesian_product2(X2,X1) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK3(X2,X1,X3),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_1823]) ).
tcf(c_1856,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X3),X1,unordered_pair(unordered_pair(sK4(X1,X2,X0),X3),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_1823]) ).
tcf(c_1857,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X3),X2,unordered_pair(unordered_pair(sK5(X1,X2,X0),X3),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_1823]) ).
tcf(c_1858,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_1823]) ).
tcf(c_1859,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_1823]) ).
tcf(c_1860,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_1823]) ).
tcf(c_1861,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_1823]) ).
tcf(c_1862,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_1823]) ).
tcf(c_1863,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_1823]) ).
tcf(c_1864,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(singleton(X2),X3) = X1 )
| ( sK2(singleton(X2),X3,X1) = X2 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK1(singleton(X2),X3,X1),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_1823]) ).
tcf(c_1865,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X1,X2) = singleton(X3) )
| ( sK1(X1,X2,singleton(X3)) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK2(X1,X2,singleton(X3)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_1823]) ).
tcf(c_1866,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X2,singleton(X3)) = X1 )
| ( sK3(X2,singleton(X3),X1) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK1(X2,singleton(X3),X1),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_1823]) ).
tcf(c_1867,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X2,X1) = singleton(X3) )
| ( sK1(X2,X1,singleton(X3)) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK3(X2,X1,singleton(X3)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_1823]) ).
tcf(c_1929,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X2,X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_899]) ).
tcf(c_1930,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK5(X1,singleton(X4),unordered_pair(unordered_pair(sK1(X2,X3,singleton(X4)),X0),singleton(X0))) = X4 )
| ( unordered_pair(unordered_pair(sK2(X2,X3,singleton(X4)),sK3(X2,X3,singleton(X4))),singleton(sK2(X2,X3,singleton(X4)))) = sK1(X2,X3,singleton(X4)) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_899]) ).
tcf(c_1931,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,singleton(X2)),X4)
| ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,singleton(X2)),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_899]) ).
tcf(c_1932,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,singleton(X2)),X3)
| ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,singleton(X2)),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_899]) ).
tcf(c_1933,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(singleton(X2),X3,X4),X4)
| ( cartesian_product2(singleton(X2),X3) = X4 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK2(singleton(X2),X3,X4),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_899]) ).
tcf(c_1934,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,singleton(X2),X4),X4)
| ( cartesian_product2(X3,singleton(X2)) = X4 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK3(X3,singleton(X2),X4),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_899]) ).
tcf(c_1935,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X4,singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,X0),X3),singleton(X3))) = X1 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(singleton(X1),X2)) ),
inference(superposition,[status(thm)],[c_60,c_899]) ).
tcf(c_1936,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X4,singleton(X2),unordered_pair(unordered_pair(sK5(X1,singleton(X2),X0),X3),singleton(X3))) = X2 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,singleton(X2))) ),
inference(superposition,[status(thm)],[c_61,c_899]) ).
tcf(c_1937,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = singleton(X2) )
| ( sK2(singleton(X3),X4,singleton(X2)) = X3 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK1(singleton(X3),X4,singleton(X2)),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_899]) ).
tcf(c_1938,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X2),X3) = singleton(X4) )
| ( sK1(singleton(X2),X3,singleton(X4)) = X4 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK2(singleton(X2),X3,singleton(X4)),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_899]) ).
tcf(c_1939,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = singleton(X2) )
| ( sK3(X3,singleton(X4),singleton(X2)) = X4 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,singleton(X4),singleton(X2)),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_899]) ).
tcf(c_1940,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X2)) = singleton(X4) )
| ( sK1(X3,singleton(X2),singleton(X4)) = X4 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK3(X3,singleton(X2),singleton(X4)),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_899]) ).
tcf(c_2030,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( unordered_pair(unordered_pair(sK2(X2,X3,X0),sK3(X2,X3,X0)),singleton(sK2(X2,X3,X0))) = sK1(X2,X3,X0) )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK1(X2,X3,X0)),singleton(sK1(X2,X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_58,c_1929]) ).
tcf(c_2031,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X2,X3,X0),X3)
| ( cartesian_product2(X2,X3) = X0 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK1(X2,X3,X0)),singleton(sK1(X2,X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_57,c_1929]) ).
tcf(c_2032,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,X0),X2)
| ( cartesian_product2(X2,X3) = X0 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK1(X2,X3,X0)),singleton(sK1(X2,X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_1929]) ).
tcf(c_2033,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK1(X0,X2,X3),X3)
| ( cartesian_product2(X0,X2) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK2(X0,X2,X3)),singleton(sK2(X0,X2,X3)))) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_1929]) ).
tcf(c_2034,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK1(X2,X0,X3),X3)
| ( cartesian_product2(X2,X0) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK3(X2,X0,X3)),singleton(sK3(X2,X0,X3)))) = X1 ) ),
inference(superposition,[status(thm)],[c_57,c_1929]) ).
tcf(c_2035,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(X1,singleton(X3),unordered_pair(unordered_pair(X3,sK4(X1,X2,X0)),singleton(sK4(X1,X2,X0)))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_1929]) ).
tcf(c_2036,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(X3,sK5(X1,X2,X0)),singleton(sK5(X1,X2,X0)))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_1929]) ).
tcf(c_2037,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(cartesian_product2(X3,X1),singleton(X4),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_1929]) ).
tcf(c_2038,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(cartesian_product2(X1,X3),singleton(X4),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))),singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_1929]) ).
tcf(c_2039,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(cartesian_product2(X1,X3),singleton(X4),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_1929]) ).
tcf(c_2040,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(cartesian_product2(X1,X3),singleton(X4),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))),singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_1929]) ).
tcf(c_2041,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(cartesian_product2(X3,X1),singleton(X4),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))),singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_1929]) ).
tcf(c_2042,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(cartesian_product2(X3,X1),singleton(X4),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))),singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_1929]) ).
tcf(c_2043,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(singleton(X2),X3) = X0 )
| ( sK2(singleton(X2),X3,X0) = X2 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK1(singleton(X2),X3,X0)),singleton(sK1(singleton(X2),X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_799,c_1929]) ).
tcf(c_2044,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X0,X2) = singleton(X3) )
| ( sK1(X0,X2,singleton(X3)) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK2(X0,X2,singleton(X3))),singleton(sK2(X0,X2,singleton(X3))))) = X1 ) ),
inference(superposition,[status(thm)],[c_800,c_1929]) ).
tcf(c_2045,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X2,singleton(X3)) = X0 )
| ( sK3(X2,singleton(X3),X0) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK1(X2,singleton(X3),X0)),singleton(sK1(X2,singleton(X3),X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_803,c_1929]) ).
tcf(c_2046,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X2,X0) = singleton(X3) )
| ( sK1(X2,X0,singleton(X3)) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK3(X2,X0,singleton(X3))),singleton(sK3(X2,X0,singleton(X3))))) = X1 ) ),
inference(superposition,[status(thm)],[c_804,c_1929]) ).
tcf(c_2097,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( sK4(singleton(X4),X2,unordered_pair(unordered_pair(X4,sK4(X2,X3,sK1(X0,X1,cartesian_product2(X2,X3)))),singleton(X4))) = X4 )
| ( unordered_pair(unordered_pair(sK2(X0,X1,cartesian_product2(X2,X3)),sK3(X0,X1,cartesian_product2(X2,X3))),singleton(sK2(X0,X1,cartesian_product2(X2,X3)))) = sK1(X0,X1,cartesian_product2(X2,X3)) ) ),
inference(superposition,[status(thm)],[c_58,c_1149]) ).
tcf(c_2098,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,cartesian_product2(X1,X2)),X4)
| ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK1(X3,X4,cartesian_product2(X1,X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_1149]) ).
tcf(c_2099,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,cartesian_product2(X1,X2)),X3)
| ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK1(X3,X4,cartesian_product2(X1,X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_1149]) ).
tcf(c_2100,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(cartesian_product2(X1,X2),X3,X4),X4)
| ( cartesian_product2(cartesian_product2(X1,X2),X3) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK2(cartesian_product2(X1,X2),X3,X4))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_1149]) ).
tcf(c_2101,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,cartesian_product2(X1,X2),X4),X4)
| ( cartesian_product2(X3,cartesian_product2(X1,X2)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK3(X3,cartesian_product2(X1,X2),X4))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_1149]) ).
tcf(c_2102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X1,unordered_pair(unordered_pair(X4,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0))),singleton(X4))) = X4 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_1149]) ).
tcf(c_2103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X2,unordered_pair(unordered_pair(X4,sK4(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0))),singleton(X4))) = X4 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_61,c_1149]) ).
tcf(c_2104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(X4,sK4(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_1149]) ).
tcf(c_2105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X1,unordered_pair(unordered_pair(X4,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_1149]) ).
tcf(c_2106,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X1,unordered_pair(unordered_pair(X4,sK4(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_1149]) ).
tcf(c_2107,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X1,unordered_pair(unordered_pair(X4,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_1149]) ).
tcf(c_2108,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(X4,sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_1149]) ).
tcf(c_2109,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(X4,sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_1149]) ).
tcf(c_2110,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = cartesian_product2(X1,X2) )
| ( sK2(singleton(X3),X4,cartesian_product2(X1,X2)) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK1(singleton(X3),X4,cartesian_product2(X1,X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_1149]) ).
tcf(c_2111,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = singleton(X4) )
| ( sK1(cartesian_product2(X1,X2),X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK2(cartesian_product2(X1,X2),X3,singleton(X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_1149]) ).
tcf(c_2112,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = cartesian_product2(X1,X2) )
| ( sK3(X3,singleton(X4),cartesian_product2(X1,X2)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK1(X3,singleton(X4),cartesian_product2(X1,X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_1149]) ).
tcf(c_2113,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = singleton(X4) )
| ( sK1(X3,cartesian_product2(X1,X2),singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK3(X3,cartesian_product2(X1,X2),singleton(X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_1149]) ).
tcf(c_2173,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(X4,sK5(X2,X3,sK1(X0,X1,cartesian_product2(X2,X3)))),singleton(X4))) = X4 )
| ( unordered_pair(unordered_pair(sK2(X0,X1,cartesian_product2(X2,X3)),sK3(X0,X1,cartesian_product2(X2,X3))),singleton(sK2(X0,X1,cartesian_product2(X2,X3)))) = sK1(X0,X1,cartesian_product2(X2,X3)) ) ),
inference(superposition,[status(thm)],[c_58,c_1150]) ).
tcf(c_2174,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,cartesian_product2(X2,X1)),X4)
| ( cartesian_product2(X2,X1) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK1(X3,X4,cartesian_product2(X2,X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_1150]) ).
tcf(c_2175,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,cartesian_product2(X2,X1)),X3)
| ( cartesian_product2(X2,X1) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK1(X3,X4,cartesian_product2(X2,X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_1150]) ).
tcf(c_2176,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(cartesian_product2(X2,X1),X3,X4),X4)
| ( cartesian_product2(cartesian_product2(X2,X1),X3) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK2(cartesian_product2(X2,X1),X3,X4))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_1150]) ).
tcf(c_2177,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,cartesian_product2(X2,X1),X4),X4)
| ( cartesian_product2(X3,cartesian_product2(X2,X1)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK3(X3,cartesian_product2(X2,X1),X4))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_1150]) ).
tcf(c_2178,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X2,unordered_pair(unordered_pair(X4,sK5(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0))),singleton(X4))) = X4 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_1150]) ).
tcf(c_2179,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(X4,sK5(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0))),singleton(X4))) = X4 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_61,c_1150]) ).
tcf(c_2180,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X1,unordered_pair(unordered_pair(X4,sK5(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_1150]) ).
tcf(c_2181,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(X4,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_1150]) ).
tcf(c_2182,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(X4,sK5(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_1150]) ).
tcf(c_2183,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(X4,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_1150]) ).
tcf(c_2184,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X1,unordered_pair(unordered_pair(X4,sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_1150]) ).
tcf(c_2185,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X1,unordered_pair(unordered_pair(X4,sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_1150]) ).
tcf(c_2186,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = cartesian_product2(X2,X1) )
| ( sK2(singleton(X3),X4,cartesian_product2(X2,X1)) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK1(singleton(X3),X4,cartesian_product2(X2,X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_1150]) ).
tcf(c_2187,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = singleton(X4) )
| ( sK1(cartesian_product2(X2,X1),X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK2(cartesian_product2(X2,X1),X3,singleton(X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_1150]) ).
tcf(c_2188,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = cartesian_product2(X2,X1) )
| ( sK3(X3,singleton(X4),cartesian_product2(X2,X1)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK1(X3,singleton(X4),cartesian_product2(X2,X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_1150]) ).
tcf(c_2189,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = singleton(X4) )
| ( sK1(X3,cartesian_product2(X2,X1),singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK3(X3,cartesian_product2(X2,X1),singleton(X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_1150]) ).
tcf(c_2277,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( sK4(singleton(X4),X2,unordered_pair(singleton(X4),unordered_pair(X4,sK4(X2,X3,sK1(X0,X1,cartesian_product2(X2,X3)))))) = X4 )
| ( unordered_pair(unordered_pair(sK2(X0,X1,cartesian_product2(X2,X3)),sK3(X0,X1,cartesian_product2(X2,X3))),singleton(sK2(X0,X1,cartesian_product2(X2,X3)))) = sK1(X0,X1,cartesian_product2(X2,X3)) ) ),
inference(superposition,[status(thm)],[c_58,c_1568]) ).
tcf(c_2278,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,cartesian_product2(X1,X2)),X4)
| ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK1(X3,X4,cartesian_product2(X1,X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_1568]) ).
tcf(c_2279,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,cartesian_product2(X1,X2)),X3)
| ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK1(X3,X4,cartesian_product2(X1,X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_1568]) ).
tcf(c_2280,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(cartesian_product2(X1,X2),X3,X4),X4)
| ( cartesian_product2(cartesian_product2(X1,X2),X3) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK2(cartesian_product2(X1,X2),X3,X4))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_1568]) ).
tcf(c_2281,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,cartesian_product2(X1,X2),X4),X4)
| ( cartesian_product2(X3,cartesian_product2(X1,X2)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK3(X3,cartesian_product2(X1,X2),X4))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_1568]) ).
tcf(c_2282,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X1,unordered_pair(singleton(X4),unordered_pair(X4,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0))))) = X4 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_1568]) ).
tcf(c_2283,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X2,unordered_pair(singleton(X4),unordered_pair(X4,sK4(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0))))) = X4 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_61,c_1568]) ).
tcf(c_2284,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(X4,sK4(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_1568]) ).
tcf(c_2285,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X1,unordered_pair(singleton(X4),unordered_pair(X4,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_1568]) ).
tcf(c_2286,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X1,unordered_pair(singleton(X4),unordered_pair(X4,sK4(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_1568]) ).
tcf(c_2287,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X1,unordered_pair(singleton(X4),unordered_pair(X4,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_1568]) ).
tcf(c_2288,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(X4,sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_1568]) ).
tcf(c_2289,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(X4,sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_1568]) ).
tcf(c_2290,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = cartesian_product2(X1,X2) )
| ( sK2(singleton(X3),X4,cartesian_product2(X1,X2)) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK1(singleton(X3),X4,cartesian_product2(X1,X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_1568]) ).
tcf(c_2291,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = singleton(X4) )
| ( sK1(cartesian_product2(X1,X2),X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK2(cartesian_product2(X1,X2),X3,singleton(X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_1568]) ).
tcf(c_2292,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = cartesian_product2(X1,X2) )
| ( sK3(X3,singleton(X4),cartesian_product2(X1,X2)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK1(X3,singleton(X4),cartesian_product2(X1,X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_1568]) ).
tcf(c_2293,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = singleton(X4) )
| ( sK1(X3,cartesian_product2(X1,X2),singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK3(X3,cartesian_product2(X1,X2),singleton(X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_1568]) ).
tcf(c_2335,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(X4,sK5(X2,X3,sK1(X0,X1,cartesian_product2(X2,X3)))))) = X4 )
| ( unordered_pair(unordered_pair(sK2(X0,X1,cartesian_product2(X2,X3)),sK3(X0,X1,cartesian_product2(X2,X3))),singleton(sK2(X0,X1,cartesian_product2(X2,X3)))) = sK1(X0,X1,cartesian_product2(X2,X3)) ) ),
inference(superposition,[status(thm)],[c_58,c_1569]) ).
tcf(c_2336,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,cartesian_product2(X2,X1)),X4)
| ( cartesian_product2(X2,X1) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK1(X3,X4,cartesian_product2(X2,X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_1569]) ).
tcf(c_2337,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,cartesian_product2(X2,X1)),X3)
| ( cartesian_product2(X2,X1) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK1(X3,X4,cartesian_product2(X2,X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_1569]) ).
tcf(c_2338,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(cartesian_product2(X2,X1),X3,X4),X4)
| ( cartesian_product2(cartesian_product2(X2,X1),X3) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK2(cartesian_product2(X2,X1),X3,X4))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_1569]) ).
tcf(c_2339,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,cartesian_product2(X2,X1),X4),X4)
| ( cartesian_product2(X3,cartesian_product2(X2,X1)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK3(X3,cartesian_product2(X2,X1),X4))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_1569]) ).
tcf(c_2340,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X2,unordered_pair(singleton(X4),unordered_pair(X4,sK5(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0))))) = X4 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_1569]) ).
tcf(c_2341,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(X4,sK5(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0))))) = X4 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_61,c_1569]) ).
tcf(c_2342,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X1,unordered_pair(singleton(X4),unordered_pair(X4,sK5(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_1569]) ).
tcf(c_2343,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(X4,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_1569]) ).
tcf(c_2344,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(X4,sK5(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_1569]) ).
tcf(c_2345,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(X4,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_1569]) ).
tcf(c_2346,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X1,unordered_pair(singleton(X4),unordered_pair(X4,sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_1569]) ).
tcf(c_2347,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X1,unordered_pair(singleton(X4),unordered_pair(X4,sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_1569]) ).
tcf(c_2348,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = cartesian_product2(X2,X1) )
| ( sK2(singleton(X3),X4,cartesian_product2(X2,X1)) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK1(singleton(X3),X4,cartesian_product2(X2,X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_1569]) ).
tcf(c_2349,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = singleton(X4) )
| ( sK1(cartesian_product2(X2,X1),X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK2(cartesian_product2(X2,X1),X3,singleton(X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_1569]) ).
tcf(c_2350,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = cartesian_product2(X2,X1) )
| ( sK3(X3,singleton(X4),cartesian_product2(X2,X1)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK1(X3,singleton(X4),cartesian_product2(X2,X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_1569]) ).
tcf(c_2351,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = singleton(X4) )
| ( sK1(X3,cartesian_product2(X2,X1),singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK3(X3,cartesian_product2(X2,X1),singleton(X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_1569]) ).
tcf(c_2384,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X0,X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_906]) ).
tcf(c_2385,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK4(singleton(X4),X1,unordered_pair(singleton(sK1(X2,X3,singleton(X4))),unordered_pair(X0,sK1(X2,X3,singleton(X4))))) = X4 )
| ( unordered_pair(unordered_pair(sK2(X2,X3,singleton(X4)),sK3(X2,X3,singleton(X4))),singleton(sK2(X2,X3,singleton(X4)))) = sK1(X2,X3,singleton(X4)) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_906]) ).
tcf(c_2386,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,singleton(X2)),X4)
| ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK1(X3,X4,singleton(X2))),unordered_pair(X0,sK1(X3,X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_906]) ).
tcf(c_2387,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,singleton(X2)),X3)
| ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK1(X3,X4,singleton(X2))),unordered_pair(X0,sK1(X3,X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_906]) ).
tcf(c_2388,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(singleton(X2),X3,X4),X4)
| ( cartesian_product2(singleton(X2),X3) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK2(singleton(X2),X3,X4)),unordered_pair(X0,sK2(singleton(X2),X3,X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_906]) ).
tcf(c_2389,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,singleton(X2),X4),X4)
| ( cartesian_product2(X3,singleton(X2)) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK3(X3,singleton(X2),X4)),unordered_pair(X0,sK3(X3,singleton(X2),X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_906]) ).
tcf(c_2390,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X1),X4,unordered_pair(singleton(sK4(singleton(X1),X2,X0)),unordered_pair(X3,sK4(singleton(X1),X2,X0)))) = X1 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(singleton(X1),X2)) ),
inference(superposition,[status(thm)],[c_60,c_906]) ).
tcf(c_2391,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X2),X4,unordered_pair(singleton(sK5(X1,singleton(X2),X0)),unordered_pair(X3,sK5(X1,singleton(X2),X0)))) = X2 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,singleton(X2))) ),
inference(superposition,[status(thm)],[c_61,c_906]) ).
tcf(c_2392,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = singleton(X2) )
| ( sK2(singleton(X3),X4,singleton(X2)) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK1(singleton(X3),X4,singleton(X2))),unordered_pair(X0,sK1(singleton(X3),X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_906]) ).
tcf(c_2393,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X2),X3) = singleton(X4) )
| ( sK1(singleton(X2),X3,singleton(X4)) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK2(singleton(X2),X3,singleton(X4))),unordered_pair(X0,sK2(singleton(X2),X3,singleton(X4))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_906]) ).
tcf(c_2394,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = singleton(X2) )
| ( sK3(X3,singleton(X4),singleton(X2)) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK1(X3,singleton(X4),singleton(X2))),unordered_pair(X0,sK1(X3,singleton(X4),singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_906]) ).
tcf(c_2395,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X2)) = singleton(X4) )
| ( sK1(X3,singleton(X2),singleton(X4)) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK3(X3,singleton(X2),singleton(X4))),unordered_pair(X0,sK3(X3,singleton(X2),singleton(X4))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_906]) ).
tcf(c_2453,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X0,X1) = X2 )
| ( sK4(singleton(X3),X2,unordered_pair(singleton(X3),unordered_pair(sK1(X0,X1,X2),X3))) = X3 )
| ( unordered_pair(unordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),singleton(sK2(X0,X1,X2))) = sK1(X0,X1,X2) ) ),
inference(superposition,[status(thm)],[c_58,c_2384]) ).
tcf(c_2454,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X2,X3,X1),X3)
| ( cartesian_product2(X2,X3) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK1(X2,X3,X1),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_2384]) ).
tcf(c_2455,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,X1),X2)
| ( cartesian_product2(X2,X3) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK1(X2,X3,X1),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_2384]) ).
tcf(c_2456,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK1(X1,X2,X3),X3)
| ( cartesian_product2(X1,X2) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK2(X1,X2,X3),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_2384]) ).
tcf(c_2457,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK1(X2,X1,X3),X3)
| ( cartesian_product2(X2,X1) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK3(X2,X1,X3),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_2384]) ).
tcf(c_2458,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X3),X1,unordered_pair(singleton(X3),unordered_pair(sK4(X1,X2,X0),X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2384]) ).
tcf(c_2459,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X3),X2,unordered_pair(singleton(X3),unordered_pair(sK5(X1,X2,X0),X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2384]) ).
tcf(c_2460,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2384]) ).
tcf(c_2461,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2384]) ).
tcf(c_2462,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2384]) ).
tcf(c_2463,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2384]) ).
tcf(c_2464,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2384]) ).
tcf(c_2465,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2384]) ).
tcf(c_2466,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(singleton(X2),X3) = X1 )
| ( sK2(singleton(X2),X3,X1) = X2 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK1(singleton(X2),X3,X1),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_2384]) ).
tcf(c_2467,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X1,X2) = singleton(X3) )
| ( sK1(X1,X2,singleton(X3)) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK2(X1,X2,singleton(X3)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_2384]) ).
tcf(c_2468,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X2,singleton(X3)) = X1 )
| ( sK3(X2,singleton(X3),X1) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK1(X2,singleton(X3),X1),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_2384]) ).
tcf(c_2469,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X2,X1) = singleton(X3) )
| ( sK1(X2,X1,singleton(X3)) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK3(X2,X1,singleton(X3)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_2384]) ).
tcf(c_2539,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X2,X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_907]) ).
tcf(c_2540,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK5(X1,singleton(X4),unordered_pair(singleton(X0),unordered_pair(sK1(X2,X3,singleton(X4)),X0))) = X4 )
| ( unordered_pair(unordered_pair(sK2(X2,X3,singleton(X4)),sK3(X2,X3,singleton(X4))),singleton(sK2(X2,X3,singleton(X4)))) = sK1(X2,X3,singleton(X4)) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_907]) ).
tcf(c_2541,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,singleton(X2)),X4)
| ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK1(X3,X4,singleton(X2)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_907]) ).
tcf(c_2542,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,singleton(X2)),X3)
| ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK1(X3,X4,singleton(X2)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_907]) ).
tcf(c_2543,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(singleton(X2),X3,X4),X4)
| ( cartesian_product2(singleton(X2),X3) = X4 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK2(singleton(X2),X3,X4),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_907]) ).
tcf(c_2544,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,singleton(X2),X4),X4)
| ( cartesian_product2(X3,singleton(X2)) = X4 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK3(X3,singleton(X2),X4),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_907]) ).
tcf(c_2545,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X4,singleton(X1),unordered_pair(singleton(X3),unordered_pair(sK4(singleton(X1),X2,X0),X3))) = X1 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(singleton(X1),X2)) ),
inference(superposition,[status(thm)],[c_60,c_907]) ).
tcf(c_2546,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X4,singleton(X2),unordered_pair(singleton(X3),unordered_pair(sK5(X1,singleton(X2),X0),X3))) = X2 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,singleton(X2))) ),
inference(superposition,[status(thm)],[c_61,c_907]) ).
tcf(c_2547,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = singleton(X2) )
| ( sK2(singleton(X3),X4,singleton(X2)) = X3 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK1(singleton(X3),X4,singleton(X2)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_907]) ).
tcf(c_2548,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X2),X3) = singleton(X4) )
| ( sK1(singleton(X2),X3,singleton(X4)) = X4 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK2(singleton(X2),X3,singleton(X4)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_907]) ).
tcf(c_2549,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = singleton(X2) )
| ( sK3(X3,singleton(X4),singleton(X2)) = X4 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK1(X3,singleton(X4),singleton(X2)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_907]) ).
tcf(c_2550,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X2)) = singleton(X4) )
| ( sK1(X3,singleton(X2),singleton(X4)) = X4 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK3(X3,singleton(X2),singleton(X4)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_907]) ).
tcf(c_2605,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( unordered_pair(unordered_pair(sK2(X2,X3,X0),sK3(X2,X3,X0)),singleton(sK2(X2,X3,X0))) = sK1(X2,X3,X0) )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,X3,X0)),unordered_pair(X1,sK1(X2,X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_58,c_2539]) ).
tcf(c_2606,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X2,X3,X0),X3)
| ( cartesian_product2(X2,X3) = X0 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,X3,X0)),unordered_pair(X1,sK1(X2,X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_57,c_2539]) ).
tcf(c_2607,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,X0),X2)
| ( cartesian_product2(X2,X3) = X0 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,X3,X0)),unordered_pair(X1,sK1(X2,X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_2539]) ).
tcf(c_2608,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK1(X0,X2,X3),X3)
| ( cartesian_product2(X0,X2) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK2(X0,X2,X3)),unordered_pair(X1,sK2(X0,X2,X3)))) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_2539]) ).
tcf(c_2609,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK1(X2,X0,X3),X3)
| ( cartesian_product2(X2,X0) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK3(X2,X0,X3)),unordered_pair(X1,sK3(X2,X0,X3)))) = X1 ) ),
inference(superposition,[status(thm)],[c_57,c_2539]) ).
tcf(c_2610,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(X1,singleton(X3),unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(X3,sK4(X1,X2,X0)))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2539]) ).
tcf(c_2611,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(X2,singleton(X3),unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(X3,sK5(X1,X2,X0)))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2539]) ).
tcf(c_2612,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(cartesian_product2(X3,X1),singleton(X4),unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2539]) ).
tcf(c_2613,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(cartesian_product2(X1,X3),singleton(X4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2539]) ).
tcf(c_2614,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(cartesian_product2(X1,X3),singleton(X4),unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2539]) ).
tcf(c_2615,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(cartesian_product2(X1,X3),singleton(X4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2539]) ).
tcf(c_2616,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(cartesian_product2(X3,X1),singleton(X4),unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2539]) ).
tcf(c_2617,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(cartesian_product2(X3,X1),singleton(X4),unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2539]) ).
tcf(c_2618,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(singleton(X2),X3) = X0 )
| ( sK2(singleton(X2),X3,X0) = X2 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(singleton(X2),X3,X0)),unordered_pair(X1,sK1(singleton(X2),X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_799,c_2539]) ).
tcf(c_2619,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X0,X2) = singleton(X3) )
| ( sK1(X0,X2,singleton(X3)) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK2(X0,X2,singleton(X3))),unordered_pair(X1,sK2(X0,X2,singleton(X3))))) = X1 ) ),
inference(superposition,[status(thm)],[c_800,c_2539]) ).
tcf(c_2620,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X2,singleton(X3)) = X0 )
| ( sK3(X2,singleton(X3),X0) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,singleton(X3),X0)),unordered_pair(X1,sK1(X2,singleton(X3),X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_803,c_2539]) ).
tcf(c_2621,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X2,X0) = singleton(X3) )
| ( sK1(X2,X0,singleton(X3)) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK3(X2,X0,singleton(X3))),unordered_pair(X1,sK3(X2,X0,singleton(X3))))) = X1 ) ),
inference(superposition,[status(thm)],[c_804,c_2539]) ).
tcf(c_2667,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( sK4(singleton(X4),X2,unordered_pair(unordered_pair(sK4(X2,X3,sK1(X0,X1,cartesian_product2(X2,X3))),X4),singleton(X4))) = X4 )
| ( unordered_pair(unordered_pair(sK2(X0,X1,cartesian_product2(X2,X3)),sK3(X0,X1,cartesian_product2(X2,X3))),singleton(sK2(X0,X1,cartesian_product2(X2,X3)))) = sK1(X0,X1,cartesian_product2(X2,X3)) ) ),
inference(superposition,[status(thm)],[c_58,c_1856]) ).
tcf(c_2668,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,cartesian_product2(X1,X2)),X4)
| ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK1(X3,X4,cartesian_product2(X1,X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_1856]) ).
tcf(c_2669,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,cartesian_product2(X1,X2)),X3)
| ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK1(X3,X4,cartesian_product2(X1,X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_1856]) ).
tcf(c_2670,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(cartesian_product2(X1,X2),X3,X4),X4)
| ( cartesian_product2(cartesian_product2(X1,X2),X3) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK2(cartesian_product2(X1,X2),X3,X4)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_1856]) ).
tcf(c_2671,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,cartesian_product2(X1,X2),X4),X4)
| ( cartesian_product2(X3,cartesian_product2(X1,X2)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK3(X3,cartesian_product2(X1,X2),X4)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_1856]) ).
tcf(c_2672,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0)),X4),singleton(X4))) = X4 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_1856]) ).
tcf(c_2673,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X2,unordered_pair(unordered_pair(sK4(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0)),X4),singleton(X4))) = X4 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_61,c_1856]) ).
tcf(c_2674,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_1856]) ).
tcf(c_2675,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_1856]) ).
tcf(c_2676,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_1856]) ).
tcf(c_2677,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_1856]) ).
tcf(c_2678,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_1856]) ).
tcf(c_2679,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_1856]) ).
tcf(c_2680,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = cartesian_product2(X1,X2) )
| ( sK2(singleton(X3),X4,cartesian_product2(X1,X2)) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK1(singleton(X3),X4,cartesian_product2(X1,X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_1856]) ).
tcf(c_2681,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = singleton(X4) )
| ( sK1(cartesian_product2(X1,X2),X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK2(cartesian_product2(X1,X2),X3,singleton(X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_1856]) ).
tcf(c_2682,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = cartesian_product2(X1,X2) )
| ( sK3(X3,singleton(X4),cartesian_product2(X1,X2)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK1(X3,singleton(X4),cartesian_product2(X1,X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_1856]) ).
tcf(c_2683,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = singleton(X4) )
| ( sK1(X3,cartesian_product2(X1,X2),singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK3(X3,cartesian_product2(X1,X2),singleton(X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_1856]) ).
tcf(c_2724,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(sK5(X2,X3,sK1(X0,X1,cartesian_product2(X2,X3))),X4),singleton(X4))) = X4 )
| ( unordered_pair(unordered_pair(sK2(X0,X1,cartesian_product2(X2,X3)),sK3(X0,X1,cartesian_product2(X2,X3))),singleton(sK2(X0,X1,cartesian_product2(X2,X3)))) = sK1(X0,X1,cartesian_product2(X2,X3)) ) ),
inference(superposition,[status(thm)],[c_58,c_1857]) ).
tcf(c_2725,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,cartesian_product2(X2,X1)),X4)
| ( cartesian_product2(X2,X1) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK1(X3,X4,cartesian_product2(X2,X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_1857]) ).
tcf(c_2726,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,cartesian_product2(X2,X1)),X3)
| ( cartesian_product2(X2,X1) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK1(X3,X4,cartesian_product2(X2,X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_1857]) ).
tcf(c_2727,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(cartesian_product2(X2,X1),X3,X4),X4)
| ( cartesian_product2(cartesian_product2(X2,X1),X3) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK2(cartesian_product2(X2,X1),X3,X4)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_1857]) ).
tcf(c_2728,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,cartesian_product2(X2,X1),X4),X4)
| ( cartesian_product2(X3,cartesian_product2(X2,X1)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK3(X3,cartesian_product2(X2,X1),X4)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_1857]) ).
tcf(c_2729,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X2,unordered_pair(unordered_pair(sK5(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0)),X4),singleton(X4))) = X4 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_1857]) ).
tcf(c_2730,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(sK5(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0)),X4),singleton(X4))) = X4 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_61,c_1857]) ).
tcf(c_2731,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_1857]) ).
tcf(c_2732,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_1857]) ).
tcf(c_2733,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_1857]) ).
tcf(c_2734,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_1857]) ).
tcf(c_2735,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_1857]) ).
tcf(c_2736,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_1857]) ).
tcf(c_2737,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = cartesian_product2(X2,X1) )
| ( sK2(singleton(X3),X4,cartesian_product2(X2,X1)) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK1(singleton(X3),X4,cartesian_product2(X2,X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_1857]) ).
tcf(c_2738,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = singleton(X4) )
| ( sK1(cartesian_product2(X2,X1),X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK2(cartesian_product2(X2,X1),X3,singleton(X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_1857]) ).
tcf(c_2739,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = cartesian_product2(X2,X1) )
| ( sK3(X3,singleton(X4),cartesian_product2(X2,X1)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK1(X3,singleton(X4),cartesian_product2(X2,X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_1857]) ).
tcf(c_2740,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = singleton(X4) )
| ( sK1(X3,cartesian_product2(X2,X1),singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK3(X3,cartesian_product2(X2,X1),singleton(X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_1857]) ).
tcf(c_2815,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( sK4(singleton(X4),X2,unordered_pair(singleton(X4),unordered_pair(sK4(X2,X3,sK1(X0,X1,cartesian_product2(X2,X3))),X4))) = X4 )
| ( unordered_pair(unordered_pair(sK2(X0,X1,cartesian_product2(X2,X3)),sK3(X0,X1,cartesian_product2(X2,X3))),singleton(sK2(X0,X1,cartesian_product2(X2,X3)))) = sK1(X0,X1,cartesian_product2(X2,X3)) ) ),
inference(superposition,[status(thm)],[c_58,c_2458]) ).
tcf(c_2816,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,cartesian_product2(X1,X2)),X4)
| ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK1(X3,X4,cartesian_product2(X1,X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_2458]) ).
tcf(c_2817,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,cartesian_product2(X1,X2)),X3)
| ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK1(X3,X4,cartesian_product2(X1,X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_2458]) ).
tcf(c_2818,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(cartesian_product2(X1,X2),X3,X4),X4)
| ( cartesian_product2(cartesian_product2(X1,X2),X3) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK2(cartesian_product2(X1,X2),X3,X4)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_2458]) ).
tcf(c_2819,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,cartesian_product2(X1,X2),X4),X4)
| ( cartesian_product2(X3,cartesian_product2(X1,X2)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK3(X3,cartesian_product2(X1,X2),X4)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_2458]) ).
tcf(c_2820,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X1,unordered_pair(singleton(X4),unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0)),X4))) = X4 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_2458]) ).
tcf(c_2821,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X2,unordered_pair(singleton(X4),unordered_pair(sK4(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0)),X4))) = X4 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_61,c_2458]) ).
tcf(c_2822,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2458]) ).
tcf(c_2823,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X1,unordered_pair(singleton(X4),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2458]) ).
tcf(c_2824,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X1,unordered_pair(singleton(X4),unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2458]) ).
tcf(c_2825,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X1,unordered_pair(singleton(X4),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2458]) ).
tcf(c_2826,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2458]) ).
tcf(c_2827,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2458]) ).
tcf(c_2828,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = cartesian_product2(X1,X2) )
| ( sK2(singleton(X3),X4,cartesian_product2(X1,X2)) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK1(singleton(X3),X4,cartesian_product2(X1,X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_2458]) ).
tcf(c_2829,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = singleton(X4) )
| ( sK1(cartesian_product2(X1,X2),X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK2(cartesian_product2(X1,X2),X3,singleton(X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_2458]) ).
tcf(c_2830,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = cartesian_product2(X1,X2) )
| ( sK3(X3,singleton(X4),cartesian_product2(X1,X2)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK1(X3,singleton(X4),cartesian_product2(X1,X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_2458]) ).
tcf(c_2831,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = singleton(X4) )
| ( sK1(X3,cartesian_product2(X1,X2),singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK3(X3,cartesian_product2(X1,X2),singleton(X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_2458]) ).
tcf(c_2891,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(sK5(X2,X3,sK1(X0,X1,cartesian_product2(X2,X3))),X4))) = X4 )
| ( unordered_pair(unordered_pair(sK2(X0,X1,cartesian_product2(X2,X3)),sK3(X0,X1,cartesian_product2(X2,X3))),singleton(sK2(X0,X1,cartesian_product2(X2,X3)))) = sK1(X0,X1,cartesian_product2(X2,X3)) ) ),
inference(superposition,[status(thm)],[c_58,c_2459]) ).
tcf(c_2892,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,cartesian_product2(X2,X1)),X4)
| ( cartesian_product2(X2,X1) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK1(X3,X4,cartesian_product2(X2,X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_2459]) ).
tcf(c_2893,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,cartesian_product2(X2,X1)),X3)
| ( cartesian_product2(X2,X1) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK1(X3,X4,cartesian_product2(X2,X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_2459]) ).
tcf(c_2894,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(cartesian_product2(X2,X1),X3,X4),X4)
| ( cartesian_product2(cartesian_product2(X2,X1),X3) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK2(cartesian_product2(X2,X1),X3,X4)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_2459]) ).
tcf(c_2895,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,cartesian_product2(X2,X1),X4),X4)
| ( cartesian_product2(X3,cartesian_product2(X2,X1)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK3(X3,cartesian_product2(X2,X1),X4)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_2459]) ).
tcf(c_2896,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X2,unordered_pair(singleton(X4),unordered_pair(sK5(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0)),X4))) = X4 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_2459]) ).
tcf(c_2897,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(sK5(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0)),X4))) = X4 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_61,c_2459]) ).
tcf(c_2898,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X1,unordered_pair(singleton(X4),unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2459]) ).
tcf(c_2899,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2459]) ).
tcf(c_2900,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2459]) ).
tcf(c_2901,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2459]) ).
tcf(c_2902,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X1,unordered_pair(singleton(X4),unordered_pair(sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2459]) ).
tcf(c_2903,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X4),X1,unordered_pair(singleton(X4),unordered_pair(sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2459]) ).
tcf(c_2904,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = cartesian_product2(X2,X1) )
| ( sK2(singleton(X3),X4,cartesian_product2(X2,X1)) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK1(singleton(X3),X4,cartesian_product2(X2,X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_2459]) ).
tcf(c_2905,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = singleton(X4) )
| ( sK1(cartesian_product2(X2,X1),X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK2(cartesian_product2(X2,X1),X3,singleton(X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_2459]) ).
tcf(c_2906,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = cartesian_product2(X2,X1) )
| ( sK3(X3,singleton(X4),cartesian_product2(X2,X1)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK1(X3,singleton(X4),cartesian_product2(X2,X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_2459]) ).
tcf(c_2907,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = singleton(X4) )
| ( sK1(X3,cartesian_product2(X2,X1),singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK3(X3,cartesian_product2(X2,X1),singleton(X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_2459]) ).
tcf(c_2949,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = cartesian_product2(X0,X1) )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X4,sK1(X0,X1,cartesian_product2(cartesian_product2(singleton(X2),X3),X4)))) = X2 )
| ( unordered_pair(unordered_pair(sK2(X0,X1,cartesian_product2(cartesian_product2(singleton(X2),X3),X4)),sK3(X0,X1,cartesian_product2(cartesian_product2(singleton(X2),X3),X4))),singleton(sK2(X0,X1,cartesian_product2(cartesian_product2(singleton(X2),X3),X4)))) = sK1(X0,X1,cartesian_product2(cartesian_product2(singleton(X2),X3),X4)) ) ),
inference(superposition,[status(thm)],[c_58,c_835]) ).
tcf(c_2950,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,cartesian_product2(cartesian_product2(singleton(X0),X1),X2)),X4)
| ( cartesian_product2(cartesian_product2(singleton(X0),X1),X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X0),X1,sK4(cartesian_product2(singleton(X0),X1),X2,sK1(X3,X4,cartesian_product2(cartesian_product2(singleton(X0),X1),X2)))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_835]) ).
tcf(c_2951,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,cartesian_product2(cartesian_product2(singleton(X0),X1),X2)),X3)
| ( cartesian_product2(cartesian_product2(singleton(X0),X1),X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X0),X1,sK4(cartesian_product2(singleton(X0),X1),X2,sK1(X3,X4,cartesian_product2(cartesian_product2(singleton(X0),X1),X2)))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_835]) ).
tcf(c_2952,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(cartesian_product2(cartesian_product2(singleton(X0),X1),X2),X3,X4),X4)
| ( cartesian_product2(cartesian_product2(cartesian_product2(singleton(X0),X1),X2),X3) = X4 )
| ( sK4(singleton(X0),X1,sK4(cartesian_product2(singleton(X0),X1),X2,sK2(cartesian_product2(cartesian_product2(singleton(X0),X1),X2),X3,X4))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_835]) ).
tcf(c_2953,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,cartesian_product2(cartesian_product2(singleton(X0),X1),X2),X4),X4)
| ( cartesian_product2(X3,cartesian_product2(cartesian_product2(singleton(X0),X1),X2)) = X4 )
| ( sK4(singleton(X0),X1,sK4(cartesian_product2(singleton(X0),X1),X2,sK3(X3,cartesian_product2(cartesian_product2(singleton(X0),X1),X2),X4))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_835]) ).
tcf(c_2954,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X1),X2,sK4(cartesian_product2(singleton(X1),X2),X3,sK4(cartesian_product2(cartesian_product2(singleton(X1),X2),X3),X4,X0))) = X1 )
| ~ in(X0,cartesian_product2(cartesian_product2(cartesian_product2(singleton(X1),X2),X3),X4)) ),
inference(superposition,[status(thm)],[c_60,c_835]) ).
tcf(c_2955,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X4,sK5(X1,cartesian_product2(cartesian_product2(singleton(X2),X3),X4),X0))) = X2 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(cartesian_product2(singleton(X2),X3),X4))) ),
inference(superposition,[status(thm)],[c_61,c_835]) ).
tcf(c_2956,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X1),X2,sK4(cartesian_product2(singleton(X1),X2),X4,unordered_pair(unordered_pair(X0,X3),singleton(X0)))) = X1 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(singleton(X1),X2)) ),
inference(superposition,[status(thm)],[c_64,c_835]) ).
tcf(c_2958,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X1),X2,sK4(cartesian_product2(singleton(X1),X2),X4,unordered_pair(unordered_pair(X3,X0),singleton(X0)))) = X1 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(singleton(X1),X2)) ),
inference(superposition,[status(thm)],[c_809,c_835]) ).
tcf(c_2959,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X1),X2,sK4(cartesian_product2(singleton(X1),X2),X4,unordered_pair(singleton(X0),unordered_pair(X3,X0)))) = X1 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(singleton(X1),X2)) ),
inference(superposition,[status(thm)],[c_882,c_835]) ).
tcf(c_2961,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X1),X2,sK4(cartesian_product2(singleton(X1),X2),X4,unordered_pair(singleton(X0),unordered_pair(X0,X3)))) = X1 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(singleton(X1),X2)) ),
inference(superposition,[status(thm)],[c_900,c_835]) ).
tcf(c_2962,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X0),X1),X2) = cartesian_product2(singleton(X3),X4) )
| ( sK2(singleton(X3),X4,cartesian_product2(cartesian_product2(singleton(X0),X1),X2)) = X3 )
| ( sK4(singleton(X0),X1,sK4(cartesian_product2(singleton(X0),X1),X2,sK1(singleton(X3),X4,cartesian_product2(cartesian_product2(singleton(X0),X1),X2)))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_835]) ).
tcf(c_2963,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(singleton(X0),X1),X2),X3) = singleton(X4) )
| ( sK1(cartesian_product2(cartesian_product2(singleton(X0),X1),X2),X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,sK4(cartesian_product2(singleton(X0),X1),X2,sK2(cartesian_product2(cartesian_product2(singleton(X0),X1),X2),X3,singleton(X4)))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_835]) ).
tcf(c_2964,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X0),X1),X2) = cartesian_product2(X3,singleton(X4)) )
| ( sK3(X3,singleton(X4),cartesian_product2(cartesian_product2(singleton(X0),X1),X2)) = X4 )
| ( sK4(singleton(X0),X1,sK4(cartesian_product2(singleton(X0),X1),X2,sK1(X3,singleton(X4),cartesian_product2(cartesian_product2(singleton(X0),X1),X2)))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_835]) ).
tcf(c_2965,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,cartesian_product2(cartesian_product2(singleton(X0),X1),X2)) = singleton(X4) )
| ( sK1(X3,cartesian_product2(cartesian_product2(singleton(X0),X1),X2),singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,sK4(cartesian_product2(singleton(X0),X1),X2,sK3(X3,cartesian_product2(cartesian_product2(singleton(X0),X1),X2),singleton(X4)))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_835]) ).
tcf(c_3005,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,cartesian_product2(singleton(X3),X4)) = cartesian_product2(X0,X1) )
| ( sK4(singleton(X3),X4,sK5(X2,cartesian_product2(singleton(X3),X4),sK1(X0,X1,cartesian_product2(X2,cartesian_product2(singleton(X3),X4))))) = X3 )
| ( unordered_pair(unordered_pair(sK2(X0,X1,cartesian_product2(X2,cartesian_product2(singleton(X3),X4))),sK3(X0,X1,cartesian_product2(X2,cartesian_product2(singleton(X3),X4)))),singleton(sK2(X0,X1,cartesian_product2(X2,cartesian_product2(singleton(X3),X4))))) = sK1(X0,X1,cartesian_product2(X2,cartesian_product2(singleton(X3),X4))) ) ),
inference(superposition,[status(thm)],[c_58,c_836]) ).
tcf(c_3006,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,cartesian_product2(X2,cartesian_product2(singleton(X0),X1))),X4)
| ( cartesian_product2(X2,cartesian_product2(singleton(X0),X1)) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X0),X1,sK5(X2,cartesian_product2(singleton(X0),X1),sK1(X3,X4,cartesian_product2(X2,cartesian_product2(singleton(X0),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_836]) ).
tcf(c_3007,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,cartesian_product2(X2,cartesian_product2(singleton(X0),X1))),X3)
| ( cartesian_product2(X2,cartesian_product2(singleton(X0),X1)) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X0),X1,sK5(X2,cartesian_product2(singleton(X0),X1),sK1(X3,X4,cartesian_product2(X2,cartesian_product2(singleton(X0),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_836]) ).
tcf(c_3008,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(cartesian_product2(X2,cartesian_product2(singleton(X0),X1)),X3,X4),X4)
| ( cartesian_product2(cartesian_product2(X2,cartesian_product2(singleton(X0),X1)),X3) = X4 )
| ( sK4(singleton(X0),X1,sK5(X2,cartesian_product2(singleton(X0),X1),sK2(cartesian_product2(X2,cartesian_product2(singleton(X0),X1)),X3,X4))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_836]) ).
tcf(c_3009,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,cartesian_product2(X2,cartesian_product2(singleton(X0),X1)),X4),X4)
| ( cartesian_product2(X3,cartesian_product2(X2,cartesian_product2(singleton(X0),X1))) = X4 )
| ( sK4(singleton(X0),X1,sK5(X2,cartesian_product2(singleton(X0),X1),sK3(X3,cartesian_product2(X2,cartesian_product2(singleton(X0),X1)),X4))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_836]) ).
tcf(c_3010,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),sK4(cartesian_product2(X1,cartesian_product2(singleton(X2),X3)),X4,X0))) = X2 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,cartesian_product2(singleton(X2),X3)),X4)) ),
inference(superposition,[status(thm)],[c_60,c_836]) ).
tcf(c_3011,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X4,sK5(X2,cartesian_product2(singleton(X3),X4),sK5(X1,cartesian_product2(X2,cartesian_product2(singleton(X3),X4)),X0))) = X3 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,cartesian_product2(singleton(X3),X4)))) ),
inference(superposition,[status(thm)],[c_61,c_836]) ).
tcf(c_3012,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X1),X2,sK5(X4,cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X3,X0),singleton(X3)))) = X1 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(singleton(X1),X2)) ),
inference(superposition,[status(thm)],[c_64,c_836]) ).
tcf(c_3014,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X1),X2,sK5(X4,cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,X3),singleton(X3)))) = X1 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(singleton(X1),X2)) ),
inference(superposition,[status(thm)],[c_809,c_836]) ).
tcf(c_3015,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X1),X2,sK5(X4,cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X3),unordered_pair(X0,X3)))) = X1 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(singleton(X1),X2)) ),
inference(superposition,[status(thm)],[c_882,c_836]) ).
tcf(c_3017,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X1),X2,sK5(X4,cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X3),unordered_pair(X3,X0)))) = X1 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(singleton(X1),X2)) ),
inference(superposition,[status(thm)],[c_900,c_836]) ).
tcf(c_3018,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,cartesian_product2(singleton(X0),X1)) = cartesian_product2(singleton(X3),X4) )
| ( sK2(singleton(X3),X4,cartesian_product2(X2,cartesian_product2(singleton(X0),X1))) = X3 )
| ( sK4(singleton(X0),X1,sK5(X2,cartesian_product2(singleton(X0),X1),sK1(singleton(X3),X4,cartesian_product2(X2,cartesian_product2(singleton(X0),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_836]) ).
tcf(c_3019,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(X2,cartesian_product2(singleton(X0),X1)),X3) = singleton(X4) )
| ( sK1(cartesian_product2(X2,cartesian_product2(singleton(X0),X1)),X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,sK5(X2,cartesian_product2(singleton(X0),X1),sK2(cartesian_product2(X2,cartesian_product2(singleton(X0),X1)),X3,singleton(X4)))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_836]) ).
tcf(c_3020,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,cartesian_product2(singleton(X0),X1)) = cartesian_product2(X3,singleton(X4)) )
| ( sK3(X3,singleton(X4),cartesian_product2(X2,cartesian_product2(singleton(X0),X1))) = X4 )
| ( sK4(singleton(X0),X1,sK5(X2,cartesian_product2(singleton(X0),X1),sK1(X3,singleton(X4),cartesian_product2(X2,cartesian_product2(singleton(X0),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_836]) ).
tcf(c_3021,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,cartesian_product2(singleton(X0),X1))) = singleton(X4) )
| ( sK1(X3,cartesian_product2(X2,cartesian_product2(singleton(X0),X1)),singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,sK5(X2,cartesian_product2(singleton(X0),X1),sK3(X3,cartesian_product2(X2,cartesian_product2(singleton(X0),X1)),singleton(X4)))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_836]) ).
tcf(c_3051,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = cartesian_product2(X0,X1) )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X4,sK1(X0,X1,cartesian_product2(cartesian_product2(X2,singleton(X3)),X4)))) = X3 )
| ( unordered_pair(unordered_pair(sK2(X0,X1,cartesian_product2(cartesian_product2(X2,singleton(X3)),X4)),sK3(X0,X1,cartesian_product2(cartesian_product2(X2,singleton(X3)),X4))),singleton(sK2(X0,X1,cartesian_product2(cartesian_product2(X2,singleton(X3)),X4)))) = sK1(X0,X1,cartesian_product2(cartesian_product2(X2,singleton(X3)),X4)) ) ),
inference(superposition,[status(thm)],[c_58,c_861]) ).
tcf(c_3052,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,cartesian_product2(cartesian_product2(X0,singleton(X1)),X2)),X4)
| ( cartesian_product2(cartesian_product2(X0,singleton(X1)),X2) = cartesian_product2(X3,X4) )
| ( sK5(X0,singleton(X1),sK4(cartesian_product2(X0,singleton(X1)),X2,sK1(X3,X4,cartesian_product2(cartesian_product2(X0,singleton(X1)),X2)))) = X1 ) ),
inference(superposition,[status(thm)],[c_57,c_861]) ).
tcf(c_3053,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,cartesian_product2(cartesian_product2(X0,singleton(X1)),X2)),X3)
| ( cartesian_product2(cartesian_product2(X0,singleton(X1)),X2) = cartesian_product2(X3,X4) )
| ( sK5(X0,singleton(X1),sK4(cartesian_product2(X0,singleton(X1)),X2,sK1(X3,X4,cartesian_product2(cartesian_product2(X0,singleton(X1)),X2)))) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_861]) ).
tcf(c_3054,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(cartesian_product2(cartesian_product2(X0,singleton(X1)),X2),X3,X4),X4)
| ( cartesian_product2(cartesian_product2(cartesian_product2(X0,singleton(X1)),X2),X3) = X4 )
| ( sK5(X0,singleton(X1),sK4(cartesian_product2(X0,singleton(X1)),X2,sK2(cartesian_product2(cartesian_product2(X0,singleton(X1)),X2),X3,X4))) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_861]) ).
tcf(c_3055,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,cartesian_product2(cartesian_product2(X0,singleton(X1)),X2),X4),X4)
| ( cartesian_product2(X3,cartesian_product2(cartesian_product2(X0,singleton(X1)),X2)) = X4 )
| ( sK5(X0,singleton(X1),sK4(cartesian_product2(X0,singleton(X1)),X2,sK3(X3,cartesian_product2(cartesian_product2(X0,singleton(X1)),X2),X4))) = X1 ) ),
inference(superposition,[status(thm)],[c_57,c_861]) ).
tcf(c_3056,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X1,singleton(X2),sK4(cartesian_product2(X1,singleton(X2)),X3,sK4(cartesian_product2(cartesian_product2(X1,singleton(X2)),X3),X4,X0))) = X2 )
| ~ in(X0,cartesian_product2(cartesian_product2(cartesian_product2(X1,singleton(X2)),X3),X4)) ),
inference(superposition,[status(thm)],[c_60,c_861]) ).
tcf(c_3057,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X4,sK5(X1,cartesian_product2(cartesian_product2(X2,singleton(X3)),X4),X0))) = X3 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(cartesian_product2(X2,singleton(X3)),X4))) ),
inference(superposition,[status(thm)],[c_61,c_861]) ).
tcf(c_3058,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X1,singleton(X2),sK4(cartesian_product2(X1,singleton(X2)),X4,unordered_pair(unordered_pair(X0,X3),singleton(X0)))) = X2 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,singleton(X2))) ),
inference(superposition,[status(thm)],[c_64,c_861]) ).
tcf(c_3060,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X1,singleton(X2),sK4(cartesian_product2(X1,singleton(X2)),X4,unordered_pair(unordered_pair(X3,X0),singleton(X0)))) = X2 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,singleton(X2))) ),
inference(superposition,[status(thm)],[c_809,c_861]) ).
tcf(c_3061,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X1,singleton(X2),sK4(cartesian_product2(X1,singleton(X2)),X4,unordered_pair(singleton(X0),unordered_pair(X3,X0)))) = X2 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,singleton(X2))) ),
inference(superposition,[status(thm)],[c_882,c_861]) ).
tcf(c_3063,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X1,singleton(X2),sK4(cartesian_product2(X1,singleton(X2)),X4,unordered_pair(singleton(X0),unordered_pair(X0,X3)))) = X2 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,singleton(X2))) ),
inference(superposition,[status(thm)],[c_900,c_861]) ).
tcf(c_3064,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(X0,singleton(X1)),X2) = cartesian_product2(singleton(X3),X4) )
| ( sK2(singleton(X3),X4,cartesian_product2(cartesian_product2(X0,singleton(X1)),X2)) = X3 )
| ( sK5(X0,singleton(X1),sK4(cartesian_product2(X0,singleton(X1)),X2,sK1(singleton(X3),X4,cartesian_product2(cartesian_product2(X0,singleton(X1)),X2)))) = X1 ) ),
inference(superposition,[status(thm)],[c_799,c_861]) ).
tcf(c_3065,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X0,singleton(X1)),X2),X3) = singleton(X4) )
| ( sK1(cartesian_product2(cartesian_product2(X0,singleton(X1)),X2),X3,singleton(X4)) = X4 )
| ( sK5(X0,singleton(X1),sK4(cartesian_product2(X0,singleton(X1)),X2,sK2(cartesian_product2(cartesian_product2(X0,singleton(X1)),X2),X3,singleton(X4)))) = X1 ) ),
inference(superposition,[status(thm)],[c_800,c_861]) ).
tcf(c_3066,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(X0,singleton(X1)),X2) = cartesian_product2(X3,singleton(X4)) )
| ( sK3(X3,singleton(X4),cartesian_product2(cartesian_product2(X0,singleton(X1)),X2)) = X4 )
| ( sK5(X0,singleton(X1),sK4(cartesian_product2(X0,singleton(X1)),X2,sK1(X3,singleton(X4),cartesian_product2(cartesian_product2(X0,singleton(X1)),X2)))) = X1 ) ),
inference(superposition,[status(thm)],[c_803,c_861]) ).
tcf(c_3067,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,cartesian_product2(cartesian_product2(X0,singleton(X1)),X2)) = singleton(X4) )
| ( sK1(X3,cartesian_product2(cartesian_product2(X0,singleton(X1)),X2),singleton(X4)) = X4 )
| ( sK5(X0,singleton(X1),sK4(cartesian_product2(X0,singleton(X1)),X2,sK3(X3,cartesian_product2(cartesian_product2(X0,singleton(X1)),X2),singleton(X4)))) = X1 ) ),
inference(superposition,[status(thm)],[c_804,c_861]) ).
tcf(c_3130,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,cartesian_product2(X3,singleton(X4))) = cartesian_product2(X0,X1) )
| ( sK5(X3,singleton(X4),sK5(X2,cartesian_product2(X3,singleton(X4)),sK1(X0,X1,cartesian_product2(X2,cartesian_product2(X3,singleton(X4)))))) = X4 )
| ( unordered_pair(unordered_pair(sK2(X0,X1,cartesian_product2(X2,cartesian_product2(X3,singleton(X4)))),sK3(X0,X1,cartesian_product2(X2,cartesian_product2(X3,singleton(X4))))),singleton(sK2(X0,X1,cartesian_product2(X2,cartesian_product2(X3,singleton(X4)))))) = sK1(X0,X1,cartesian_product2(X2,cartesian_product2(X3,singleton(X4)))) ) ),
inference(superposition,[status(thm)],[c_58,c_862]) ).
tcf(c_3131,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,cartesian_product2(X2,cartesian_product2(X0,singleton(X1)))),X4)
| ( cartesian_product2(X2,cartesian_product2(X0,singleton(X1))) = cartesian_product2(X3,X4) )
| ( sK5(X0,singleton(X1),sK5(X2,cartesian_product2(X0,singleton(X1)),sK1(X3,X4,cartesian_product2(X2,cartesian_product2(X0,singleton(X1)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_57,c_862]) ).
tcf(c_3132,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,cartesian_product2(X2,cartesian_product2(X0,singleton(X1)))),X3)
| ( cartesian_product2(X2,cartesian_product2(X0,singleton(X1))) = cartesian_product2(X3,X4) )
| ( sK5(X0,singleton(X1),sK5(X2,cartesian_product2(X0,singleton(X1)),sK1(X3,X4,cartesian_product2(X2,cartesian_product2(X0,singleton(X1)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_862]) ).
tcf(c_3133,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(cartesian_product2(X2,cartesian_product2(X0,singleton(X1))),X3,X4),X4)
| ( cartesian_product2(cartesian_product2(X2,cartesian_product2(X0,singleton(X1))),X3) = X4 )
| ( sK5(X0,singleton(X1),sK5(X2,cartesian_product2(X0,singleton(X1)),sK2(cartesian_product2(X2,cartesian_product2(X0,singleton(X1))),X3,X4))) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_862]) ).
tcf(c_3134,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,cartesian_product2(X2,cartesian_product2(X0,singleton(X1))),X4),X4)
| ( cartesian_product2(X3,cartesian_product2(X2,cartesian_product2(X0,singleton(X1)))) = X4 )
| ( sK5(X0,singleton(X1),sK5(X2,cartesian_product2(X0,singleton(X1)),sK3(X3,cartesian_product2(X2,cartesian_product2(X0,singleton(X1))),X4))) = X1 ) ),
inference(superposition,[status(thm)],[c_57,c_862]) ).
tcf(c_3135,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),sK4(cartesian_product2(X1,cartesian_product2(X2,singleton(X3))),X4,X0))) = X3 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,cartesian_product2(X2,singleton(X3))),X4)) ),
inference(superposition,[status(thm)],[c_60,c_862]) ).
tcf(c_3136,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X3,singleton(X4),sK5(X2,cartesian_product2(X3,singleton(X4)),sK5(X1,cartesian_product2(X2,cartesian_product2(X3,singleton(X4))),X0))) = X4 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,cartesian_product2(X3,singleton(X4))))) ),
inference(superposition,[status(thm)],[c_61,c_862]) ).
tcf(c_3137,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X1,singleton(X2),sK5(X4,cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X3,X0),singleton(X3)))) = X2 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,singleton(X2))) ),
inference(superposition,[status(thm)],[c_64,c_862]) ).
tcf(c_3139,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X1,singleton(X2),sK5(X4,cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,X3),singleton(X3)))) = X2 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,singleton(X2))) ),
inference(superposition,[status(thm)],[c_809,c_862]) ).
tcf(c_3140,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X1,singleton(X2),sK5(X4,cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X3),unordered_pair(X0,X3)))) = X2 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,singleton(X2))) ),
inference(superposition,[status(thm)],[c_882,c_862]) ).
tcf(c_3142,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X1,singleton(X2),sK5(X4,cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X3),unordered_pair(X3,X0)))) = X2 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,singleton(X2))) ),
inference(superposition,[status(thm)],[c_900,c_862]) ).
tcf(c_3143,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,cartesian_product2(X0,singleton(X1))) = cartesian_product2(singleton(X3),X4) )
| ( sK2(singleton(X3),X4,cartesian_product2(X2,cartesian_product2(X0,singleton(X1)))) = X3 )
| ( sK5(X0,singleton(X1),sK5(X2,cartesian_product2(X0,singleton(X1)),sK1(singleton(X3),X4,cartesian_product2(X2,cartesian_product2(X0,singleton(X1)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_799,c_862]) ).
tcf(c_3144,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(X2,cartesian_product2(X0,singleton(X1))),X3) = singleton(X4) )
| ( sK1(cartesian_product2(X2,cartesian_product2(X0,singleton(X1))),X3,singleton(X4)) = X4 )
| ( sK5(X0,singleton(X1),sK5(X2,cartesian_product2(X0,singleton(X1)),sK2(cartesian_product2(X2,cartesian_product2(X0,singleton(X1))),X3,singleton(X4)))) = X1 ) ),
inference(superposition,[status(thm)],[c_800,c_862]) ).
tcf(c_3145,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,cartesian_product2(X0,singleton(X1))) = cartesian_product2(X3,singleton(X4)) )
| ( sK3(X3,singleton(X4),cartesian_product2(X2,cartesian_product2(X0,singleton(X1)))) = X4 )
| ( sK5(X0,singleton(X1),sK5(X2,cartesian_product2(X0,singleton(X1)),sK1(X3,singleton(X4),cartesian_product2(X2,cartesian_product2(X0,singleton(X1)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_803,c_862]) ).
tcf(c_3146,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,cartesian_product2(X0,singleton(X1)))) = singleton(X4) )
| ( sK1(X3,cartesian_product2(X2,cartesian_product2(X0,singleton(X1))),singleton(X4)) = X4 )
| ( sK5(X0,singleton(X1),sK5(X2,cartesian_product2(X0,singleton(X1)),sK3(X3,cartesian_product2(X2,cartesian_product2(X0,singleton(X1))),singleton(X4)))) = X1 ) ),
inference(superposition,[status(thm)],[c_804,c_862]) ).
tcf(c_3169,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( unordered_pair(unordered_pair(sK2(X3,X4,cartesian_product2(X0,X2)),sK3(X3,X4,cartesian_product2(X0,X2))),singleton(sK2(X3,X4,cartesian_product2(X0,X2)))) = sK1(X3,X4,cartesian_product2(X0,X2)) )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2))),X1),singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_58,c_1388]) ).
tcf(c_3170,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,cartesian_product2(X0,X2)),X4)
| ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2))),X1),singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_57,c_1388]) ).
tcf(c_3171,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,cartesian_product2(X0,X2)),X3)
| ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2))),X1),singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_1388]) ).
tcf(c_3172,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(cartesian_product2(X0,X2),X3,X4),X4)
| ( cartesian_product2(cartesian_product2(X0,X2),X3) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4)),X1),singleton(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_1388]) ).
tcf(c_3173,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,cartesian_product2(X0,X2),X4),X4)
| ( cartesian_product2(X3,cartesian_product2(X0,X2)) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4)),X1),singleton(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_57,c_1388]) ).
tcf(c_3174,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X1,singleton(X4),unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0)),X4),singleton(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0))))) = X4 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_1388]) ).
tcf(c_3175,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X2,singleton(X4),unordered_pair(unordered_pair(sK4(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0)),X4),singleton(sK4(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0))))) = X4 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_61,c_1388]) ).
tcf(c_3176,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X3,singleton(X4),unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2))),X4),singleton(sK4(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_1388]) ).
tcf(c_3177,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X1,singleton(X4),unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2))),X4),singleton(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_1388]) ).
tcf(c_3178,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X1,singleton(X4),unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0))),X4),singleton(sK4(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_1388]) ).
tcf(c_3179,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X1,singleton(X4),unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0))),X4),singleton(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_1388]) ).
tcf(c_3180,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X3,singleton(X4),unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2))),X4),singleton(sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_1388]) ).
tcf(c_3181,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X3,singleton(X4),unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0))),X4),singleton(sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_1388]) ).
tcf(c_3182,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = cartesian_product2(X0,X2) )
| ( sK2(singleton(X3),X4,cartesian_product2(X0,X2)) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK4(X0,X2,sK1(singleton(X3),X4,cartesian_product2(X0,X2))),X1),singleton(sK4(X0,X2,sK1(singleton(X3),X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_799,c_1388]) ).
tcf(c_3183,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(X0,X2),X3) = singleton(X4) )
| ( sK1(cartesian_product2(X0,X2),X3,singleton(X4)) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,singleton(X4))),X1),singleton(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,singleton(X4)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_800,c_1388]) ).
tcf(c_3184,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = cartesian_product2(X0,X2) )
| ( sK3(X3,singleton(X4),cartesian_product2(X0,X2)) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK4(X0,X2,sK1(X3,singleton(X4),cartesian_product2(X0,X2))),X1),singleton(sK4(X0,X2,sK1(X3,singleton(X4),cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_803,c_1388]) ).
tcf(c_3185,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,cartesian_product2(X0,X2)) = singleton(X4) )
| ( sK1(X3,cartesian_product2(X0,X2),singleton(X4)) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),singleton(X4))),X1),singleton(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),singleton(X4)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_804,c_1388]) ).
tcf(c_3255,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( unordered_pair(unordered_pair(sK2(X3,X4,cartesian_product2(X2,X0)),sK3(X3,X4,cartesian_product2(X2,X0))),singleton(sK2(X3,X4,cartesian_product2(X2,X0)))) = sK1(X3,X4,cartesian_product2(X2,X0)) )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0))),X1),singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_58,c_1389]) ).
tcf(c_3256,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,cartesian_product2(X2,X0)),X4)
| ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0))),X1),singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_57,c_1389]) ).
tcf(c_3257,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,cartesian_product2(X2,X0)),X3)
| ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0))),X1),singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_1389]) ).
tcf(c_3258,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(cartesian_product2(X2,X0),X3,X4),X4)
| ( cartesian_product2(cartesian_product2(X2,X0),X3) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4)),X1),singleton(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_1389]) ).
tcf(c_3259,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,cartesian_product2(X2,X0),X4),X4)
| ( cartesian_product2(X3,cartesian_product2(X2,X0)) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4)),X1),singleton(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_57,c_1389]) ).
tcf(c_3260,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X2,singleton(X4),unordered_pair(unordered_pair(sK5(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0)),X4),singleton(sK5(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0))))) = X4 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_1389]) ).
tcf(c_3261,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X3,singleton(X4),unordered_pair(unordered_pair(sK5(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0)),X4),singleton(sK5(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0))))) = X4 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_61,c_1389]) ).
tcf(c_3262,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X1,singleton(X4),unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2))),X4),singleton(sK5(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_1389]) ).
tcf(c_3263,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X3,singleton(X4),unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2))),X4),singleton(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_1389]) ).
tcf(c_3264,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X3,singleton(X4),unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0))),X4),singleton(sK5(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_1389]) ).
tcf(c_3265,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X3,singleton(X4),unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0))),X4),singleton(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_1389]) ).
tcf(c_3266,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X1,singleton(X4),unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2))),X4),singleton(sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_1389]) ).
tcf(c_3267,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X1,singleton(X4),unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0))),X4),singleton(sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_1389]) ).
tcf(c_3268,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = cartesian_product2(X2,X0) )
| ( sK2(singleton(X3),X4,cartesian_product2(X2,X0)) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK5(X2,X0,sK1(singleton(X3),X4,cartesian_product2(X2,X0))),X1),singleton(sK5(X2,X0,sK1(singleton(X3),X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_799,c_1389]) ).
tcf(c_3269,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(X2,X0),X3) = singleton(X4) )
| ( sK1(cartesian_product2(X2,X0),X3,singleton(X4)) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,singleton(X4))),X1),singleton(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,singleton(X4)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_800,c_1389]) ).
tcf(c_3270,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = cartesian_product2(X2,X0) )
| ( sK3(X3,singleton(X4),cartesian_product2(X2,X0)) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK5(X2,X0,sK1(X3,singleton(X4),cartesian_product2(X2,X0))),X1),singleton(sK5(X2,X0,sK1(X3,singleton(X4),cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_803,c_1389]) ).
tcf(c_3271,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X0)) = singleton(X4) )
| ( sK1(X3,cartesian_product2(X2,X0),singleton(X4)) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),singleton(X4))),X1),singleton(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),singleton(X4)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_804,c_1389]) ).
tcf(c_3304,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( unordered_pair(unordered_pair(sK2(X3,X4,cartesian_product2(X0,X2)),sK3(X3,X4,cartesian_product2(X0,X2))),singleton(sK2(X3,X4,cartesian_product2(X0,X2)))) = sK1(X3,X4,cartesian_product2(X0,X2)) )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))),unordered_pair(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2))),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_58,c_1702]) ).
tcf(c_3305,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,cartesian_product2(X0,X2)),X4)
| ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))),unordered_pair(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2))),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_57,c_1702]) ).
tcf(c_3306,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,cartesian_product2(X0,X2)),X3)
| ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))),unordered_pair(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2))),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_1702]) ).
tcf(c_3307,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(cartesian_product2(X0,X2),X3,X4),X4)
| ( cartesian_product2(cartesian_product2(X0,X2),X3) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))),unordered_pair(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4)),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_1702]) ).
tcf(c_3308,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,cartesian_product2(X0,X2),X4),X4)
| ( cartesian_product2(X3,cartesian_product2(X0,X2)) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))),unordered_pair(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4)),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_57,c_1702]) ).
tcf(c_3309,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X1,singleton(X4),unordered_pair(singleton(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0))),unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0)),X4))) = X4 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_1702]) ).
tcf(c_3310,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X2,singleton(X4),unordered_pair(singleton(sK4(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0))),unordered_pair(sK4(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0)),X4))) = X4 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_61,c_1702]) ).
tcf(c_3311,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X3,singleton(X4),unordered_pair(singleton(sK4(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2)))),unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_1702]) ).
tcf(c_3312,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X1,singleton(X4),unordered_pair(singleton(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2)))),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_1702]) ).
tcf(c_3313,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X1,singleton(X4),unordered_pair(singleton(sK4(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0)))),unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_1702]) ).
tcf(c_3314,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X1,singleton(X4),unordered_pair(singleton(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0)))),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_1702]) ).
tcf(c_3315,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X3,singleton(X4),unordered_pair(singleton(sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2)))),unordered_pair(sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_1702]) ).
tcf(c_3316,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X3,singleton(X4),unordered_pair(singleton(sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0)))),unordered_pair(sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_1702]) ).
tcf(c_3317,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = cartesian_product2(X0,X2) )
| ( sK2(singleton(X3),X4,cartesian_product2(X0,X2)) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK1(singleton(X3),X4,cartesian_product2(X0,X2)))),unordered_pair(sK4(X0,X2,sK1(singleton(X3),X4,cartesian_product2(X0,X2))),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_799,c_1702]) ).
tcf(c_3318,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(X0,X2),X3) = singleton(X4) )
| ( sK1(cartesian_product2(X0,X2),X3,singleton(X4)) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,singleton(X4)))),unordered_pair(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,singleton(X4))),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_800,c_1702]) ).
tcf(c_3319,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = cartesian_product2(X0,X2) )
| ( sK3(X3,singleton(X4),cartesian_product2(X0,X2)) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK1(X3,singleton(X4),cartesian_product2(X0,X2)))),unordered_pair(sK4(X0,X2,sK1(X3,singleton(X4),cartesian_product2(X0,X2))),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_803,c_1702]) ).
tcf(c_3320,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,cartesian_product2(X0,X2)) = singleton(X4) )
| ( sK1(X3,cartesian_product2(X0,X2),singleton(X4)) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),singleton(X4)))),unordered_pair(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),singleton(X4))),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_804,c_1702]) ).
tcf(c_3417,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( unordered_pair(unordered_pair(sK2(X3,X4,cartesian_product2(X2,X0)),sK3(X3,X4,cartesian_product2(X2,X0))),singleton(sK2(X3,X4,cartesian_product2(X2,X0)))) = sK1(X3,X4,cartesian_product2(X2,X0)) )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))),unordered_pair(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0))),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_58,c_1703]) ).
tcf(c_3418,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,cartesian_product2(X2,X0)),X4)
| ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))),unordered_pair(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0))),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_57,c_1703]) ).
tcf(c_3419,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,cartesian_product2(X2,X0)),X3)
| ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))),unordered_pair(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0))),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_1703]) ).
tcf(c_3420,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(cartesian_product2(X2,X0),X3,X4),X4)
| ( cartesian_product2(cartesian_product2(X2,X0),X3) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))),unordered_pair(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4)),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_1703]) ).
tcf(c_3421,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,cartesian_product2(X2,X0),X4),X4)
| ( cartesian_product2(X3,cartesian_product2(X2,X0)) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))),unordered_pair(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4)),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_57,c_1703]) ).
tcf(c_3422,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X2,singleton(X4),unordered_pair(singleton(sK5(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0))),unordered_pair(sK5(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0)),X4))) = X4 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_1703]) ).
tcf(c_3423,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X3,singleton(X4),unordered_pair(singleton(sK5(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0))),unordered_pair(sK5(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0)),X4))) = X4 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_61,c_1703]) ).
tcf(c_3424,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X1,singleton(X4),unordered_pair(singleton(sK5(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2)))),unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_1703]) ).
tcf(c_3425,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X3,singleton(X4),unordered_pair(singleton(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2)))),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_1703]) ).
tcf(c_3426,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X3,singleton(X4),unordered_pair(singleton(sK5(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0)))),unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_1703]) ).
tcf(c_3427,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X3,singleton(X4),unordered_pair(singleton(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0)))),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_1703]) ).
tcf(c_3428,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X1,singleton(X4),unordered_pair(singleton(sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2)))),unordered_pair(sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_1703]) ).
tcf(c_3429,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X1,singleton(X4),unordered_pair(singleton(sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0)))),unordered_pair(sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_1703]) ).
tcf(c_3430,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = cartesian_product2(X2,X0) )
| ( sK2(singleton(X3),X4,cartesian_product2(X2,X0)) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK1(singleton(X3),X4,cartesian_product2(X2,X0)))),unordered_pair(sK5(X2,X0,sK1(singleton(X3),X4,cartesian_product2(X2,X0))),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_799,c_1703]) ).
tcf(c_3431,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(X2,X0),X3) = singleton(X4) )
| ( sK1(cartesian_product2(X2,X0),X3,singleton(X4)) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,singleton(X4)))),unordered_pair(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,singleton(X4))),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_800,c_1703]) ).
tcf(c_3432,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = cartesian_product2(X2,X0) )
| ( sK3(X3,singleton(X4),cartesian_product2(X2,X0)) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK1(X3,singleton(X4),cartesian_product2(X2,X0)))),unordered_pair(sK5(X2,X0,sK1(X3,singleton(X4),cartesian_product2(X2,X0))),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_803,c_1703]) ).
tcf(c_3433,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X0)) = singleton(X4) )
| ( sK1(X3,cartesian_product2(X2,X0),singleton(X4)) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),singleton(X4)))),unordered_pair(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),singleton(X4))),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_804,c_1703]) ).
tcf(c_3576,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( unordered_pair(unordered_pair(sK2(X3,X4,cartesian_product2(X0,X2)),sK3(X3,X4,cartesian_product2(X0,X2))),singleton(sK2(X3,X4,cartesian_product2(X0,X2)))) = sK1(X3,X4,cartesian_product2(X0,X2)) )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))),singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_58,c_2035]) ).
tcf(c_3577,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,cartesian_product2(X0,X2)),X4)
| ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))),singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_57,c_2035]) ).
tcf(c_3578,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,cartesian_product2(X0,X2)),X3)
| ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))),singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_2035]) ).
tcf(c_3579,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(cartesian_product2(X0,X2),X3,X4),X4)
| ( cartesian_product2(cartesian_product2(X0,X2),X3) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))),singleton(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_2035]) ).
tcf(c_3580,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,cartesian_product2(X0,X2),X4),X4)
| ( cartesian_product2(X3,cartesian_product2(X0,X2)) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))),singleton(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_57,c_2035]) ).
tcf(c_3581,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X1,singleton(X4),unordered_pair(unordered_pair(X4,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0))),singleton(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0))))) = X4 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_2035]) ).
tcf(c_3582,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X2,singleton(X4),unordered_pair(unordered_pair(X4,sK4(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0))),singleton(sK4(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0))))) = X4 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_61,c_2035]) ).
tcf(c_3583,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X3,singleton(X4),unordered_pair(unordered_pair(X4,sK4(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2)))),singleton(sK4(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2035]) ).
tcf(c_3584,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X1,singleton(X4),unordered_pair(unordered_pair(X4,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2)))),singleton(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2035]) ).
tcf(c_3585,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X1,singleton(X4),unordered_pair(unordered_pair(X4,sK4(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0)))),singleton(sK4(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2035]) ).
tcf(c_3586,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X1,singleton(X4),unordered_pair(unordered_pair(X4,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0)))),singleton(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2035]) ).
tcf(c_3587,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X3,singleton(X4),unordered_pair(unordered_pair(X4,sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2)))),singleton(sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2035]) ).
tcf(c_3588,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X3,singleton(X4),unordered_pair(unordered_pair(X4,sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0)))),singleton(sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2035]) ).
tcf(c_3589,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = cartesian_product2(X0,X2) )
| ( sK2(singleton(X3),X4,cartesian_product2(X0,X2)) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK4(X0,X2,sK1(singleton(X3),X4,cartesian_product2(X0,X2)))),singleton(sK4(X0,X2,sK1(singleton(X3),X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_799,c_2035]) ).
tcf(c_3590,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(X0,X2),X3) = singleton(X4) )
| ( sK1(cartesian_product2(X0,X2),X3,singleton(X4)) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,singleton(X4)))),singleton(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,singleton(X4)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_800,c_2035]) ).
tcf(c_3591,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = cartesian_product2(X0,X2) )
| ( sK3(X3,singleton(X4),cartesian_product2(X0,X2)) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK4(X0,X2,sK1(X3,singleton(X4),cartesian_product2(X0,X2)))),singleton(sK4(X0,X2,sK1(X3,singleton(X4),cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_803,c_2035]) ).
tcf(c_3592,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,cartesian_product2(X0,X2)) = singleton(X4) )
| ( sK1(X3,cartesian_product2(X0,X2),singleton(X4)) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),singleton(X4)))),singleton(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),singleton(X4)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_804,c_2035]) ).
tcf(c_3763,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( unordered_pair(unordered_pair(sK2(X3,X4,cartesian_product2(X2,X0)),sK3(X3,X4,cartesian_product2(X2,X0))),singleton(sK2(X3,X4,cartesian_product2(X2,X0)))) = sK1(X3,X4,cartesian_product2(X2,X0)) )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))),singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_58,c_2036]) ).
tcf(c_3764,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,cartesian_product2(X2,X0)),X4)
| ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))),singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_57,c_2036]) ).
tcf(c_3765,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,cartesian_product2(X2,X0)),X3)
| ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))),singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_2036]) ).
tcf(c_3766,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(cartesian_product2(X2,X0),X3,X4),X4)
| ( cartesian_product2(cartesian_product2(X2,X0),X3) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))),singleton(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_2036]) ).
tcf(c_3767,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,cartesian_product2(X2,X0),X4),X4)
| ( cartesian_product2(X3,cartesian_product2(X2,X0)) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))),singleton(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_57,c_2036]) ).
tcf(c_3768,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X2,singleton(X4),unordered_pair(unordered_pair(X4,sK5(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0))),singleton(sK5(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0))))) = X4 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_2036]) ).
tcf(c_3769,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X3,singleton(X4),unordered_pair(unordered_pair(X4,sK5(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0))),singleton(sK5(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0))))) = X4 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_61,c_2036]) ).
tcf(c_3770,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X1,singleton(X4),unordered_pair(unordered_pair(X4,sK5(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2)))),singleton(sK5(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2036]) ).
tcf(c_3771,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X3,singleton(X4),unordered_pair(unordered_pair(X4,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2)))),singleton(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2036]) ).
tcf(c_3772,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X3,singleton(X4),unordered_pair(unordered_pair(X4,sK5(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0)))),singleton(sK5(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2036]) ).
tcf(c_3773,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X3,singleton(X4),unordered_pair(unordered_pair(X4,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0)))),singleton(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2036]) ).
tcf(c_3774,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X1,singleton(X4),unordered_pair(unordered_pair(X4,sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2)))),singleton(sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2036]) ).
tcf(c_3775,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X1,singleton(X4),unordered_pair(unordered_pair(X4,sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0)))),singleton(sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2036]) ).
tcf(c_3776,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = cartesian_product2(X2,X0) )
| ( sK2(singleton(X3),X4,cartesian_product2(X2,X0)) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK5(X2,X0,sK1(singleton(X3),X4,cartesian_product2(X2,X0)))),singleton(sK5(X2,X0,sK1(singleton(X3),X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_799,c_2036]) ).
tcf(c_3777,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(X2,X0),X3) = singleton(X4) )
| ( sK1(cartesian_product2(X2,X0),X3,singleton(X4)) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,singleton(X4)))),singleton(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,singleton(X4)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_800,c_2036]) ).
tcf(c_3778,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = cartesian_product2(X2,X0) )
| ( sK3(X3,singleton(X4),cartesian_product2(X2,X0)) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK5(X2,X0,sK1(X3,singleton(X4),cartesian_product2(X2,X0)))),singleton(sK5(X2,X0,sK1(X3,singleton(X4),cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_803,c_2036]) ).
tcf(c_3779,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X0)) = singleton(X4) )
| ( sK1(X3,cartesian_product2(X2,X0),singleton(X4)) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),singleton(X4)))),singleton(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),singleton(X4)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_804,c_2036]) ).
tcf(c_3791,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( unordered_pair(unordered_pair(sK2(X3,X4,cartesian_product2(X0,X2)),sK3(X3,X4,cartesian_product2(X0,X2))),singleton(sK2(X3,X4,cartesian_product2(X0,X2)))) = sK1(X3,X4,cartesian_product2(X0,X2)) )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))),unordered_pair(X1,sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_58,c_2610]) ).
tcf(c_3792,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,cartesian_product2(X0,X2)),X4)
| ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))),unordered_pair(X1,sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_57,c_2610]) ).
tcf(c_3793,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,cartesian_product2(X0,X2)),X3)
| ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))),unordered_pair(X1,sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_2610]) ).
tcf(c_3794,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(cartesian_product2(X0,X2),X3,X4),X4)
| ( cartesian_product2(cartesian_product2(X0,X2),X3) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))),unordered_pair(X1,sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_2610]) ).
tcf(c_3795,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,cartesian_product2(X0,X2),X4),X4)
| ( cartesian_product2(X3,cartesian_product2(X0,X2)) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))),unordered_pair(X1,sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_57,c_2610]) ).
tcf(c_3796,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X1,singleton(X4),unordered_pair(singleton(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0))),unordered_pair(X4,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0))))) = X4 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_2610]) ).
tcf(c_3797,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X2,singleton(X4),unordered_pair(singleton(sK4(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0))),unordered_pair(X4,sK4(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0))))) = X4 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_61,c_2610]) ).
tcf(c_3798,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X3,singleton(X4),unordered_pair(singleton(sK4(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2)))),unordered_pair(X4,sK4(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2610]) ).
tcf(c_3799,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X1,singleton(X4),unordered_pair(singleton(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2)))),unordered_pair(X4,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2610]) ).
tcf(c_3800,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X1,singleton(X4),unordered_pair(singleton(sK4(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0)))),unordered_pair(X4,sK4(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2610]) ).
tcf(c_3801,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X1,singleton(X4),unordered_pair(singleton(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0)))),unordered_pair(X4,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2610]) ).
tcf(c_3802,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X3,singleton(X4),unordered_pair(singleton(sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2)))),unordered_pair(X4,sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2610]) ).
tcf(c_3803,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X3,singleton(X4),unordered_pair(singleton(sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0)))),unordered_pair(X4,sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2610]) ).
tcf(c_3804,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = cartesian_product2(X0,X2) )
| ( sK2(singleton(X3),X4,cartesian_product2(X0,X2)) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK1(singleton(X3),X4,cartesian_product2(X0,X2)))),unordered_pair(X1,sK4(X0,X2,sK1(singleton(X3),X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_799,c_2610]) ).
tcf(c_3805,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(X0,X2),X3) = singleton(X4) )
| ( sK1(cartesian_product2(X0,X2),X3,singleton(X4)) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,singleton(X4)))),unordered_pair(X1,sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,singleton(X4)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_800,c_2610]) ).
tcf(c_3806,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = cartesian_product2(X0,X2) )
| ( sK3(X3,singleton(X4),cartesian_product2(X0,X2)) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK1(X3,singleton(X4),cartesian_product2(X0,X2)))),unordered_pair(X1,sK4(X0,X2,sK1(X3,singleton(X4),cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_803,c_2610]) ).
tcf(c_3807,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,cartesian_product2(X0,X2)) = singleton(X4) )
| ( sK1(X3,cartesian_product2(X0,X2),singleton(X4)) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),singleton(X4)))),unordered_pair(X1,sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),singleton(X4)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_804,c_2610]) ).
tcf(c_3871,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( unordered_pair(unordered_pair(sK2(X3,X4,cartesian_product2(X2,X0)),sK3(X3,X4,cartesian_product2(X2,X0))),singleton(sK2(X3,X4,cartesian_product2(X2,X0)))) = sK1(X3,X4,cartesian_product2(X2,X0)) )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))),unordered_pair(X1,sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_58,c_2611]) ).
tcf(c_3872,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,cartesian_product2(X2,X0)),X4)
| ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))),unordered_pair(X1,sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_57,c_2611]) ).
tcf(c_3873,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,cartesian_product2(X2,X0)),X3)
| ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))),unordered_pair(X1,sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_2611]) ).
tcf(c_3874,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(cartesian_product2(X2,X0),X3,X4),X4)
| ( cartesian_product2(cartesian_product2(X2,X0),X3) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))),unordered_pair(X1,sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_2611]) ).
tcf(c_3875,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,cartesian_product2(X2,X0),X4),X4)
| ( cartesian_product2(X3,cartesian_product2(X2,X0)) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))),unordered_pair(X1,sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_57,c_2611]) ).
tcf(c_3876,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X2,singleton(X4),unordered_pair(singleton(sK5(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0))),unordered_pair(X4,sK5(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0))))) = X4 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_2611]) ).
tcf(c_3877,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X3,singleton(X4),unordered_pair(singleton(sK5(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0))),unordered_pair(X4,sK5(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0))))) = X4 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_61,c_2611]) ).
tcf(c_3878,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X1,singleton(X4),unordered_pair(singleton(sK5(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2)))),unordered_pair(X4,sK5(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2611]) ).
tcf(c_3879,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X3,singleton(X4),unordered_pair(singleton(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2)))),unordered_pair(X4,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2611]) ).
tcf(c_3880,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X3,singleton(X4),unordered_pair(singleton(sK5(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0)))),unordered_pair(X4,sK5(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2611]) ).
tcf(c_3881,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X3,singleton(X4),unordered_pair(singleton(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0)))),unordered_pair(X4,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2611]) ).
tcf(c_3882,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X1,singleton(X4),unordered_pair(singleton(sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2)))),unordered_pair(X4,sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2611]) ).
tcf(c_3883,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X1,singleton(X4),unordered_pair(singleton(sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0)))),unordered_pair(X4,sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2611]) ).
tcf(c_3884,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = cartesian_product2(X2,X0) )
| ( sK2(singleton(X3),X4,cartesian_product2(X2,X0)) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK1(singleton(X3),X4,cartesian_product2(X2,X0)))),unordered_pair(X1,sK5(X2,X0,sK1(singleton(X3),X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_799,c_2611]) ).
tcf(c_3885,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(X2,X0),X3) = singleton(X4) )
| ( sK1(cartesian_product2(X2,X0),X3,singleton(X4)) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,singleton(X4)))),unordered_pair(X1,sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,singleton(X4)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_800,c_2611]) ).
tcf(c_3886,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = cartesian_product2(X2,X0) )
| ( sK3(X3,singleton(X4),cartesian_product2(X2,X0)) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK1(X3,singleton(X4),cartesian_product2(X2,X0)))),unordered_pair(X1,sK5(X2,X0,sK1(X3,singleton(X4),cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_803,c_2611]) ).
tcf(c_3887,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X0)) = singleton(X4) )
| ( sK1(X3,cartesian_product2(X2,X0),singleton(X4)) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),singleton(X4)))),unordered_pair(X1,sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),singleton(X4)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_804,c_2611]) ).
tcf(c_3929,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,singleton(X1))
| in(sK1(X0,singleton(X1),singleton(X2)),singleton(X2))
| ( cartesian_product2(X0,singleton(X1)) = singleton(X2) )
| ( sK1(X0,singleton(X1),singleton(X2)) = X2 ) ),
inference(superposition,[status(thm)],[c_1032,c_57]) ).
tcf(c_3930,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,singleton(X1))
| ( cartesian_product2(X0,singleton(X1)) = singleton(X2) )
| ( sK1(X0,singleton(X1),singleton(X2)) = X2 ) ),
inference(superposition,[status(thm)],[c_1032,c_804]) ).
tcf(c_3956,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,singleton(X3))
| ( cartesian_product2(X2,singleton(X3)) = singleton(X1) )
| ( sK1(X2,singleton(X3),singleton(X1)) = X1 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK1(X2,singleton(X3),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1032,c_1145]) ).
tcf(c_3957,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X0) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(X4,sK1(X2,X0,X3)),singleton(X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK3(X2,X0,X3)),unordered_pair(X1,sK3(X2,X0,X3)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1145,c_2539]) ).
tcf(c_3958,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X1 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(sK3(X2,X3,X1),X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK1(X2,X3,X1)),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_2384]) ).
tcf(c_3959,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X0) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(X4,sK1(X2,X0,X3)),singleton(X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK3(X2,X0,X3)),singleton(sK3(X2,X0,X3)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1145,c_1929]) ).
tcf(c_3960,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X1 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(sK3(X2,X3,X1),X4),singleton(X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK1(X2,X3,X1)),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_1823]) ).
tcf(c_3961,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X0) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(X4,sK1(X2,X0,X3)),singleton(X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK3(X2,X0,X3)),unordered_pair(sK3(X2,X0,X3),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1145,c_1643]) ).
tcf(c_3962,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X1 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(X4,sK3(X2,X3,X1)))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK1(X2,X3,X1)),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_1524]) ).
tcf(c_3963,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X0) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(X4,sK1(X2,X0,X3)),singleton(X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK3(X2,X0,X3),X1),singleton(sK3(X2,X0,X3)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1145,c_1306]) ).
tcf(c_3964,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X1 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(X4,sK3(X2,X3,X1)),singleton(X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK1(X2,X3,X1)),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_1060]) ).
tcf(c_3965,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(sK3(X4,singleton(X5),X3),X0))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK1(X4,singleton(X5),X3)),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_907]) ).
tcf(c_3966,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,singleton(X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,singleton(X2),X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK3(X3,singleton(X2),X4)),unordered_pair(X0,sK3(X3,singleton(X2),X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_906]) ).
tcf(c_3967,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(sK3(X4,singleton(X5),X3),X0),singleton(X0))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK1(X4,singleton(X5),X3)),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_899]) ).
tcf(c_3968,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,singleton(X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,singleton(X2),X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X0,sK3(X3,singleton(X2),X4)),singleton(sK3(X3,singleton(X2),X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_898]) ).
tcf(c_3969,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,singleton(X5),X3)))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK1(X4,singleton(X5),X3)),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_889]) ).
tcf(c_3970,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,singleton(X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,singleton(X2),X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK3(X3,singleton(X2),X4)),unordered_pair(sK3(X3,singleton(X2),X4),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_888]) ).
tcf(c_3971,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(X0,sK3(X4,singleton(X5),X3)),singleton(X0))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK1(X4,singleton(X5),X3)),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_863]) ).
tcf(c_3972,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,singleton(X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,singleton(X2),X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK3(X3,singleton(X2),X4),X0),singleton(sK3(X3,singleton(X2),X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_837]) ).
tcf(c_3974,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X0)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,cartesian_product2(X2,X0),X4)),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))),unordered_pair(X1,sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1145,c_2611]) ).
tcf(c_3975,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X0,X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,cartesian_product2(X0,X2),X4)),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))),unordered_pair(X1,sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1145,c_2610]) ).
tcf(c_3976,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X0)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,cartesian_product2(X2,X0),X4)),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))),singleton(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1145,c_2036]) ).
tcf(c_3977,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X0,X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,cartesian_product2(X0,X2),X4)),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))),singleton(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1145,c_2035]) ).
tcf(c_3978,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X0)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,cartesian_product2(X2,X0),X4)),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))),unordered_pair(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4)),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1145,c_1703]) ).
tcf(c_3979,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X0,X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,cartesian_product2(X0,X2),X4)),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))),unordered_pair(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4)),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1145,c_1702]) ).
tcf(c_3980,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X0)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,cartesian_product2(X2,X0),X4)),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4)),X1),singleton(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1145,c_1389]) ).
tcf(c_3981,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X0,X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,cartesian_product2(X0,X2),X4)),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4)),X1),singleton(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1145,c_1388]) ).
tcf(c_3982,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,cartesian_product2(X2,X1),X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK3(X3,cartesian_product2(X2,X1),X4)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_2459]) ).
tcf(c_3983,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,cartesian_product2(X1,X2),X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK3(X3,cartesian_product2(X1,X2),X4)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_2458]) ).
tcf(c_3984,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,cartesian_product2(X2,X1),X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK3(X3,cartesian_product2(X2,X1),X4)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_1857]) ).
tcf(c_3985,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,cartesian_product2(X1,X2),X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK3(X3,cartesian_product2(X1,X2),X4)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_1856]) ).
tcf(c_3986,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,cartesian_product2(X2,X1),X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK3(X3,cartesian_product2(X2,X1),X4))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_1569]) ).
tcf(c_3987,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,cartesian_product2(X1,X2),X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK3(X3,cartesian_product2(X1,X2),X4))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_1568]) ).
tcf(c_3988,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,cartesian_product2(X2,X1),X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK3(X3,cartesian_product2(X2,X1),X4))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_1150]) ).
tcf(c_3989,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,cartesian_product2(X1,X2),X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK3(X3,cartesian_product2(X1,X2),X4))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_1149]) ).
tcf(c_3990,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,cartesian_product2(X0,X1)) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(X4,sK1(X2,cartesian_product2(X0,X1),X3)),singleton(X4))) = X4 )
| ( unordered_pair(unordered_pair(sK4(X0,X1,sK3(X2,cartesian_product2(X0,X1),X3)),sK5(X0,X1,sK3(X2,cartesian_product2(X0,X1),X3))),singleton(sK4(X0,X1,sK3(X2,cartesian_product2(X0,X1),X3)))) = sK3(X2,cartesian_product2(X0,X1),X3) ) ),
inference(superposition,[status(thm)],[c_1145,c_62]) ).
tcf(c_3991,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,cartesian_product2(singleton(X3),X4)) = X1 )
| ( sK4(singleton(X3),X4,sK3(X2,cartesian_product2(singleton(X3),X4),X1)) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK1(X2,cartesian_product2(singleton(X3),X4),X1)),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_787]) ).
tcf(c_3992,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,cartesian_product2(X3,singleton(X4))) = X1 )
| ( sK5(X3,singleton(X4),sK3(X2,cartesian_product2(X3,singleton(X4)),X1)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK1(X2,cartesian_product2(X3,singleton(X4)),X1)),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_789]) ).
tcf(c_3993,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(cartesian_product2(singleton(X0),X1),X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,cartesian_product2(cartesian_product2(singleton(X0),X1),X2),X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,sK4(cartesian_product2(singleton(X0),X1),X2,sK3(X3,cartesian_product2(cartesian_product2(singleton(X0),X1),X2),X4))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_835]) ).
tcf(c_3994,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,cartesian_product2(singleton(X0),X1))) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,cartesian_product2(X2,cartesian_product2(singleton(X0),X1)),X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,sK5(X2,cartesian_product2(singleton(X0),X1),sK3(X3,cartesian_product2(X2,cartesian_product2(singleton(X0),X1)),X4))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_836]) ).
tcf(c_3995,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(cartesian_product2(X0,singleton(X1)),X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,cartesian_product2(cartesian_product2(X0,singleton(X1)),X2),X4)),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),sK4(cartesian_product2(X0,singleton(X1)),X2,sK3(X3,cartesian_product2(cartesian_product2(X0,singleton(X1)),X2),X4))) = X1 ) ),
inference(superposition,[status(thm)],[c_1145,c_861]) ).
tcf(c_3996,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,cartesian_product2(X0,singleton(X1)))) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,cartesian_product2(X2,cartesian_product2(X0,singleton(X1))),X4)),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),sK5(X2,cartesian_product2(X0,singleton(X1)),sK3(X3,cartesian_product2(X2,cartesian_product2(X0,singleton(X1))),X4))) = X1 ) ),
inference(superposition,[status(thm)],[c_1145,c_862]) ).
tcf(c_4185,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X2,singleton(X2))
| ( cartesian_product2(singleton(X2),X3) = singleton(X1) )
| ( sK1(singleton(X2),X3,singleton(X1)) = X1 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK1(singleton(X2),X3,singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1009,c_1146]) ).
tcf(c_4186,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X2) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(X4,sK1(X0,X2,X3)),singleton(X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK2(X0,X2,X3)),unordered_pair(X1,sK2(X0,X2,X3)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1146,c_2539]) ).
tcf(c_4187,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X1 )
| ( sK4(singleton(X4),X2,unordered_pair(singleton(X4),unordered_pair(sK2(X2,X3,X1),X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK1(X2,X3,X1)),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_2384]) ).
tcf(c_4188,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X2) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(X4,sK1(X0,X2,X3)),singleton(X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK2(X0,X2,X3)),singleton(sK2(X0,X2,X3)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1146,c_1929]) ).
tcf(c_4189,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X1 )
| ( sK4(singleton(X4),X2,unordered_pair(unordered_pair(sK2(X2,X3,X1),X4),singleton(X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK1(X2,X3,X1)),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_1823]) ).
tcf(c_4190,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X2) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(X4,sK1(X0,X2,X3)),singleton(X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK2(X0,X2,X3)),unordered_pair(sK2(X0,X2,X3),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1146,c_1643]) ).
tcf(c_4191,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X1 )
| ( sK4(singleton(X4),X2,unordered_pair(singleton(X4),unordered_pair(X4,sK2(X2,X3,X1)))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK1(X2,X3,X1)),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_1524]) ).
tcf(c_4192,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X2) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(X4,sK1(X0,X2,X3)),singleton(X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK2(X0,X2,X3),X1),singleton(sK2(X0,X2,X3)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1146,c_1306]) ).
tcf(c_4193,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X1 )
| ( sK4(singleton(X4),X2,unordered_pair(unordered_pair(X4,sK2(X2,X3,X1)),singleton(X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK1(X2,X3,X1)),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_1060]) ).
tcf(c_4194,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK5(X1,singleton(X4),unordered_pair(singleton(X0),unordered_pair(sK2(singleton(X4),X5,X3),X0))) = X4 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK1(singleton(X4),X5,X3)),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_907]) ).
tcf(c_4195,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(singleton(X2),X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK2(singleton(X2),X3,X4)),unordered_pair(X0,sK2(singleton(X2),X3,X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_906]) ).
tcf(c_4196,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK5(X1,singleton(X4),unordered_pair(unordered_pair(sK2(singleton(X4),X5,X3),X0),singleton(X0))) = X4 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK1(singleton(X4),X5,X3)),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_899]) ).
tcf(c_4197,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(singleton(X2),X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X0,sK2(singleton(X2),X3,X4)),singleton(sK2(singleton(X2),X3,X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_898]) ).
tcf(c_4198,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK5(X1,singleton(X4),unordered_pair(singleton(X0),unordered_pair(X0,sK2(singleton(X4),X5,X3)))) = X4 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK1(singleton(X4),X5,X3)),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_889]) ).
tcf(c_4199,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(singleton(X2),X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK2(singleton(X2),X3,X4)),unordered_pair(sK2(singleton(X2),X3,X4),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_888]) ).
tcf(c_4200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK5(X1,singleton(X4),unordered_pair(unordered_pair(X0,sK2(singleton(X4),X5,X3)),singleton(X0))) = X4 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK1(singleton(X4),X5,X3)),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_863]) ).
tcf(c_4201,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(singleton(X2),X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK2(singleton(X2),X3,X4),X0),singleton(sK2(singleton(X2),X3,X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_837]) ).
tcf(c_4203,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X0),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(cartesian_product2(X2,X0),X3,X4)),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))),unordered_pair(X1,sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1146,c_2611]) ).
tcf(c_4204,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X0,X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(cartesian_product2(X0,X2),X3,X4)),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))),unordered_pair(X1,sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1146,c_2610]) ).
tcf(c_4205,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X0),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(cartesian_product2(X2,X0),X3,X4)),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))),singleton(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1146,c_2036]) ).
tcf(c_4206,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X0,X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(cartesian_product2(X0,X2),X3,X4)),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))),singleton(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1146,c_2035]) ).
tcf(c_4207,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X0),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(cartesian_product2(X2,X0),X3,X4)),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))),unordered_pair(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4)),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1146,c_1703]) ).
tcf(c_4208,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X0,X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(cartesian_product2(X0,X2),X3,X4)),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))),unordered_pair(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4)),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1146,c_1702]) ).
tcf(c_4209,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X0),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(cartesian_product2(X2,X0),X3,X4)),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4)),X1),singleton(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1146,c_1389]) ).
tcf(c_4210,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X0,X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(cartesian_product2(X0,X2),X3,X4)),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4)),X1),singleton(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1146,c_1388]) ).
tcf(c_4211,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(cartesian_product2(X2,X1),X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK2(cartesian_product2(X2,X1),X3,X4)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_2459]) ).
tcf(c_4212,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(cartesian_product2(X1,X2),X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK2(cartesian_product2(X1,X2),X3,X4)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_2458]) ).
tcf(c_4213,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(cartesian_product2(X2,X1),X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK2(cartesian_product2(X2,X1),X3,X4)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_1857]) ).
tcf(c_4214,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(cartesian_product2(X1,X2),X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK2(cartesian_product2(X1,X2),X3,X4)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_1856]) ).
tcf(c_4215,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(cartesian_product2(X2,X1),X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK2(cartesian_product2(X2,X1),X3,X4))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_1569]) ).
tcf(c_4216,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(cartesian_product2(X1,X2),X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK2(cartesian_product2(X1,X2),X3,X4))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_1568]) ).
tcf(c_4217,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(cartesian_product2(X2,X1),X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK2(cartesian_product2(X2,X1),X3,X4))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_1150]) ).
tcf(c_4218,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(cartesian_product2(X1,X2),X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK2(cartesian_product2(X1,X2),X3,X4))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_1149]) ).
tcf(c_4219,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(X0,X1),X2) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(X4,sK1(cartesian_product2(X0,X1),X2,X3)),singleton(X4))) = X4 )
| ( unordered_pair(unordered_pair(sK4(X0,X1,sK2(cartesian_product2(X0,X1),X2,X3)),sK5(X0,X1,sK2(cartesian_product2(X0,X1),X2,X3))),singleton(sK4(X0,X1,sK2(cartesian_product2(X0,X1),X2,X3)))) = sK2(cartesian_product2(X0,X1),X2,X3) ) ),
inference(superposition,[status(thm)],[c_1146,c_62]) ).
tcf(c_4220,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X1 )
| ( sK4(singleton(X2),X3,sK2(cartesian_product2(singleton(X2),X3),X4,X1)) = X2 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK1(cartesian_product2(singleton(X2),X3),X4,X1)),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_787]) ).
tcf(c_4221,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X1 )
| ( sK5(X2,singleton(X3),sK2(cartesian_product2(X2,singleton(X3)),X4,X1)) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK1(cartesian_product2(X2,singleton(X3)),X4,X1)),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_789]) ).
tcf(c_4222,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(singleton(X0),X1),X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(cartesian_product2(cartesian_product2(singleton(X0),X1),X2),X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,sK4(cartesian_product2(singleton(X0),X1),X2,sK2(cartesian_product2(cartesian_product2(singleton(X0),X1),X2),X3,X4))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_835]) ).
tcf(c_4223,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,cartesian_product2(singleton(X0),X1)),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(cartesian_product2(X2,cartesian_product2(singleton(X0),X1)),X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,sK5(X2,cartesian_product2(singleton(X0),X1),sK2(cartesian_product2(X2,cartesian_product2(singleton(X0),X1)),X3,X4))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_836]) ).
tcf(c_4224,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X0,singleton(X1)),X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(cartesian_product2(cartesian_product2(X0,singleton(X1)),X2),X3,X4)),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),sK4(cartesian_product2(X0,singleton(X1)),X2,sK2(cartesian_product2(cartesian_product2(X0,singleton(X1)),X2),X3,X4))) = X1 ) ),
inference(superposition,[status(thm)],[c_1146,c_861]) ).
tcf(c_4225,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,cartesian_product2(X0,singleton(X1))),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(cartesian_product2(X2,cartesian_product2(X0,singleton(X1))),X3,X4)),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),sK5(X2,cartesian_product2(X0,singleton(X1)),sK2(cartesian_product2(X2,cartesian_product2(X0,singleton(X1))),X3,X4))) = X1 ) ),
inference(superposition,[status(thm)],[c_1146,c_862]) ).
tcf(c_4450,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK4(singleton(X4),X2,unordered_pair(unordered_pair(X4,sK2(X2,X3,X0)),singleton(X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,X3,X0)),unordered_pair(X1,sK1(X2,X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1147,c_2539]) ).
tcf(c_4451,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X2) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(sK1(X1,X2,X3),X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK2(X1,X2,X3)),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_2384]) ).
tcf(c_4452,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK4(singleton(X4),X2,unordered_pair(unordered_pair(X4,sK2(X2,X3,X0)),singleton(X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK1(X2,X3,X0)),singleton(sK1(X2,X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1147,c_1929]) ).
tcf(c_4453,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X2) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(sK1(X1,X2,X3),X4),singleton(X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK2(X1,X2,X3)),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_1823]) ).
tcf(c_4454,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK4(singleton(X4),X2,unordered_pair(unordered_pair(X4,sK2(X2,X3,X0)),singleton(X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,X3,X0)),unordered_pair(sK1(X2,X3,X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1147,c_1643]) ).
tcf(c_4455,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X2) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(X4,sK1(X1,X2,X3)))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK2(X1,X2,X3)),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_1524]) ).
tcf(c_4456,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK4(singleton(X4),X2,unordered_pair(unordered_pair(X4,sK2(X2,X3,X0)),singleton(X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(X2,X3,X0),X1),singleton(sK1(X2,X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1147,c_1306]) ).
tcf(c_4457,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X2) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(X4,sK1(X1,X2,X3)),singleton(X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK2(X1,X2,X3)),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_1060]) ).
tcf(c_4458,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(sK1(X3,X4,singleton(X5)),X0))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK2(X3,X4,singleton(X5))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_907]) ).
tcf(c_4459,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,singleton(X2))),singleton(X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK1(X3,X4,singleton(X2))),unordered_pair(X0,sK1(X3,X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_906]) ).
tcf(c_4460,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X4,singleton(X5)),X0),singleton(X0))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK2(X3,X4,singleton(X5))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_899]) ).
tcf(c_4461,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,singleton(X2))),singleton(X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X0,sK1(X3,X4,singleton(X2))),singleton(sK1(X3,X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_898]) ).
tcf(c_4462,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X3,X4,singleton(X5))))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK2(X3,X4,singleton(X5))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_889]) ).
tcf(c_4463,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,singleton(X2))),singleton(X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK1(X3,X4,singleton(X2))),unordered_pair(sK1(X3,X4,singleton(X2)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_888]) ).
tcf(c_4464,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(X0,sK1(X3,X4,singleton(X5))),singleton(X0))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK2(X3,X4,singleton(X5))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_863]) ).
tcf(c_4465,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,singleton(X2))),singleton(X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,singleton(X2)),X0),singleton(sK1(X3,X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_837]) ).
tcf(c_4467,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,cartesian_product2(X2,X0))),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))),unordered_pair(X1,sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1147,c_2611]) ).
tcf(c_4468,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,cartesian_product2(X0,X2))),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))),unordered_pair(X1,sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1147,c_2610]) ).
tcf(c_4469,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,cartesian_product2(X2,X0))),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))),singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1147,c_2036]) ).
tcf(c_4470,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,cartesian_product2(X0,X2))),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))),singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1147,c_2035]) ).
tcf(c_4471,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,cartesian_product2(X2,X0))),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))),unordered_pair(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0))),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1147,c_1703]) ).
tcf(c_4472,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,cartesian_product2(X0,X2))),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))),unordered_pair(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2))),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1147,c_1702]) ).
tcf(c_4473,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,cartesian_product2(X2,X0))),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0))),X1),singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1147,c_1389]) ).
tcf(c_4474,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,cartesian_product2(X0,X2))),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2))),X1),singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1147,c_1388]) ).
tcf(c_4475,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X1) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,cartesian_product2(X2,X1))),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK1(X3,X4,cartesian_product2(X2,X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_2459]) ).
tcf(c_4476,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,cartesian_product2(X1,X2))),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK1(X3,X4,cartesian_product2(X1,X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_2458]) ).
tcf(c_4477,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X1) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,cartesian_product2(X2,X1))),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK1(X3,X4,cartesian_product2(X2,X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_1857]) ).
tcf(c_4478,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,cartesian_product2(X1,X2))),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK1(X3,X4,cartesian_product2(X1,X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_1856]) ).
tcf(c_4479,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X1) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,cartesian_product2(X2,X1))),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK1(X3,X4,cartesian_product2(X2,X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_1569]) ).
tcf(c_4480,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,cartesian_product2(X1,X2))),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK1(X3,X4,cartesian_product2(X1,X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_1568]) ).
tcf(c_4481,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X1) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,cartesian_product2(X2,X1))),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK1(X3,X4,cartesian_product2(X2,X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_1150]) ).
tcf(c_4482,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,cartesian_product2(X1,X2))),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK1(X3,X4,cartesian_product2(X1,X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_1149]) ).
tcf(c_4483,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( sK4(singleton(X4),X2,unordered_pair(unordered_pair(X4,sK2(X2,X3,cartesian_product2(X0,X1))),singleton(X4))) = X4 )
| ( unordered_pair(unordered_pair(sK4(X0,X1,sK1(X2,X3,cartesian_product2(X0,X1))),sK5(X0,X1,sK1(X2,X3,cartesian_product2(X0,X1)))),singleton(sK4(X0,X1,sK1(X2,X3,cartesian_product2(X0,X1))))) = sK1(X2,X3,cartesian_product2(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_1147,c_62]) ).
tcf(c_4484,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = cartesian_product2(X1,X2) )
| ( sK4(singleton(X3),X4,sK1(X1,X2,cartesian_product2(singleton(X3),X4))) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK2(X1,X2,cartesian_product2(singleton(X3),X4))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_787]) ).
tcf(c_4485,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = cartesian_product2(X1,X2) )
| ( sK5(X3,singleton(X4),sK1(X1,X2,cartesian_product2(X3,singleton(X4)))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK2(X1,X2,cartesian_product2(X3,singleton(X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_789]) ).
tcf(c_4486,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X0),X1),X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,cartesian_product2(cartesian_product2(singleton(X0),X1),X2))),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,sK4(cartesian_product2(singleton(X0),X1),X2,sK1(X3,X4,cartesian_product2(cartesian_product2(singleton(X0),X1),X2)))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_835]) ).
tcf(c_4487,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(singleton(X0),X1)) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,cartesian_product2(X2,cartesian_product2(singleton(X0),X1)))),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,sK5(X2,cartesian_product2(singleton(X0),X1),sK1(X3,X4,cartesian_product2(X2,cartesian_product2(singleton(X0),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_836]) ).
tcf(c_4488,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X0,singleton(X1)),X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,cartesian_product2(cartesian_product2(X0,singleton(X1)),X2))),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),sK4(cartesian_product2(X0,singleton(X1)),X2,sK1(X3,X4,cartesian_product2(cartesian_product2(X0,singleton(X1)),X2)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1147,c_861]) ).
tcf(c_4489,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(X0,singleton(X1))) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,cartesian_product2(X2,cartesian_product2(X0,singleton(X1))))),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),sK5(X2,cartesian_product2(X0,singleton(X1)),sK1(X3,X4,cartesian_product2(X2,cartesian_product2(X0,singleton(X1)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1147,c_862]) ).
tcf(c_4650,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(X4,sK3(X2,X3,X0)),singleton(X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,X3,X0)),unordered_pair(X1,sK1(X2,X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1148,c_2539]) ).
tcf(c_4651,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X1) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(sK1(X2,X1,X3),X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK3(X2,X1,X3)),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_2384]) ).
tcf(c_4652,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(X4,sK3(X2,X3,X0)),singleton(X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK1(X2,X3,X0)),singleton(sK1(X2,X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1148,c_1929]) ).
tcf(c_4653,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X1) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(sK1(X2,X1,X3),X4),singleton(X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK3(X2,X1,X3)),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_1823]) ).
tcf(c_4654,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(X4,sK3(X2,X3,X0)),singleton(X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,X3,X0)),unordered_pair(sK1(X2,X3,X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1148,c_1643]) ).
tcf(c_4655,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X1) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(X4,sK1(X2,X1,X3)))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK3(X2,X1,X3)),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_1524]) ).
tcf(c_4656,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(X4,sK3(X2,X3,X0)),singleton(X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(X2,X3,X0),X1),singleton(sK1(X2,X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1148,c_1306]) ).
tcf(c_4657,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X1) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(X4,sK1(X2,X1,X3)),singleton(X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK3(X2,X1,X3)),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_1060]) ).
tcf(c_4658,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(sK1(X4,X3,singleton(X5)),X0))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK3(X4,X3,singleton(X5))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_907]) ).
tcf(c_4659,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,singleton(X2))),singleton(X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK1(X3,X4,singleton(X2))),unordered_pair(X0,sK1(X3,X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_906]) ).
tcf(c_4660,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(sK1(X4,X3,singleton(X5)),X0),singleton(X0))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK3(X4,X3,singleton(X5))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_899]) ).
tcf(c_4661,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,singleton(X2))),singleton(X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X0,sK1(X3,X4,singleton(X2))),singleton(sK1(X3,X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_898]) ).
tcf(c_4662,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X3,singleton(X5))))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK3(X4,X3,singleton(X5))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_889]) ).
tcf(c_4663,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,singleton(X2))),singleton(X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK1(X3,X4,singleton(X2))),unordered_pair(sK1(X3,X4,singleton(X2)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_888]) ).
tcf(c_4664,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(X0,sK1(X4,X3,singleton(X5))),singleton(X0))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK3(X4,X3,singleton(X5))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_863]) ).
tcf(c_4665,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,singleton(X2))),singleton(X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,singleton(X2)),X0),singleton(sK1(X3,X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_837]) ).
tcf(c_4667,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,cartesian_product2(X2,X0))),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))),unordered_pair(X1,sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1148,c_2611]) ).
tcf(c_4668,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,cartesian_product2(X0,X2))),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))),unordered_pair(X1,sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1148,c_2610]) ).
tcf(c_4669,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,cartesian_product2(X2,X0))),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))),singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1148,c_2036]) ).
tcf(c_4670,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,cartesian_product2(X0,X2))),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))),singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1148,c_2035]) ).
tcf(c_4671,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,cartesian_product2(X2,X0))),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))),unordered_pair(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0))),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1148,c_1703]) ).
tcf(c_4672,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,cartesian_product2(X0,X2))),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))),unordered_pair(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2))),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1148,c_1702]) ).
tcf(c_4673,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,cartesian_product2(X2,X0))),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0))),X1),singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1148,c_1389]) ).
tcf(c_4674,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,cartesian_product2(X0,X2))),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2))),X1),singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1148,c_1388]) ).
tcf(c_4675,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X1) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,cartesian_product2(X2,X1))),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK1(X3,X4,cartesian_product2(X2,X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_2459]) ).
tcf(c_4676,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,cartesian_product2(X1,X2))),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK1(X3,X4,cartesian_product2(X1,X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_2458]) ).
tcf(c_4677,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X1) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,cartesian_product2(X2,X1))),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK1(X3,X4,cartesian_product2(X2,X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_1857]) ).
tcf(c_4678,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,cartesian_product2(X1,X2))),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK1(X3,X4,cartesian_product2(X1,X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_1856]) ).
tcf(c_4679,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X1) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,cartesian_product2(X2,X1))),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK1(X3,X4,cartesian_product2(X2,X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_1569]) ).
tcf(c_4680,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,cartesian_product2(X1,X2))),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK1(X3,X4,cartesian_product2(X1,X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_1568]) ).
tcf(c_4681,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X1) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,cartesian_product2(X2,X1))),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK1(X3,X4,cartesian_product2(X2,X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_1150]) ).
tcf(c_4682,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,cartesian_product2(X1,X2))),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK1(X3,X4,cartesian_product2(X1,X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_1149]) ).
tcf(c_4683,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(X4,sK3(X2,X3,cartesian_product2(X0,X1))),singleton(X4))) = X4 )
| ( unordered_pair(unordered_pair(sK4(X0,X1,sK1(X2,X3,cartesian_product2(X0,X1))),sK5(X0,X1,sK1(X2,X3,cartesian_product2(X0,X1)))),singleton(sK4(X0,X1,sK1(X2,X3,cartesian_product2(X0,X1))))) = sK1(X2,X3,cartesian_product2(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_1148,c_62]) ).
tcf(c_4684,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = cartesian_product2(X2,X1) )
| ( sK4(singleton(X3),X4,sK1(X2,X1,cartesian_product2(singleton(X3),X4))) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK3(X2,X1,cartesian_product2(singleton(X3),X4))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_787]) ).
tcf(c_4685,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = cartesian_product2(X2,X1) )
| ( sK5(X3,singleton(X4),sK1(X2,X1,cartesian_product2(X3,singleton(X4)))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK3(X2,X1,cartesian_product2(X3,singleton(X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_789]) ).
tcf(c_4686,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X0),X1),X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,cartesian_product2(cartesian_product2(singleton(X0),X1),X2))),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,sK4(cartesian_product2(singleton(X0),X1),X2,sK1(X3,X4,cartesian_product2(cartesian_product2(singleton(X0),X1),X2)))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_835]) ).
tcf(c_4687,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(singleton(X0),X1)) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,cartesian_product2(X2,cartesian_product2(singleton(X0),X1)))),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,sK5(X2,cartesian_product2(singleton(X0),X1),sK1(X3,X4,cartesian_product2(X2,cartesian_product2(singleton(X0),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_836]) ).
tcf(c_4688,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X0,singleton(X1)),X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,cartesian_product2(cartesian_product2(X0,singleton(X1)),X2))),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),sK4(cartesian_product2(X0,singleton(X1)),X2,sK1(X3,X4,cartesian_product2(cartesian_product2(X0,singleton(X1)),X2)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1148,c_861]) ).
tcf(c_4689,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(X0,singleton(X1))) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,cartesian_product2(X2,cartesian_product2(X0,singleton(X1))))),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),sK5(X2,cartesian_product2(X0,singleton(X1)),sK1(X3,X4,cartesian_product2(X2,cartesian_product2(X0,singleton(X1)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1148,c_862]) ).
tcf(c_4798,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),cartesian_product2(X1,singleton(X3)),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,X3),singleton(X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_1151]) ).
tcf(c_4799,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_1151]) ).
tcf(c_4800,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1151]) ).
tcf(c_4801,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1151]) ).
tcf(c_4802,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1151]) ).
tcf(c_4803,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1151]) ).
tcf(c_4804,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X4,X1),unordered_pair(unordered_pair(X5,unordered_pair(unordered_pair(X3,sK4(X1,X2,X0)),singleton(X3))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_1151]) ).
tcf(c_4805,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X4,X2),unordered_pair(unordered_pair(X5,unordered_pair(unordered_pair(X3,sK5(X1,X2,X0)),singleton(X3))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_1151]) ).
tcf(c_4806,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X3,X1)),unordered_pair(unordered_pair(X6,unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))),singleton(X4))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_1151]) ).
tcf(c_4807,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X1,X3)),unordered_pair(unordered_pair(X6,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))),singleton(X4))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_1151]) ).
tcf(c_4808,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X1,X3)),unordered_pair(unordered_pair(X6,unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))),singleton(X4))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_1151]) ).
tcf(c_4809,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X1,X3)),unordered_pair(unordered_pair(X6,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))),singleton(X4))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_1151]) ).
tcf(c_4810,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X3,X1)),unordered_pair(unordered_pair(X6,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))),singleton(X4))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_1151]) ).
tcf(c_4811,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X3,X1)),unordered_pair(unordered_pair(X6,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))),singleton(X4))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_1151]) ).
tcf(c_4813,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(singleton(X4),X5,X3)),singleton(X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_1151]) ).
tcf(c_4814,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK2(X3,X4,singleton(X5))),singleton(X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_1151]) ).
tcf(c_4815,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,singleton(X5),X3)),singleton(X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_1151]) ).
tcf(c_4816,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK3(X4,X3,singleton(X5))),singleton(X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_1151]) ).
tcf(c_4817,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_1151]) ).
tcf(c_4818,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_1151]) ).
tcf(c_4819,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_1151]) ).
tcf(c_4820,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_1151]) ).
tcf(c_4927,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),cartesian_product2(singleton(X1),singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),singleton(X1))),singleton(X0))) = X0,
inference(superposition,[status(thm)],[c_53,c_4798]) ).
tcf(c_4928,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X1),sK3(X3,X4,X1)),singleton(sK2(X3,X4,X1))) = sK1(X3,X4,X1) )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_4798]) ).
tcf(c_4929,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X1),X4)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_4798]) ).
tcf(c_4930,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X1),X3)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_4798]) ).
tcf(c_4931,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X1,X3,X4),X4)
| ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_4798]) ).
tcf(c_4932,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X1,X4),X4)
| ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_4798]) ).
tcf(c_4933,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(X1,singleton(X4)),unordered_pair(unordered_pair(X3,unordered_pair(unordered_pair(sK4(X1,X2,X0),X4),singleton(sK4(X1,X2,X0)))),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_4798]) ).
tcf(c_4934,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(X2,singleton(X4)),unordered_pair(unordered_pair(X3,unordered_pair(unordered_pair(sK5(X1,X2,X0),X4),singleton(sK5(X1,X2,X0)))),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_4798]) ).
tcf(c_4935,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X3,X1),singleton(X5)),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_4798]) ).
tcf(c_4936,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X1,X3),singleton(X5)),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5),singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_4798]) ).
tcf(c_4937,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X1,X3),singleton(X5)),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_4798]) ).
tcf(c_4938,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X1,X3),singleton(X5)),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5),singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_4798]) ).
tcf(c_4939,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X3,X1),singleton(X5)),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5),singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_4798]) ).
tcf(c_4940,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X3,X1),singleton(X5)),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5),singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_4798]) ).
tcf(c_4942,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X1 )
| ( sK2(singleton(X3),X4,X1) = X3 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK1(singleton(X3),X4,X1),X2),singleton(sK1(singleton(X3),X4,X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_4798]) ).
tcf(c_4943,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X3) = singleton(X4) )
| ( sK1(X1,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK2(X1,X3,singleton(X4)),X2),singleton(sK2(X1,X3,singleton(X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_4798]) ).
tcf(c_4944,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X1 )
| ( sK3(X3,singleton(X4),X1) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,singleton(X4),X1),X2),singleton(sK1(X3,singleton(X4),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_4798]) ).
tcf(c_4945,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X1) = singleton(X4) )
| ( sK1(X3,X1,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK3(X3,X1,singleton(X4)),X2),singleton(sK3(X3,X1,singleton(X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_4798]) ).
tcf(c_4946,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X1,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_4798]) ).
tcf(c_4947,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X1,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_4798]) ).
tcf(c_4948,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_4798]) ).
tcf(c_4949,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_4798]) ).
tcf(c_5074,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),cartesian_product2(singleton(X1),singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),singleton(X1))))) = X0,
inference(superposition,[status(thm)],[c_50,c_4927]) ).
tcf(c_5076,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),cartesian_product2(singleton(X1),singleton(X2)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X0),singleton(X0))) = X0,
inference(superposition,[status(thm)],[c_50,c_4927]) ).
tcf(c_5078,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),cartesian_product2(singleton(X1),singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,X2))),singleton(X0))) = X0,
inference(superposition,[status(thm)],[c_50,c_4927]) ).
tcf(c_5080,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),cartesian_product2(singleton(X1),singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(X2,X1),singleton(X1))),singleton(X0))) = X0,
inference(superposition,[status(thm)],[c_50,c_4927]) ).
tcf(c_5128,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),cartesian_product2(singleton(X1),singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X0))) = X0,
inference(superposition,[status(thm)],[c_50,c_5074]) ).
tcf(c_5130,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),cartesian_product2(singleton(X1),singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,X2))))) = X0,
inference(superposition,[status(thm)],[c_50,c_5074]) ).
tcf(c_5132,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),cartesian_product2(singleton(X1),singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(X2,X1),singleton(X1))))) = X0,
inference(superposition,[status(thm)],[c_50,c_5074]) ).
tcf(c_5141,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),cartesian_product2(singleton(X1),singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X0),singleton(X0))) = X0,
inference(superposition,[status(thm)],[c_50,c_5076]) ).
tcf(c_5143,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),cartesian_product2(singleton(X1),singleton(X2)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X1),singleton(X1)),X0),singleton(X0))) = X0,
inference(superposition,[status(thm)],[c_50,c_5076]) ).
tcf(c_5145,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,singleton(X2))
| ~ in(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2),singleton(X2)),cartesian_product2(singleton(X2),cartesian_product2(singleton(X0),singleton(X1)))) ),
inference(superposition,[status(thm)],[c_5076,c_60]) ).
tcf(c_5151,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),cartesian_product2(singleton(X1),singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X2,X1))),singleton(X0))) = X0,
inference(superposition,[status(thm)],[c_50,c_5078]) ).
tcf(c_5165,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),cartesian_product2(singleton(X1),singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X0))) = X0,
inference(superposition,[status(thm)],[c_50,c_5128]) ).
tcf(c_5167,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),cartesian_product2(singleton(X1),singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(X2,X1),singleton(X1)),X0))) = X0,
inference(superposition,[status(thm)],[c_50,c_5128]) ).
tcf(c_5173,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),cartesian_product2(singleton(X1),singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X2,X1))))) = X0,
inference(superposition,[status(thm)],[c_50,c_5130]) ).
tcf(c_5187,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),cartesian_product2(singleton(X1),singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X2,X1)),X0),singleton(X0))) = X0,
inference(superposition,[status(thm)],[c_50,c_5141]) ).
tcf(c_5189,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,singleton(X2))
| ~ in(unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2),singleton(X2)),cartesian_product2(singleton(X2),cartesian_product2(singleton(X0),singleton(X1)))) ),
inference(superposition,[status(thm)],[c_5141,c_60]) ).
tcf(c_5198,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,singleton(X2))
| ~ in(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X1),singleton(X1)),X2),singleton(X2)),cartesian_product2(singleton(X2),cartesian_product2(singleton(X1),singleton(X0)))) ),
inference(superposition,[status(thm)],[c_5143,c_60]) ).
tcf(c_5208,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),cartesian_product2(singleton(X1),singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X2,X1)),X0))) = X0,
inference(superposition,[status(thm)],[c_50,c_5165]) ).
tcf(c_5229,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,singleton(X2))
| ~ in(unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2),singleton(X2)),cartesian_product2(singleton(X2),cartesian_product2(singleton(X0),singleton(X1)))) ),
inference(superposition,[status(thm)],[c_5187,c_60]) ).
tcf(c_5291,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),cartesian_product2(singleton(X3),X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X3),unordered_pair(X3,X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_1152]) ).
tcf(c_5292,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_1152]) ).
tcf(c_5293,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1152]) ).
tcf(c_5294,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1152]) ).
tcf(c_5295,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1152]) ).
tcf(c_5296,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1152]) ).
tcf(c_5297,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X1,X4),unordered_pair(unordered_pair(X5,unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(sK4(X1,X2,X0),X3))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_1152]) ).
tcf(c_5298,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X2,X4),unordered_pair(unordered_pair(X5,unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(sK5(X1,X2,X0),X3))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_1152]) ).
tcf(c_5299,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X3,X1),X5),unordered_pair(unordered_pair(X6,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X4))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_1152]) ).
tcf(c_5300,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X1,X3),X5),unordered_pair(unordered_pair(X6,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X4))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_1152]) ).
tcf(c_5301,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X1,X3),X5),unordered_pair(unordered_pair(X6,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X4))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_1152]) ).
tcf(c_5302,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X1,X3),X5),unordered_pair(unordered_pair(X6,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X4))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_1152]) ).
tcf(c_5303,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X3,X1),X5),unordered_pair(unordered_pair(X6,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X4))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_1152]) ).
tcf(c_5304,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X3,X1),X5),unordered_pair(unordered_pair(X6,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X4))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_1152]) ).
tcf(c_5306,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK1(singleton(X4),X5,X3)),unordered_pair(sK1(singleton(X4),X5,X3),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_1152]) ).
tcf(c_5307,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK2(X3,X4,singleton(X5))),unordered_pair(sK2(X3,X4,singleton(X5)),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_1152]) ).
tcf(c_5308,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK1(X4,singleton(X5),X3)),unordered_pair(sK1(X4,singleton(X5),X3),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_1152]) ).
tcf(c_5309,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK3(X4,X3,singleton(X5))),unordered_pair(sK3(X4,X3,singleton(X5)),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_1152]) ).
tcf(c_5310,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_1152]) ).
tcf(c_5311,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_1152]) ).
tcf(c_5312,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_1152]) ).
tcf(c_5313,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_1152]) ).
tcf(c_5390,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X2),sK3(X3,X4,X2)),singleton(sK2(X3,X4,X2))) = sK1(X3,X4,X2) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_5291]) ).
tcf(c_5391,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X2),X4)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_5291]) ).
tcf(c_5392,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X2),X3)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_5291]) ).
tcf(c_5393,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X2,X3,X4),X4)
| ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_5291]) ).
tcf(c_5394,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X2,X4),X4)
| ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_5291]) ).
tcf(c_5395,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(singleton(X4),X1),unordered_pair(unordered_pair(X3,unordered_pair(singleton(X4),unordered_pair(X4,sK4(X1,X2,X0)))),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_5291]) ).
tcf(c_5396,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(singleton(X4),X2),unordered_pair(unordered_pair(X3,unordered_pair(singleton(X4),unordered_pair(X4,sK5(X1,X2,X0)))),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_5291]) ).
tcf(c_5397,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X3,X1)),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X2))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_5291]) ).
tcf(c_5398,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X1,X3)),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X0,X2))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_5291]) ).
tcf(c_5399,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X1,X3)),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X0))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_5291]) ).
tcf(c_5400,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X1,X3)),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X2,X0))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_5291]) ).
tcf(c_5401,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X3,X1)),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X0,X2))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_5291]) ).
tcf(c_5402,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X3,X1)),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X2,X0))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_5291]) ).
tcf(c_5404,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X2 )
| ( sK2(singleton(X3),X4,X2) = X3 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK1(singleton(X3),X4,X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_5291]) ).
tcf(c_5405,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK1(X2,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,singleton(X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_5291]) ).
tcf(c_5406,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X2 )
| ( sK3(X3,singleton(X4),X2) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,singleton(X4),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_5291]) ).
tcf(c_5407,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X2) = singleton(X4) )
| ( sK1(X3,X2,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,singleton(X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_5291]) ).
tcf(c_5408,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X2,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_5291]) ).
tcf(c_5409,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X2,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_5291]) ).
tcf(c_5410,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_5291]) ).
tcf(c_5411,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_5291]) ).
tcf(c_5518,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),cartesian_product2(singleton(X3),X1),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,X3),singleton(X3))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_1153]) ).
tcf(c_5519,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_1153]) ).
tcf(c_5520,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1153]) ).
tcf(c_5521,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1153]) ).
tcf(c_5522,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1153]) ).
tcf(c_5523,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1153]) ).
tcf(c_5524,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X1,X4),unordered_pair(unordered_pair(X5,unordered_pair(unordered_pair(X3,sK4(X1,X2,X0)),singleton(sK4(X1,X2,X0)))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_1153]) ).
tcf(c_5525,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X2,X4),unordered_pair(unordered_pair(X5,unordered_pair(unordered_pair(X3,sK5(X1,X2,X0)),singleton(sK5(X1,X2,X0)))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_1153]) ).
tcf(c_5526,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X3,X1),X5),unordered_pair(unordered_pair(X6,unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_1153]) ).
tcf(c_5527,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X1,X3),X5),unordered_pair(unordered_pair(X6,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))),singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_1153]) ).
tcf(c_5528,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X1,X3),X5),unordered_pair(unordered_pair(X6,unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_1153]) ).
tcf(c_5529,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X1,X3),X5),unordered_pair(unordered_pair(X6,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))),singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_1153]) ).
tcf(c_5530,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X3,X1),X5),unordered_pair(unordered_pair(X6,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))),singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_1153]) ).
tcf(c_5531,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X3,X1),X5),unordered_pair(unordered_pair(X6,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))),singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_1153]) ).
tcf(c_5533,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(singleton(X4),X5,X3)),singleton(sK1(singleton(X4),X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_1153]) ).
tcf(c_5534,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK2(X3,X4,singleton(X5))),singleton(sK2(X3,X4,singleton(X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_1153]) ).
tcf(c_5535,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,singleton(X5),X3)),singleton(sK1(X4,singleton(X5),X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_1153]) ).
tcf(c_5536,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK3(X4,X3,singleton(X5))),singleton(sK3(X4,X3,singleton(X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_1153]) ).
tcf(c_5537,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_1153]) ).
tcf(c_5538,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_1153]) ).
tcf(c_5539,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_1153]) ).
tcf(c_5540,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_1153]) ).
tcf(c_5636,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X2),sK3(X3,X4,X2)),singleton(sK2(X3,X4,X2))) = sK1(X3,X4,X2) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_5518]) ).
tcf(c_5637,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X2),X4)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_5518]) ).
tcf(c_5638,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X2),X3)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_5518]) ).
tcf(c_5639,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X2,X3,X4),X4)
| ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_5518]) ).
tcf(c_5640,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X2,X4),X4)
| ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_5518]) ).
tcf(c_5641,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(singleton(X4),X1),unordered_pair(unordered_pair(X3,unordered_pair(unordered_pair(sK4(X1,X2,X0),X4),singleton(X4))),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_5518]) ).
tcf(c_5642,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(singleton(X4),X2),unordered_pair(unordered_pair(X3,unordered_pair(unordered_pair(sK5(X1,X2,X0),X4),singleton(X4))),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_5518]) ).
tcf(c_5643,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X3,X1)),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5),singleton(X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_5518]) ).
tcf(c_5644,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X1,X3)),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5),singleton(X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_5518]) ).
tcf(c_5645,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X1,X3)),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5),singleton(X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_5518]) ).
tcf(c_5646,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X1,X3)),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5),singleton(X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_5518]) ).
tcf(c_5647,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X3,X1)),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5),singleton(X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_5518]) ).
tcf(c_5648,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X3,X1)),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5),singleton(X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_5518]) ).
tcf(c_5650,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X2 )
| ( sK2(singleton(X3),X4,X2) = X3 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK1(singleton(X3),X4,X2),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_5518]) ).
tcf(c_5651,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK1(X2,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK2(X2,X3,singleton(X4)),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_5518]) ).
tcf(c_5652,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X2 )
| ( sK3(X3,singleton(X4),X2) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,singleton(X4),X2),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_5518]) ).
tcf(c_5653,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X2) = singleton(X4) )
| ( sK1(X3,X2,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK3(X3,X2,singleton(X4)),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_5518]) ).
tcf(c_5654,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X2,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_5518]) ).
tcf(c_5655,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X2,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_5518]) ).
tcf(c_5656,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_5518]) ).
tcf(c_5657,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_5518]) ).
tcf(c_5758,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),cartesian_product2(singleton(X3),X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X3),unordered_pair(X0,X3))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_1154]) ).
tcf(c_5759,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_1154]) ).
tcf(c_5760,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1154]) ).
tcf(c_5761,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1154]) ).
tcf(c_5762,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1154]) ).
tcf(c_5763,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1154]) ).
tcf(c_5764,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X1,X4),unordered_pair(unordered_pair(X5,unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(X3,sK4(X1,X2,X0)))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_1154]) ).
tcf(c_5765,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X2,X4),unordered_pair(unordered_pair(X5,unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(X3,sK5(X1,X2,X0)))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_1154]) ).
tcf(c_5766,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X3,X1),X5),unordered_pair(unordered_pair(X6,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_1154]) ).
tcf(c_5767,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X1,X3),X5),unordered_pair(unordered_pair(X6,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_1154]) ).
tcf(c_5768,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X1,X3),X5),unordered_pair(unordered_pair(X6,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_1154]) ).
tcf(c_5769,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X1,X3),X5),unordered_pair(unordered_pair(X6,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_1154]) ).
tcf(c_5770,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X3,X1),X5),unordered_pair(unordered_pair(X6,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_1154]) ).
tcf(c_5771,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X3,X1),X5),unordered_pair(unordered_pair(X6,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_1154]) ).
tcf(c_5773,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK1(singleton(X4),X5,X3)),unordered_pair(X0,sK1(singleton(X4),X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_1154]) ).
tcf(c_5774,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK2(X3,X4,singleton(X5))),unordered_pair(X0,sK2(X3,X4,singleton(X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_1154]) ).
tcf(c_5775,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK1(X4,singleton(X5),X3)),unordered_pair(X0,sK1(X4,singleton(X5),X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_1154]) ).
tcf(c_5776,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK3(X4,X3,singleton(X5))),unordered_pair(X0,sK3(X4,X3,singleton(X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_1154]) ).
tcf(c_5777,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_1154]) ).
tcf(c_5778,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_1154]) ).
tcf(c_5779,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_1154]) ).
tcf(c_5780,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_1154]) ).
tcf(c_5819,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X2),sK3(X3,X4,X2)),singleton(sK2(X3,X4,X2))) = sK1(X3,X4,X2) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_5758]) ).
tcf(c_5820,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X2),X4)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_5758]) ).
tcf(c_5821,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X2),X3)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_5758]) ).
tcf(c_5822,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X2,X3,X4),X4)
| ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_5758]) ).
tcf(c_5823,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X2,X4),X4)
| ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_5758]) ).
tcf(c_5824,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(singleton(X4),X1),unordered_pair(unordered_pair(X3,unordered_pair(singleton(X4),unordered_pair(sK4(X1,X2,X0),X4))),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_5758]) ).
tcf(c_5825,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(singleton(X4),X2),unordered_pair(unordered_pair(X3,unordered_pair(singleton(X4),unordered_pair(sK5(X1,X2,X0),X4))),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_5758]) ).
tcf(c_5826,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X3,X1)),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_5758]) ).
tcf(c_5827,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X1,X3)),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_5758]) ).
tcf(c_5828,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X1,X3)),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_5758]) ).
tcf(c_5829,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X1,X3)),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_5758]) ).
tcf(c_5830,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X3,X1)),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_5758]) ).
tcf(c_5831,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X3,X1)),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_5758]) ).
tcf(c_5833,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X2 )
| ( sK2(singleton(X3),X4,X2) = X3 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK1(singleton(X3),X4,X2),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_5758]) ).
tcf(c_5834,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK1(X2,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,singleton(X4)),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_5758]) ).
tcf(c_5835,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X2 )
| ( sK3(X3,singleton(X4),X2) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK1(X3,singleton(X4),X2),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_5758]) ).
tcf(c_5836,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X2) = singleton(X4) )
| ( sK1(X3,X2,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,singleton(X4)),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_5758]) ).
tcf(c_5837,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X2,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_5758]) ).
tcf(c_5838,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X2,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_5758]) ).
tcf(c_5839,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_5758]) ).
tcf(c_5840,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_5758]) ).
tcf(c_5987,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),cartesian_product2(X1,singleton(X3)),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X3,X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_1155]) ).
tcf(c_5988,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_1155]) ).
tcf(c_5989,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1155]) ).
tcf(c_5990,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1155]) ).
tcf(c_5991,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1155]) ).
tcf(c_5992,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1155]) ).
tcf(c_5993,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X4,X1),unordered_pair(unordered_pair(X5,unordered_pair(singleton(X3),unordered_pair(sK4(X1,X2,X0),X3))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_1155]) ).
tcf(c_5994,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X4,X2),unordered_pair(unordered_pair(X5,unordered_pair(singleton(X3),unordered_pair(sK5(X1,X2,X0),X3))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_1155]) ).
tcf(c_5995,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X3,X1)),unordered_pair(unordered_pair(X6,unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X4))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_1155]) ).
tcf(c_5996,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X1,X3)),unordered_pair(unordered_pair(X6,unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X4))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_1155]) ).
tcf(c_5997,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X1,X3)),unordered_pair(unordered_pair(X6,unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X4))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_1155]) ).
tcf(c_5998,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X1,X3)),unordered_pair(unordered_pair(X6,unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X4))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_1155]) ).
tcf(c_5999,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X3,X1)),unordered_pair(unordered_pair(X6,unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X4))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_1155]) ).
tcf(c_6000,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X3,X1)),unordered_pair(unordered_pair(X6,unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X4))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_1155]) ).
tcf(c_6002,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK1(singleton(X4),X5,X3),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_1155]) ).
tcf(c_6003,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,singleton(X5)),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_1155]) ).
tcf(c_6004,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK1(X4,singleton(X5),X3),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_1155]) ).
tcf(c_6005,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,singleton(X5)),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_1155]) ).
tcf(c_6006,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_1155]) ).
tcf(c_6007,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_1155]) ).
tcf(c_6008,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_1155]) ).
tcf(c_6009,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_1155]) ).
tcf(c_6088,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X1),sK3(X3,X4,X1)),singleton(sK2(X3,X4,X1))) = sK1(X3,X4,X1) )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_5987]) ).
tcf(c_6089,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X1),X4)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_5987]) ).
tcf(c_6090,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X1),X3)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_5987]) ).
tcf(c_6091,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X1,X3,X4),X4)
| ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_5987]) ).
tcf(c_6092,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X1,X4),X4)
| ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_5987]) ).
tcf(c_6093,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(X1,singleton(X4)),unordered_pair(unordered_pair(X3,unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(X4,sK4(X1,X2,X0)))),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_5987]) ).
tcf(c_6094,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(X2,singleton(X4)),unordered_pair(unordered_pair(X3,unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(X4,sK5(X1,X2,X0)))),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_5987]) ).
tcf(c_6095,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X3,X1),singleton(X5)),unordered_pair(unordered_pair(X4,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X2))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_5987]) ).
tcf(c_6096,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X1,X3),singleton(X5)),unordered_pair(unordered_pair(X4,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X0,X2))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_5987]) ).
tcf(c_6097,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X1,X3),singleton(X5)),unordered_pair(unordered_pair(X4,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X0))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_5987]) ).
tcf(c_6098,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X1,X3),singleton(X5)),unordered_pair(unordered_pair(X4,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X2,X0))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_5987]) ).
tcf(c_6099,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X3,X1),singleton(X5)),unordered_pair(unordered_pair(X4,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X0,X2))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_5987]) ).
tcf(c_6100,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X3,X1),singleton(X5)),unordered_pair(unordered_pair(X4,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X2,X0))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_5987]) ).
tcf(c_6102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X1 )
| ( sK2(singleton(X3),X4,X1) = X3 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK1(singleton(X3),X4,X1)),unordered_pair(X2,sK1(singleton(X3),X4,X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_5987]) ).
tcf(c_6103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X3) = singleton(X4) )
| ( sK1(X1,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK2(X1,X3,singleton(X4))),unordered_pair(X2,sK2(X1,X3,singleton(X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_5987]) ).
tcf(c_6104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X1 )
| ( sK3(X3,singleton(X4),X1) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK1(X3,singleton(X4),X1)),unordered_pair(X2,sK1(X3,singleton(X4),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_5987]) ).
tcf(c_6105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X1) = singleton(X4) )
| ( sK1(X3,X1,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK3(X3,X1,singleton(X4))),unordered_pair(X2,sK3(X3,X1,singleton(X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_5987]) ).
tcf(c_6106,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X1,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_5987]) ).
tcf(c_6107,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X1,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_5987]) ).
tcf(c_6108,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_5987]) ).
tcf(c_6109,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_5987]) ).
tcf(c_6164,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),cartesian_product2(X1,singleton(X3)),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,X3))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_1156]) ).
tcf(c_6165,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_1156]) ).
tcf(c_6166,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1156]) ).
tcf(c_6167,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1156]) ).
tcf(c_6168,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1156]) ).
tcf(c_6169,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1156]) ).
tcf(c_6170,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X4,X1),unordered_pair(unordered_pair(X5,unordered_pair(singleton(X3),unordered_pair(X3,sK4(X1,X2,X0)))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_1156]) ).
tcf(c_6171,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X4,X2),unordered_pair(unordered_pair(X5,unordered_pair(singleton(X3),unordered_pair(X3,sK5(X1,X2,X0)))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_1156]) ).
tcf(c_6172,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X3,X1)),unordered_pair(unordered_pair(X6,unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_1156]) ).
tcf(c_6173,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X1,X3)),unordered_pair(unordered_pair(X6,unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_1156]) ).
tcf(c_6174,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X1,X3)),unordered_pair(unordered_pair(X6,unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_1156]) ).
tcf(c_6175,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X1,X3)),unordered_pair(unordered_pair(X6,unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_1156]) ).
tcf(c_6176,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X3,X1)),unordered_pair(unordered_pair(X6,unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_1156]) ).
tcf(c_6177,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X3,X1)),unordered_pair(unordered_pair(X6,unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_1156]) ).
tcf(c_6179,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK1(singleton(X4),X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_1156]) ).
tcf(c_6180,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,singleton(X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_1156]) ).
tcf(c_6181,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,singleton(X5),X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_1156]) ).
tcf(c_6182,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,singleton(X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_1156]) ).
tcf(c_6183,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_1156]) ).
tcf(c_6184,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_1156]) ).
tcf(c_6185,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_1156]) ).
tcf(c_6186,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_1156]) ).
tcf(c_6271,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X1),sK3(X3,X4,X1)),singleton(sK2(X3,X4,X1))) = sK1(X3,X4,X1) )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_6164]) ).
tcf(c_6272,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X1),X4)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_6164]) ).
tcf(c_6273,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X1),X3)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_6164]) ).
tcf(c_6274,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X1,X3,X4),X4)
| ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_6164]) ).
tcf(c_6275,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X1,X4),X4)
| ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_6164]) ).
tcf(c_6276,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(X1,singleton(X4)),unordered_pair(unordered_pair(X3,unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(sK4(X1,X2,X0),X4))),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_6164]) ).
tcf(c_6277,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(X2,singleton(X4)),unordered_pair(unordered_pair(X3,unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(sK5(X1,X2,X0),X4))),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_6164]) ).
tcf(c_6278,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X3,X1),singleton(X5)),unordered_pair(unordered_pair(X4,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_6164]) ).
tcf(c_6279,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X1,X3),singleton(X5)),unordered_pair(unordered_pair(X4,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_6164]) ).
tcf(c_6280,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X1,X3),singleton(X5)),unordered_pair(unordered_pair(X4,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_6164]) ).
tcf(c_6281,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X1,X3),singleton(X5)),unordered_pair(unordered_pair(X4,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_6164]) ).
tcf(c_6282,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X3,X1),singleton(X5)),unordered_pair(unordered_pair(X4,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_6164]) ).
tcf(c_6283,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X3,X1),singleton(X5)),unordered_pair(unordered_pair(X4,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_6164]) ).
tcf(c_6285,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X1 )
| ( sK2(singleton(X3),X4,X1) = X3 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK1(singleton(X3),X4,X1)),unordered_pair(sK1(singleton(X3),X4,X1),X2))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_6164]) ).
tcf(c_6286,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X3) = singleton(X4) )
| ( sK1(X1,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK2(X1,X3,singleton(X4))),unordered_pair(sK2(X1,X3,singleton(X4)),X2))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_6164]) ).
tcf(c_6287,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X1 )
| ( sK3(X3,singleton(X4),X1) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK1(X3,singleton(X4),X1)),unordered_pair(sK1(X3,singleton(X4),X1),X2))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_6164]) ).
tcf(c_6288,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X1) = singleton(X4) )
| ( sK1(X3,X1,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK3(X3,X1,singleton(X4))),unordered_pair(sK3(X3,X1,singleton(X4)),X2))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_6164]) ).
tcf(c_6289,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X1,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_6164]) ).
tcf(c_6290,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X1,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_6164]) ).
tcf(c_6291,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_6164]) ).
tcf(c_6292,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_6164]) ).
tcf(c_6332,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X2,X3) )
| ( sK5(X1,singleton(X4),unordered_pair(unordered_pair(X0,sK4(singleton(X4),X5,sK1(X2,X3,cartesian_product2(singleton(X4),X5)))),singleton(X0))) = X4 )
| ( unordered_pair(unordered_pair(sK2(X2,X3,cartesian_product2(singleton(X4),X5)),sK3(X2,X3,cartesian_product2(singleton(X4),X5))),singleton(sK2(X2,X3,cartesian_product2(singleton(X4),X5)))) = sK1(X2,X3,cartesian_product2(singleton(X4),X5)) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_1312]) ).
tcf(c_6333,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X5)
| ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK4(singleton(X2),X3,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1312]) ).
tcf(c_6334,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X4)
| ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK4(singleton(X2),X3,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1312]) ).
tcf(c_6335,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK4(singleton(X2),X3,sK2(cartesian_product2(singleton(X2),X3),X4,X5))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1312]) ).
tcf(c_6336,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK4(singleton(X2),X3,sK3(X4,cartesian_product2(singleton(X2),X3),X5))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1312]) ).
tcf(c_6337,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X1),unordered_pair(unordered_pair(X4,sK4(singleton(X1),X2,sK4(cartesian_product2(singleton(X1),X2),X3,X0))),singleton(X4))) = X1 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(cartesian_product2(singleton(X1),X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_1312]) ).
tcf(c_6338,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X2),unordered_pair(unordered_pair(X4,sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),X0))),singleton(X4))) = X2 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(X1,cartesian_product2(singleton(X2),X3))) ),
inference(superposition,[status(thm)],[c_61,c_1312]) ).
tcf(c_6339,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X1),unordered_pair(unordered_pair(X4,sK4(singleton(X1),X3,unordered_pair(unordered_pair(X0,X2),singleton(X0)))),singleton(X4))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_64,c_1312]) ).
tcf(c_6341,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X1),unordered_pair(unordered_pair(X4,sK4(singleton(X1),X3,unordered_pair(unordered_pair(X2,X0),singleton(X0)))),singleton(X4))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_809,c_1312]) ).
tcf(c_6342,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X1),unordered_pair(unordered_pair(X4,sK4(singleton(X1),X3,unordered_pair(singleton(X0),unordered_pair(X2,X0)))),singleton(X4))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_882,c_1312]) ).
tcf(c_6344,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X1),unordered_pair(unordered_pair(X4,sK4(singleton(X1),X3,unordered_pair(singleton(X0),unordered_pair(X0,X2)))),singleton(X4))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_900,c_1312]) ).
tcf(c_6345,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(singleton(X4),X5) )
| ( sK2(singleton(X4),X5,cartesian_product2(singleton(X2),X3)) = X4 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK4(singleton(X2),X3,sK1(singleton(X4),X5,cartesian_product2(singleton(X2),X3)))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_1312]) ).
tcf(c_6346,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = singleton(X5) )
| ( sK1(cartesian_product2(singleton(X2),X3),X4,singleton(X5)) = X5 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK4(singleton(X2),X3,sK2(cartesian_product2(singleton(X2),X3),X4,singleton(X5)))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_1312]) ).
tcf(c_6347,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,singleton(X5)) )
| ( sK3(X4,singleton(X5),cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK4(singleton(X2),X3,sK1(X4,singleton(X5),cartesian_product2(singleton(X2),X3)))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_1312]) ).
tcf(c_6348,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(singleton(X2),X3),singleton(X5)) = X5 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK4(singleton(X2),X3,sK3(X4,cartesian_product2(singleton(X2),X3),singleton(X5)))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_1312]) ).
tcf(c_6349,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(singleton(X2),X3),X5)),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK4(singleton(X2),X3,sK3(X4,cartesian_product2(singleton(X2),X3),X5))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_1312]) ).
tcf(c_6350,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(singleton(X2),X3),X4,X5)),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK4(singleton(X2),X3,sK2(cartesian_product2(singleton(X2),X3),X4,X5))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_1312]) ).
tcf(c_6351,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK4(singleton(X2),X3,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_1312]) ).
tcf(c_6352,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK4(singleton(X2),X3,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_1312]) ).
tcf(c_6410,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = cartesian_product2(X2,X3) )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(X0,sK5(X4,singleton(X5),sK1(X2,X3,cartesian_product2(X4,singleton(X5))))),singleton(X0))) = X5 )
| ( unordered_pair(unordered_pair(sK2(X2,X3,cartesian_product2(X4,singleton(X5))),sK3(X2,X3,cartesian_product2(X4,singleton(X5)))),singleton(sK2(X2,X3,cartesian_product2(X4,singleton(X5))))) = sK1(X2,X3,cartesian_product2(X4,singleton(X5))) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_1313]) ).
tcf(c_6411,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X3,singleton(X2))),X5)
| ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,X5) )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK5(X3,singleton(X2),sK1(X4,X5,cartesian_product2(X3,singleton(X2))))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1313]) ).
tcf(c_6412,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X3,singleton(X2))),X4)
| ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,X5) )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK5(X3,singleton(X2),sK1(X4,X5,cartesian_product2(X3,singleton(X2))))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1313]) ).
tcf(c_6413,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X3,singleton(X2)),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X3,singleton(X2)),X4) = X5 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK5(X3,singleton(X2),sK2(cartesian_product2(X3,singleton(X2)),X4,X5))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1313]) ).
tcf(c_6414,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X3,singleton(X2)),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X3,singleton(X2))) = X5 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK5(X3,singleton(X2),sK3(X4,cartesian_product2(X3,singleton(X2)),X5))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1313]) ).
tcf(c_6415,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X2),unordered_pair(unordered_pair(X4,sK5(X1,singleton(X2),sK4(cartesian_product2(X1,singleton(X2)),X3,X0))),singleton(X4))) = X2 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(cartesian_product2(X1,singleton(X2)),X3)) ),
inference(superposition,[status(thm)],[c_60,c_1313]) ).
tcf(c_6416,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X3),unordered_pair(unordered_pair(X4,sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),X0))),singleton(X4))) = X3 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,singleton(X3)))) ),
inference(superposition,[status(thm)],[c_61,c_1313]) ).
tcf(c_6417,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X1),unordered_pair(unordered_pair(X4,sK5(X3,singleton(X1),unordered_pair(unordered_pair(X2,X0),singleton(X2)))),singleton(X4))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_64,c_1313]) ).
tcf(c_6419,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X1),unordered_pair(unordered_pair(X4,sK5(X3,singleton(X1),unordered_pair(unordered_pair(X0,X2),singleton(X2)))),singleton(X4))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_809,c_1313]) ).
tcf(c_6420,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X1),unordered_pair(unordered_pair(X4,sK5(X3,singleton(X1),unordered_pair(singleton(X2),unordered_pair(X0,X2)))),singleton(X4))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_882,c_1313]) ).
tcf(c_6422,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X1),unordered_pair(unordered_pair(X4,sK5(X3,singleton(X1),unordered_pair(singleton(X2),unordered_pair(X2,X0)))),singleton(X4))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_900,c_1313]) ).
tcf(c_6423,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X3,singleton(X2)) )
| ( sK2(singleton(X4),X5,cartesian_product2(X3,singleton(X2))) = X4 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK5(X3,singleton(X2),sK1(singleton(X4),X5,cartesian_product2(X3,singleton(X2))))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_1313]) ).
tcf(c_6424,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X3,singleton(X2)),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X3,singleton(X2)),X4,singleton(X5)) = X5 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK5(X3,singleton(X2),sK2(cartesian_product2(X3,singleton(X2)),X4,singleton(X5)))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_1313]) ).
tcf(c_6425,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,singleton(X5)) )
| ( sK3(X4,singleton(X5),cartesian_product2(X3,singleton(X2))) = X5 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK5(X3,singleton(X2),sK1(X4,singleton(X5),cartesian_product2(X3,singleton(X2))))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_1313]) ).
tcf(c_6426,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,singleton(X2))) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X3,singleton(X2)),singleton(X5)) = X5 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK5(X3,singleton(X2),sK3(X4,cartesian_product2(X3,singleton(X2)),singleton(X5)))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_1313]) ).
tcf(c_6427,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,singleton(X2))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X3,singleton(X2)),X5)),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK5(X3,singleton(X2),sK3(X4,cartesian_product2(X3,singleton(X2)),X5))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_1313]) ).
tcf(c_6428,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,singleton(X2)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X3,singleton(X2)),X4,X5)),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK5(X3,singleton(X2),sK2(cartesian_product2(X3,singleton(X2)),X4,X5))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_1313]) ).
tcf(c_6429,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,singleton(X2)))),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK5(X3,singleton(X2),sK1(X4,X5,cartesian_product2(X3,singleton(X2))))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_1313]) ).
tcf(c_6430,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,singleton(X2)))),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK5(X3,singleton(X2),sK1(X4,X5,cartesian_product2(X3,singleton(X2))))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_1313]) ).
tcf(c_6467,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,singleton(X3))
| ( cartesian_product2(X2,singleton(X3)) = singleton(X1) )
| ( sK1(X2,singleton(X3),singleton(X1)) = X1 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X2,singleton(X3),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1032,c_1564]) ).
tcf(c_6468,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_6164]) ).
tcf(c_6469,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_1156]) ).
tcf(c_6470,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_5987]) ).
tcf(c_6471,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_1155]) ).
tcf(c_6472,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_5758]) ).
tcf(c_6473,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_1154]) ).
tcf(c_6474,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_5518]) ).
tcf(c_6475,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_1153]) ).
tcf(c_6476,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_5291]) ).
tcf(c_6477,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_1152]) ).
tcf(c_6478,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_4798]) ).
tcf(c_6479,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_1151]) ).
tcf(c_6480,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X0) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(X4,sK1(X2,X0,X3)))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK3(X2,X0,X3)),unordered_pair(X1,sK3(X2,X0,X3)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1564,c_2539]) ).
tcf(c_6481,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X1 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(sK3(X2,X3,X1),X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X2,X3,X1)))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_2384]) ).
tcf(c_6482,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X0) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(X4,sK1(X2,X0,X3)))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK3(X2,X0,X3)),singleton(sK3(X2,X0,X3)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1564,c_1929]) ).
tcf(c_6483,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X1 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(sK3(X2,X3,X1),X4),singleton(X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X2,X3,X1)))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_1823]) ).
tcf(c_6484,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X0) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(X4,sK1(X2,X0,X3)))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK3(X2,X0,X3)),unordered_pair(sK3(X2,X0,X3),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1564,c_1643]) ).
tcf(c_6485,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X1 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(X4,sK3(X2,X3,X1)))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X2,X3,X1)))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_1524]) ).
tcf(c_6486,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X0) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(X4,sK1(X2,X0,X3)))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK3(X2,X0,X3),X1),singleton(sK3(X2,X0,X3)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1564,c_1306]) ).
tcf(c_6487,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X1 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(X4,sK3(X2,X3,X1)),singleton(X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X2,X3,X1)))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_1060]) ).
tcf(c_6488,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(sK3(X4,singleton(X5),X3),X0))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X4,singleton(X5),X3)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_907]) ).
tcf(c_6489,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,singleton(X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,singleton(X2),X4)))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK3(X3,singleton(X2),X4)),unordered_pair(X0,sK3(X3,singleton(X2),X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_906]) ).
tcf(c_6490,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(sK3(X4,singleton(X5),X3),X0),singleton(X0))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X4,singleton(X5),X3)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_899]) ).
tcf(c_6491,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,singleton(X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,singleton(X2),X4)))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X0,sK3(X3,singleton(X2),X4)),singleton(sK3(X3,singleton(X2),X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_898]) ).
tcf(c_6492,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,singleton(X5),X3)))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X4,singleton(X5),X3)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_889]) ).
tcf(c_6493,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,singleton(X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,singleton(X2),X4)))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK3(X3,singleton(X2),X4)),unordered_pair(sK3(X3,singleton(X2),X4),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_888]) ).
tcf(c_6494,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(X0,sK3(X4,singleton(X5),X3)),singleton(X0))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X4,singleton(X5),X3)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_863]) ).
tcf(c_6495,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,singleton(X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,singleton(X2),X4)))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK3(X3,singleton(X2),X4),X0),singleton(sK3(X3,singleton(X2),X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_837]) ).
tcf(c_6497,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X0)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,cartesian_product2(X2,X0),X4)))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))),unordered_pair(X1,sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1564,c_2611]) ).
tcf(c_6498,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X0,X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,cartesian_product2(X0,X2),X4)))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))),unordered_pair(X1,sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1564,c_2610]) ).
tcf(c_6499,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X0)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,cartesian_product2(X2,X0),X4)))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))),singleton(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1564,c_2036]) ).
tcf(c_6500,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X0,X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,cartesian_product2(X0,X2),X4)))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))),singleton(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1564,c_2035]) ).
tcf(c_6501,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X0)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,cartesian_product2(X2,X0),X4)))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))),unordered_pair(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4)),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1564,c_1703]) ).
tcf(c_6502,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X0,X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,cartesian_product2(X0,X2),X4)))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))),unordered_pair(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4)),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1564,c_1702]) ).
tcf(c_6503,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X0)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,cartesian_product2(X2,X0),X4)))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4)),X1),singleton(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1564,c_1389]) ).
tcf(c_6504,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X0,X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,cartesian_product2(X0,X2),X4)))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4)),X1),singleton(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1564,c_1388]) ).
tcf(c_6505,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,cartesian_product2(X2,X1),X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK3(X3,cartesian_product2(X2,X1),X4)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_2459]) ).
tcf(c_6506,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,cartesian_product2(X1,X2),X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK3(X3,cartesian_product2(X1,X2),X4)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_2458]) ).
tcf(c_6507,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,cartesian_product2(X2,X1),X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK3(X3,cartesian_product2(X2,X1),X4)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_1857]) ).
tcf(c_6508,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,cartesian_product2(X1,X2),X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK3(X3,cartesian_product2(X1,X2),X4)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_1856]) ).
tcf(c_6509,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,cartesian_product2(X2,X1),X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK3(X3,cartesian_product2(X2,X1),X4))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_1569]) ).
tcf(c_6510,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,cartesian_product2(X1,X2),X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK3(X3,cartesian_product2(X1,X2),X4))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_1568]) ).
tcf(c_6511,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,cartesian_product2(X2,X1),X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK3(X3,cartesian_product2(X2,X1),X4))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_1150]) ).
tcf(c_6512,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,cartesian_product2(X1,X2),X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK3(X3,cartesian_product2(X1,X2),X4))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_1149]) ).
tcf(c_6513,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,cartesian_product2(X0,X1)) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(X4,sK1(X2,cartesian_product2(X0,X1),X3)))) = X4 )
| ( unordered_pair(unordered_pair(sK4(X0,X1,sK3(X2,cartesian_product2(X0,X1),X3)),sK5(X0,X1,sK3(X2,cartesian_product2(X0,X1),X3))),singleton(sK4(X0,X1,sK3(X2,cartesian_product2(X0,X1),X3)))) = sK3(X2,cartesian_product2(X0,X1),X3) ) ),
inference(superposition,[status(thm)],[c_1564,c_62]) ).
tcf(c_6514,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(singleton(X2),X3),X5)))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK4(singleton(X2),X3,sK3(X4,cartesian_product2(singleton(X2),X3),X5))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_1312]) ).
tcf(c_6515,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,cartesian_product2(singleton(X3),X4)) = X1 )
| ( sK4(singleton(X3),X4,sK3(X2,cartesian_product2(singleton(X3),X4),X1)) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X2,cartesian_product2(singleton(X3),X4),X1)))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_787]) ).
tcf(c_6516,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,singleton(X2))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X3,singleton(X2)),X5)))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK5(X3,singleton(X2),sK3(X4,cartesian_product2(X3,singleton(X2)),X5))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_1313]) ).
tcf(c_6517,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,cartesian_product2(X3,singleton(X4))) = X1 )
| ( sK5(X3,singleton(X4),sK3(X2,cartesian_product2(X3,singleton(X4)),X1)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X2,cartesian_product2(X3,singleton(X4)),X1)))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_789]) ).
tcf(c_6518,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(cartesian_product2(singleton(X0),X1),X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,cartesian_product2(cartesian_product2(singleton(X0),X1),X2),X4)))) = X5 )
| ( sK4(singleton(X0),X1,sK4(cartesian_product2(singleton(X0),X1),X2,sK3(X3,cartesian_product2(cartesian_product2(singleton(X0),X1),X2),X4))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_835]) ).
tcf(c_6519,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,cartesian_product2(singleton(X0),X1))) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,cartesian_product2(X2,cartesian_product2(singleton(X0),X1)),X4)))) = X5 )
| ( sK4(singleton(X0),X1,sK5(X2,cartesian_product2(singleton(X0),X1),sK3(X3,cartesian_product2(X2,cartesian_product2(singleton(X0),X1)),X4))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_836]) ).
tcf(c_6520,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(cartesian_product2(X0,singleton(X1)),X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,cartesian_product2(cartesian_product2(X0,singleton(X1)),X2),X4)))) = X5 )
| ( sK5(X0,singleton(X1),sK4(cartesian_product2(X0,singleton(X1)),X2,sK3(X3,cartesian_product2(cartesian_product2(X0,singleton(X1)),X2),X4))) = X1 ) ),
inference(superposition,[status(thm)],[c_1564,c_861]) ).
tcf(c_6521,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,cartesian_product2(X0,singleton(X1)))) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,cartesian_product2(X2,cartesian_product2(X0,singleton(X1))),X4)))) = X5 )
| ( sK5(X0,singleton(X1),sK5(X2,cartesian_product2(X0,singleton(X1)),sK3(X3,cartesian_product2(X2,cartesian_product2(X0,singleton(X1))),X4))) = X1 ) ),
inference(superposition,[status(thm)],[c_1564,c_862]) ).
tcf(c_6670,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X2,singleton(X2))
| ( cartesian_product2(singleton(X2),X3) = singleton(X1) )
| ( sK1(singleton(X2),X3,singleton(X1)) = X1 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK1(singleton(X2),X3,singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1009,c_1565]) ).
tcf(c_6671,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_6164]) ).
tcf(c_6672,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_1156]) ).
tcf(c_6673,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_5987]) ).
tcf(c_6674,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_1155]) ).
tcf(c_6675,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_5758]) ).
tcf(c_6676,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_1154]) ).
tcf(c_6677,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_5518]) ).
tcf(c_6678,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_1153]) ).
tcf(c_6679,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_5291]) ).
tcf(c_6680,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_1152]) ).
tcf(c_6681,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_4798]) ).
tcf(c_6682,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_1151]) ).
tcf(c_6683,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X2) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(X4,sK1(X0,X2,X3)))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK2(X0,X2,X3)),unordered_pair(X1,sK2(X0,X2,X3)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1565,c_2539]) ).
tcf(c_6684,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X1 )
| ( sK4(singleton(X4),X2,unordered_pair(singleton(X4),unordered_pair(sK2(X2,X3,X1),X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X2,X3,X1)))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_2384]) ).
tcf(c_6685,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X2) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(X4,sK1(X0,X2,X3)))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK2(X0,X2,X3)),singleton(sK2(X0,X2,X3)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1565,c_1929]) ).
tcf(c_6686,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X1 )
| ( sK4(singleton(X4),X2,unordered_pair(unordered_pair(sK2(X2,X3,X1),X4),singleton(X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X2,X3,X1)))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_1823]) ).
tcf(c_6687,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X2) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(X4,sK1(X0,X2,X3)))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK2(X0,X2,X3)),unordered_pair(sK2(X0,X2,X3),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1565,c_1643]) ).
tcf(c_6688,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X1 )
| ( sK4(singleton(X4),X2,unordered_pair(singleton(X4),unordered_pair(X4,sK2(X2,X3,X1)))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X2,X3,X1)))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_1524]) ).
tcf(c_6689,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X2) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(X4,sK1(X0,X2,X3)))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK2(X0,X2,X3),X1),singleton(sK2(X0,X2,X3)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1565,c_1306]) ).
tcf(c_6690,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X1 )
| ( sK4(singleton(X4),X2,unordered_pair(unordered_pair(X4,sK2(X2,X3,X1)),singleton(X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X2,X3,X1)))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_1060]) ).
tcf(c_6691,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK5(X1,singleton(X4),unordered_pair(singleton(X0),unordered_pair(sK2(singleton(X4),X5,X3),X0))) = X4 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK1(singleton(X4),X5,X3)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_907]) ).
tcf(c_6692,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(singleton(X2),X3,X4)))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK2(singleton(X2),X3,X4)),unordered_pair(X0,sK2(singleton(X2),X3,X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_906]) ).
tcf(c_6693,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK5(X1,singleton(X4),unordered_pair(unordered_pair(sK2(singleton(X4),X5,X3),X0),singleton(X0))) = X4 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK1(singleton(X4),X5,X3)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_899]) ).
tcf(c_6694,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(singleton(X2),X3,X4)))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X0,sK2(singleton(X2),X3,X4)),singleton(sK2(singleton(X2),X3,X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_898]) ).
tcf(c_6695,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK5(X1,singleton(X4),unordered_pair(singleton(X0),unordered_pair(X0,sK2(singleton(X4),X5,X3)))) = X4 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK1(singleton(X4),X5,X3)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_889]) ).
tcf(c_6696,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(singleton(X2),X3,X4)))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK2(singleton(X2),X3,X4)),unordered_pair(sK2(singleton(X2),X3,X4),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_888]) ).
tcf(c_6697,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK5(X1,singleton(X4),unordered_pair(unordered_pair(X0,sK2(singleton(X4),X5,X3)),singleton(X0))) = X4 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK1(singleton(X4),X5,X3)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_863]) ).
tcf(c_6698,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(singleton(X2),X3,X4)))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK2(singleton(X2),X3,X4),X0),singleton(sK2(singleton(X2),X3,X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_837]) ).
tcf(c_6700,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X0),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(cartesian_product2(X2,X0),X3,X4)))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))),unordered_pair(X1,sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1565,c_2611]) ).
tcf(c_6701,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X0,X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(cartesian_product2(X0,X2),X3,X4)))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))),unordered_pair(X1,sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1565,c_2610]) ).
tcf(c_6702,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X0),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(cartesian_product2(X2,X0),X3,X4)))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))),singleton(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1565,c_2036]) ).
tcf(c_6703,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X0,X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(cartesian_product2(X0,X2),X3,X4)))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))),singleton(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1565,c_2035]) ).
tcf(c_6704,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X0),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(cartesian_product2(X2,X0),X3,X4)))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))),unordered_pair(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4)),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1565,c_1703]) ).
tcf(c_6705,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X0,X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(cartesian_product2(X0,X2),X3,X4)))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))),unordered_pair(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4)),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1565,c_1702]) ).
tcf(c_6706,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X0),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(cartesian_product2(X2,X0),X3,X4)))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4)),X1),singleton(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1565,c_1389]) ).
tcf(c_6707,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X0,X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(cartesian_product2(X0,X2),X3,X4)))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4)),X1),singleton(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1565,c_1388]) ).
tcf(c_6708,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(cartesian_product2(X2,X1),X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK2(cartesian_product2(X2,X1),X3,X4)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_2459]) ).
tcf(c_6709,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(cartesian_product2(X1,X2),X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK2(cartesian_product2(X1,X2),X3,X4)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_2458]) ).
tcf(c_6710,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(cartesian_product2(X2,X1),X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK2(cartesian_product2(X2,X1),X3,X4)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_1857]) ).
tcf(c_6711,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(cartesian_product2(X1,X2),X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK2(cartesian_product2(X1,X2),X3,X4)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_1856]) ).
tcf(c_6712,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(cartesian_product2(X2,X1),X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK2(cartesian_product2(X2,X1),X3,X4))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_1569]) ).
tcf(c_6713,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(cartesian_product2(X1,X2),X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK2(cartesian_product2(X1,X2),X3,X4))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_1568]) ).
tcf(c_6714,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(cartesian_product2(X2,X1),X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK2(cartesian_product2(X2,X1),X3,X4))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_1150]) ).
tcf(c_6715,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(cartesian_product2(X1,X2),X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK2(cartesian_product2(X1,X2),X3,X4))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_1149]) ).
tcf(c_6716,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(X0,X1),X2) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(X4,sK1(cartesian_product2(X0,X1),X2,X3)))) = X4 )
| ( unordered_pair(unordered_pair(sK4(X0,X1,sK2(cartesian_product2(X0,X1),X2,X3)),sK5(X0,X1,sK2(cartesian_product2(X0,X1),X2,X3))),singleton(sK4(X0,X1,sK2(cartesian_product2(X0,X1),X2,X3)))) = sK2(cartesian_product2(X0,X1),X2,X3) ) ),
inference(superposition,[status(thm)],[c_1565,c_62]) ).
tcf(c_6717,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(singleton(X2),X3),X4,X5)))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK4(singleton(X2),X3,sK2(cartesian_product2(singleton(X2),X3),X4,X5))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_1312]) ).
tcf(c_6718,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X1 )
| ( sK4(singleton(X2),X3,sK2(cartesian_product2(singleton(X2),X3),X4,X1)) = X2 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK1(cartesian_product2(singleton(X2),X3),X4,X1)))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_787]) ).
tcf(c_6719,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,singleton(X2)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X3,singleton(X2)),X4,X5)))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK5(X3,singleton(X2),sK2(cartesian_product2(X3,singleton(X2)),X4,X5))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_1313]) ).
tcf(c_6720,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X1 )
| ( sK5(X2,singleton(X3),sK2(cartesian_product2(X2,singleton(X3)),X4,X1)) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK1(cartesian_product2(X2,singleton(X3)),X4,X1)))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_789]) ).
tcf(c_6721,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(singleton(X0),X1),X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(cartesian_product2(cartesian_product2(singleton(X0),X1),X2),X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,sK4(cartesian_product2(singleton(X0),X1),X2,sK2(cartesian_product2(cartesian_product2(singleton(X0),X1),X2),X3,X4))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_835]) ).
tcf(c_6722,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,cartesian_product2(singleton(X0),X1)),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(cartesian_product2(X2,cartesian_product2(singleton(X0),X1)),X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,sK5(X2,cartesian_product2(singleton(X0),X1),sK2(cartesian_product2(X2,cartesian_product2(singleton(X0),X1)),X3,X4))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_836]) ).
tcf(c_6723,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X0,singleton(X1)),X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(cartesian_product2(cartesian_product2(X0,singleton(X1)),X2),X3,X4)))) = X5 )
| ( sK5(X0,singleton(X1),sK4(cartesian_product2(X0,singleton(X1)),X2,sK2(cartesian_product2(cartesian_product2(X0,singleton(X1)),X2),X3,X4))) = X1 ) ),
inference(superposition,[status(thm)],[c_1565,c_861]) ).
tcf(c_6724,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,cartesian_product2(X0,singleton(X1))),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(cartesian_product2(X2,cartesian_product2(X0,singleton(X1))),X3,X4)))) = X5 )
| ( sK5(X0,singleton(X1),sK5(X2,cartesian_product2(X0,singleton(X1)),sK2(cartesian_product2(X2,cartesian_product2(X0,singleton(X1))),X3,X4))) = X1 ) ),
inference(superposition,[status(thm)],[c_1565,c_862]) ).
tcf(c_6937,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_6164]) ).
tcf(c_6938,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_1156]) ).
tcf(c_6939,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_5987]) ).
tcf(c_6940,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_1155]) ).
tcf(c_6941,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_5758]) ).
tcf(c_6942,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_1154]) ).
tcf(c_6943,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_5518]) ).
tcf(c_6944,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_1153]) ).
tcf(c_6945,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_5291]) ).
tcf(c_6946,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_1152]) ).
tcf(c_6947,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_4798]) ).
tcf(c_6948,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_1151]) ).
tcf(c_6949,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK4(singleton(X4),X2,unordered_pair(singleton(X4),unordered_pair(X4,sK2(X2,X3,X0)))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,X3,X0)),unordered_pair(X1,sK1(X2,X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1566,c_2539]) ).
tcf(c_6950,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X2) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(sK1(X1,X2,X3),X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X1,X2,X3)))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_2384]) ).
tcf(c_6951,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK4(singleton(X4),X2,unordered_pair(singleton(X4),unordered_pair(X4,sK2(X2,X3,X0)))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK1(X2,X3,X0)),singleton(sK1(X2,X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1566,c_1929]) ).
tcf(c_6952,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X2) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(sK1(X1,X2,X3),X4),singleton(X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X1,X2,X3)))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_1823]) ).
tcf(c_6953,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK4(singleton(X4),X2,unordered_pair(singleton(X4),unordered_pair(X4,sK2(X2,X3,X0)))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,X3,X0)),unordered_pair(sK1(X2,X3,X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1566,c_1643]) ).
tcf(c_6954,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X2) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(X4,sK1(X1,X2,X3)))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X1,X2,X3)))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_1524]) ).
tcf(c_6955,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK4(singleton(X4),X2,unordered_pair(singleton(X4),unordered_pair(X4,sK2(X2,X3,X0)))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(X2,X3,X0),X1),singleton(sK1(X2,X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1566,c_1306]) ).
tcf(c_6956,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X2) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(X4,sK1(X1,X2,X3)),singleton(X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X1,X2,X3)))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_1060]) ).
tcf(c_6957,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(sK1(X3,X4,singleton(X5)),X0))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK2(X3,X4,singleton(X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_907]) ).
tcf(c_6958,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,singleton(X2))))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK1(X3,X4,singleton(X2))),unordered_pair(X0,sK1(X3,X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_906]) ).
tcf(c_6959,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X4,singleton(X5)),X0),singleton(X0))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK2(X3,X4,singleton(X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_899]) ).
tcf(c_6960,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,singleton(X2))))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X0,sK1(X3,X4,singleton(X2))),singleton(sK1(X3,X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_898]) ).
tcf(c_6961,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X3,X4,singleton(X5))))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK2(X3,X4,singleton(X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_889]) ).
tcf(c_6962,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,singleton(X2))))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK1(X3,X4,singleton(X2))),unordered_pair(sK1(X3,X4,singleton(X2)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_888]) ).
tcf(c_6963,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(X0,sK1(X3,X4,singleton(X5))),singleton(X0))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK2(X3,X4,singleton(X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_863]) ).
tcf(c_6964,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,singleton(X2))))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,singleton(X2)),X0),singleton(sK1(X3,X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_837]) ).
tcf(c_6966,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,cartesian_product2(X2,X0))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))),unordered_pair(X1,sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1566,c_2611]) ).
tcf(c_6967,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,cartesian_product2(X0,X2))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))),unordered_pair(X1,sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1566,c_2610]) ).
tcf(c_6968,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,cartesian_product2(X2,X0))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))),singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1566,c_2036]) ).
tcf(c_6969,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,cartesian_product2(X0,X2))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))),singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1566,c_2035]) ).
tcf(c_6970,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,cartesian_product2(X2,X0))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))),unordered_pair(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0))),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1566,c_1703]) ).
tcf(c_6971,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,cartesian_product2(X0,X2))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))),unordered_pair(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2))),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1566,c_1702]) ).
tcf(c_6972,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,cartesian_product2(X2,X0))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0))),X1),singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1566,c_1389]) ).
tcf(c_6973,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,cartesian_product2(X0,X2))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2))),X1),singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1566,c_1388]) ).
tcf(c_6974,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X1) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,cartesian_product2(X2,X1))))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK1(X3,X4,cartesian_product2(X2,X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_2459]) ).
tcf(c_6975,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,cartesian_product2(X1,X2))))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK1(X3,X4,cartesian_product2(X1,X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_2458]) ).
tcf(c_6976,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X1) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,cartesian_product2(X2,X1))))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK1(X3,X4,cartesian_product2(X2,X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_1857]) ).
tcf(c_6977,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,cartesian_product2(X1,X2))))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK1(X3,X4,cartesian_product2(X1,X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_1856]) ).
tcf(c_6978,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X1) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,cartesian_product2(X2,X1))))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK1(X3,X4,cartesian_product2(X2,X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_1569]) ).
tcf(c_6979,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,cartesian_product2(X1,X2))))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK1(X3,X4,cartesian_product2(X1,X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_1568]) ).
tcf(c_6980,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X1) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,cartesian_product2(X2,X1))))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK1(X3,X4,cartesian_product2(X2,X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_1150]) ).
tcf(c_6981,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,cartesian_product2(X1,X2))))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK1(X3,X4,cartesian_product2(X1,X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_1149]) ).
tcf(c_6982,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( sK4(singleton(X4),X2,unordered_pair(singleton(X4),unordered_pair(X4,sK2(X2,X3,cartesian_product2(X0,X1))))) = X4 )
| ( unordered_pair(unordered_pair(sK4(X0,X1,sK1(X2,X3,cartesian_product2(X0,X1))),sK5(X0,X1,sK1(X2,X3,cartesian_product2(X0,X1)))),singleton(sK4(X0,X1,sK1(X2,X3,cartesian_product2(X0,X1))))) = sK1(X2,X3,cartesian_product2(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_1566,c_62]) ).
tcf(c_6983,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(singleton(X2),X3))))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK4(singleton(X2),X3,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_1312]) ).
tcf(c_6984,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = cartesian_product2(X1,X2) )
| ( sK4(singleton(X3),X4,sK1(X1,X2,cartesian_product2(singleton(X3),X4))) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X1,X2,cartesian_product2(singleton(X3),X4))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_787]) ).
tcf(c_6985,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,singleton(X2)))))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK5(X3,singleton(X2),sK1(X4,X5,cartesian_product2(X3,singleton(X2))))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_1313]) ).
tcf(c_6986,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = cartesian_product2(X1,X2) )
| ( sK5(X3,singleton(X4),sK1(X1,X2,cartesian_product2(X3,singleton(X4)))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X1,X2,cartesian_product2(X3,singleton(X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_789]) ).
tcf(c_6987,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X0),X1),X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,cartesian_product2(cartesian_product2(singleton(X0),X1),X2))))) = X5 )
| ( sK4(singleton(X0),X1,sK4(cartesian_product2(singleton(X0),X1),X2,sK1(X3,X4,cartesian_product2(cartesian_product2(singleton(X0),X1),X2)))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_835]) ).
tcf(c_6988,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(singleton(X0),X1)) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,cartesian_product2(X2,cartesian_product2(singleton(X0),X1)))))) = X5 )
| ( sK4(singleton(X0),X1,sK5(X2,cartesian_product2(singleton(X0),X1),sK1(X3,X4,cartesian_product2(X2,cartesian_product2(singleton(X0),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_836]) ).
tcf(c_6989,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X0,singleton(X1)),X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,cartesian_product2(cartesian_product2(X0,singleton(X1)),X2))))) = X5 )
| ( sK5(X0,singleton(X1),sK4(cartesian_product2(X0,singleton(X1)),X2,sK1(X3,X4,cartesian_product2(cartesian_product2(X0,singleton(X1)),X2)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1566,c_861]) ).
tcf(c_6990,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(X0,singleton(X1))) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,cartesian_product2(X2,cartesian_product2(X0,singleton(X1))))))) = X5 )
| ( sK5(X0,singleton(X1),sK5(X2,cartesian_product2(X0,singleton(X1)),sK1(X3,X4,cartesian_product2(X2,cartesian_product2(X0,singleton(X1)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1566,c_862]) ).
tcf(c_7274,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_6164]) ).
tcf(c_7275,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_1156]) ).
tcf(c_7276,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_5987]) ).
tcf(c_7277,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_1155]) ).
tcf(c_7278,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_5758]) ).
tcf(c_7279,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_1154]) ).
tcf(c_7280,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_5518]) ).
tcf(c_7281,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_1153]) ).
tcf(c_7282,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_5291]) ).
tcf(c_7283,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_1152]) ).
tcf(c_7284,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_4798]) ).
tcf(c_7285,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_1151]) ).
tcf(c_7286,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(X4,sK3(X2,X3,X0)))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,X3,X0)),unordered_pair(X1,sK1(X2,X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1567,c_2539]) ).
tcf(c_7287,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X1) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(sK1(X2,X1,X3),X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X2,X1,X3)))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_2384]) ).
tcf(c_7288,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(X4,sK3(X2,X3,X0)))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK1(X2,X3,X0)),singleton(sK1(X2,X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1567,c_1929]) ).
tcf(c_7289,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X1) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(sK1(X2,X1,X3),X4),singleton(X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X2,X1,X3)))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_1823]) ).
tcf(c_7290,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(X4,sK3(X2,X3,X0)))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,X3,X0)),unordered_pair(sK1(X2,X3,X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1567,c_1643]) ).
tcf(c_7291,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X1) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(X4,sK1(X2,X1,X3)))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X2,X1,X3)))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_1524]) ).
tcf(c_7292,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(X4,sK3(X2,X3,X0)))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(X2,X3,X0),X1),singleton(sK1(X2,X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1567,c_1306]) ).
tcf(c_7293,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X1) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(X4,sK1(X2,X1,X3)),singleton(X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X2,X1,X3)))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_1060]) ).
tcf(c_7294,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(sK1(X4,X3,singleton(X5)),X0))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK3(X4,X3,singleton(X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_907]) ).
tcf(c_7295,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,singleton(X2))))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK1(X3,X4,singleton(X2))),unordered_pair(X0,sK1(X3,X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_906]) ).
tcf(c_7296,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(sK1(X4,X3,singleton(X5)),X0),singleton(X0))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK3(X4,X3,singleton(X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_899]) ).
tcf(c_7297,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,singleton(X2))))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X0,sK1(X3,X4,singleton(X2))),singleton(sK1(X3,X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_898]) ).
tcf(c_7298,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X3,singleton(X5))))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK3(X4,X3,singleton(X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_889]) ).
tcf(c_7299,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,singleton(X2))))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK1(X3,X4,singleton(X2))),unordered_pair(sK1(X3,X4,singleton(X2)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_888]) ).
tcf(c_7300,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(X0,sK1(X4,X3,singleton(X5))),singleton(X0))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK3(X4,X3,singleton(X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_863]) ).
tcf(c_7301,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,singleton(X2))))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,singleton(X2)),X0),singleton(sK1(X3,X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_837]) ).
tcf(c_7303,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,cartesian_product2(X2,X0))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))),unordered_pair(X1,sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1567,c_2611]) ).
tcf(c_7304,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,cartesian_product2(X0,X2))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))),unordered_pair(X1,sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1567,c_2610]) ).
tcf(c_7305,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,cartesian_product2(X2,X0))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))),singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1567,c_2036]) ).
tcf(c_7306,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,cartesian_product2(X0,X2))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))),singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1567,c_2035]) ).
tcf(c_7307,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,cartesian_product2(X2,X0))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))),unordered_pair(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0))),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1567,c_1703]) ).
tcf(c_7308,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,cartesian_product2(X0,X2))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))),unordered_pair(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2))),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1567,c_1702]) ).
tcf(c_7309,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,cartesian_product2(X2,X0))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0))),X1),singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1567,c_1389]) ).
tcf(c_7310,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,cartesian_product2(X0,X2))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2))),X1),singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1567,c_1388]) ).
tcf(c_7311,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X1) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,cartesian_product2(X2,X1))))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK1(X3,X4,cartesian_product2(X2,X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_2459]) ).
tcf(c_7312,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,cartesian_product2(X1,X2))))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK1(X3,X4,cartesian_product2(X1,X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_2458]) ).
tcf(c_7313,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X1) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,cartesian_product2(X2,X1))))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK1(X3,X4,cartesian_product2(X2,X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_1857]) ).
tcf(c_7314,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,cartesian_product2(X1,X2))))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK1(X3,X4,cartesian_product2(X1,X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_1856]) ).
tcf(c_7315,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X1) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,cartesian_product2(X2,X1))))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK1(X3,X4,cartesian_product2(X2,X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_1569]) ).
tcf(c_7316,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,cartesian_product2(X1,X2))))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK1(X3,X4,cartesian_product2(X1,X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_1568]) ).
tcf(c_7317,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X1) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,cartesian_product2(X2,X1))))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK1(X3,X4,cartesian_product2(X2,X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_1150]) ).
tcf(c_7318,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,cartesian_product2(X1,X2))))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK1(X3,X4,cartesian_product2(X1,X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_1149]) ).
tcf(c_7319,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(X4,sK3(X2,X3,cartesian_product2(X0,X1))))) = X4 )
| ( unordered_pair(unordered_pair(sK4(X0,X1,sK1(X2,X3,cartesian_product2(X0,X1))),sK5(X0,X1,sK1(X2,X3,cartesian_product2(X0,X1)))),singleton(sK4(X0,X1,sK1(X2,X3,cartesian_product2(X0,X1))))) = sK1(X2,X3,cartesian_product2(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_1567,c_62]) ).
tcf(c_7320,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(singleton(X2),X3))))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK4(singleton(X2),X3,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_1312]) ).
tcf(c_7321,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = cartesian_product2(X2,X1) )
| ( sK4(singleton(X3),X4,sK1(X2,X1,cartesian_product2(singleton(X3),X4))) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X2,X1,cartesian_product2(singleton(X3),X4))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_787]) ).
tcf(c_7322,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,singleton(X2)))))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK5(X3,singleton(X2),sK1(X4,X5,cartesian_product2(X3,singleton(X2))))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_1313]) ).
tcf(c_7323,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = cartesian_product2(X2,X1) )
| ( sK5(X3,singleton(X4),sK1(X2,X1,cartesian_product2(X3,singleton(X4)))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X2,X1,cartesian_product2(X3,singleton(X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_789]) ).
tcf(c_7324,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X0),X1),X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,cartesian_product2(cartesian_product2(singleton(X0),X1),X2))))) = X5 )
| ( sK4(singleton(X0),X1,sK4(cartesian_product2(singleton(X0),X1),X2,sK1(X3,X4,cartesian_product2(cartesian_product2(singleton(X0),X1),X2)))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_835]) ).
tcf(c_7325,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(singleton(X0),X1)) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,cartesian_product2(X2,cartesian_product2(singleton(X0),X1)))))) = X5 )
| ( sK4(singleton(X0),X1,sK5(X2,cartesian_product2(singleton(X0),X1),sK1(X3,X4,cartesian_product2(X2,cartesian_product2(singleton(X0),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_836]) ).
tcf(c_7326,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X0,singleton(X1)),X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,cartesian_product2(cartesian_product2(X0,singleton(X1)),X2))))) = X5 )
| ( sK5(X0,singleton(X1),sK4(cartesian_product2(X0,singleton(X1)),X2,sK1(X3,X4,cartesian_product2(cartesian_product2(X0,singleton(X1)),X2)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1567,c_861]) ).
tcf(c_7327,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(X0,singleton(X1))) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,cartesian_product2(X2,cartesian_product2(X0,singleton(X1))))))) = X5 )
| ( sK5(X0,singleton(X1),sK5(X2,cartesian_product2(X0,singleton(X1)),sK1(X3,X4,cartesian_product2(X2,cartesian_product2(X0,singleton(X1)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1567,c_862]) ).
tcf(c_7495,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),cartesian_product2(X1,singleton(X3)),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,X3),singleton(X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_1570]) ).
tcf(c_7496,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_1570]) ).
tcf(c_7497,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1570]) ).
tcf(c_7498,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1570]) ).
tcf(c_7499,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1570]) ).
tcf(c_7500,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1570]) ).
tcf(c_7501,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X4,X1),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(unordered_pair(X3,sK4(X1,X2,X0)),singleton(X3))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_1570]) ).
tcf(c_7502,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X4,X2),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(unordered_pair(X3,sK5(X1,X2,X0)),singleton(X3))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_1570]) ).
tcf(c_7503,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X3,X1)),unordered_pair(singleton(X6),unordered_pair(X6,unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))),singleton(X4))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_1570]) ).
tcf(c_7504,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X1,X3)),unordered_pair(singleton(X6),unordered_pair(X6,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))),singleton(X4))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_1570]) ).
tcf(c_7505,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X1,X3)),unordered_pair(singleton(X6),unordered_pair(X6,unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))),singleton(X4))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_1570]) ).
tcf(c_7506,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X1,X3)),unordered_pair(singleton(X6),unordered_pair(X6,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))),singleton(X4))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_1570]) ).
tcf(c_7507,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X3,X1)),unordered_pair(singleton(X6),unordered_pair(X6,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))),singleton(X4))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_1570]) ).
tcf(c_7508,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X3,X1)),unordered_pair(singleton(X6),unordered_pair(X6,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))),singleton(X4))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_1570]) ).
tcf(c_7510,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(singleton(X4),X5,X3)),singleton(X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_1570]) ).
tcf(c_7511,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK2(X3,X4,singleton(X5))),singleton(X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_1570]) ).
tcf(c_7512,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,singleton(X5),X3)),singleton(X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_1570]) ).
tcf(c_7513,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK3(X4,X3,singleton(X5))),singleton(X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_1570]) ).
tcf(c_7514,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_1570]) ).
tcf(c_7515,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_1570]) ).
tcf(c_7516,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_1570]) ).
tcf(c_7517,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_1570]) ).
tcf(c_7518,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_1570]) ).
tcf(c_7519,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_1570]) ).
tcf(c_7520,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_1570]) ).
tcf(c_7521,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_1570]) ).
tcf(c_7634,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X1),sK3(X3,X4,X1)),singleton(sK2(X3,X4,X1))) = sK1(X3,X4,X1) )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_7495]) ).
tcf(c_7635,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X1),X4)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_7495]) ).
tcf(c_7636,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X1),X3)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_7495]) ).
tcf(c_7637,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X1,X3,X4),X4)
| ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_7495]) ).
tcf(c_7638,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X1,X4),X4)
| ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_7495]) ).
tcf(c_7639,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(X1,singleton(X4)),unordered_pair(singleton(X3),unordered_pair(X3,unordered_pair(unordered_pair(sK4(X1,X2,X0),X4),singleton(sK4(X1,X2,X0)))))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_7495]) ).
tcf(c_7640,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(X2,singleton(X4)),unordered_pair(singleton(X3),unordered_pair(X3,unordered_pair(unordered_pair(sK5(X1,X2,X0),X4),singleton(sK5(X1,X2,X0)))))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_7495]) ).
tcf(c_7641,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X3,X1),singleton(X5)),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_7495]) ).
tcf(c_7642,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X1,X3),singleton(X5)),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5),singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_7495]) ).
tcf(c_7643,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X1,X3),singleton(X5)),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_7495]) ).
tcf(c_7644,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X1,X3),singleton(X5)),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5),singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_7495]) ).
tcf(c_7645,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X3,X1),singleton(X5)),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5),singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_7495]) ).
tcf(c_7646,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X3,X1),singleton(X5)),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5),singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_7495]) ).
tcf(c_7648,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X1 )
| ( sK2(singleton(X3),X4,X1) = X3 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK1(singleton(X3),X4,X1),X2),singleton(sK1(singleton(X3),X4,X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_7495]) ).
tcf(c_7649,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X3) = singleton(X4) )
| ( sK1(X1,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK2(X1,X3,singleton(X4)),X2),singleton(sK2(X1,X3,singleton(X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_7495]) ).
tcf(c_7650,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X1 )
| ( sK3(X3,singleton(X4),X1) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,singleton(X4),X1),X2),singleton(sK1(X3,singleton(X4),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_7495]) ).
tcf(c_7651,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X1) = singleton(X4) )
| ( sK1(X3,X1,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK3(X3,X1,singleton(X4)),X2),singleton(sK3(X3,X1,singleton(X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_7495]) ).
tcf(c_7652,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_7495]) ).
tcf(c_7653,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X1,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_7495]) ).
tcf(c_7654,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_7495]) ).
tcf(c_7655,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X1,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_7495]) ).
tcf(c_7656,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_7495]) ).
tcf(c_7657,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_7495]) ).
tcf(c_7658,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_7495]) ).
tcf(c_7659,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_7495]) ).
tcf(c_7766,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),cartesian_product2(singleton(X3),X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X3),unordered_pair(X3,X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_1571]) ).
tcf(c_7767,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_1571]) ).
tcf(c_7768,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1571]) ).
tcf(c_7769,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1571]) ).
tcf(c_7770,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1571]) ).
tcf(c_7771,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1571]) ).
tcf(c_7772,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X1,X4),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(sK4(X1,X2,X0),X3))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_1571]) ).
tcf(c_7773,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X2,X4),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(sK5(X1,X2,X0),X3))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_1571]) ).
tcf(c_7774,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X3,X1),X5),unordered_pair(singleton(X6),unordered_pair(X6,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X4))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_1571]) ).
tcf(c_7775,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X1,X3),X5),unordered_pair(singleton(X6),unordered_pair(X6,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X4))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_1571]) ).
tcf(c_7776,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X1,X3),X5),unordered_pair(singleton(X6),unordered_pair(X6,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X4))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_1571]) ).
tcf(c_7777,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X1,X3),X5),unordered_pair(singleton(X6),unordered_pair(X6,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X4))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_1571]) ).
tcf(c_7778,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X3,X1),X5),unordered_pair(singleton(X6),unordered_pair(X6,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X4))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_1571]) ).
tcf(c_7779,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X3,X1),X5),unordered_pair(singleton(X6),unordered_pair(X6,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X4))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_1571]) ).
tcf(c_7781,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK1(singleton(X4),X5,X3)),unordered_pair(sK1(singleton(X4),X5,X3),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_1571]) ).
tcf(c_7782,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK2(X3,X4,singleton(X5))),unordered_pair(sK2(X3,X4,singleton(X5)),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_1571]) ).
tcf(c_7783,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK1(X4,singleton(X5),X3)),unordered_pair(sK1(X4,singleton(X5),X3),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_1571]) ).
tcf(c_7784,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK3(X4,X3,singleton(X5))),unordered_pair(sK3(X4,X3,singleton(X5)),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_1571]) ).
tcf(c_7785,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_1571]) ).
tcf(c_7786,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_1571]) ).
tcf(c_7787,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_1571]) ).
tcf(c_7788,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_1571]) ).
tcf(c_7789,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_1571]) ).
tcf(c_7790,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_1571]) ).
tcf(c_7791,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_1571]) ).
tcf(c_7792,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_1571]) ).
tcf(c_7848,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X2),sK3(X3,X4,X2)),singleton(sK2(X3,X4,X2))) = sK1(X3,X4,X2) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_7766]) ).
tcf(c_7849,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X2),X4)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_7766]) ).
tcf(c_7850,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X2),X3)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_7766]) ).
tcf(c_7851,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X2,X3,X4),X4)
| ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_7766]) ).
tcf(c_7852,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X2,X4),X4)
| ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_7766]) ).
tcf(c_7853,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(singleton(X4),X1),unordered_pair(singleton(X3),unordered_pair(X3,unordered_pair(singleton(X4),unordered_pair(X4,sK4(X1,X2,X0)))))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_7766]) ).
tcf(c_7854,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(singleton(X4),X2),unordered_pair(singleton(X3),unordered_pair(X3,unordered_pair(singleton(X4),unordered_pair(X4,sK5(X1,X2,X0)))))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_7766]) ).
tcf(c_7855,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X3,X1)),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X2))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_7766]) ).
tcf(c_7856,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X1,X3)),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X0,X2))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_7766]) ).
tcf(c_7857,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X1,X3)),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X0))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_7766]) ).
tcf(c_7858,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X1,X3)),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X2,X0))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_7766]) ).
tcf(c_7859,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X3,X1)),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X0,X2))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_7766]) ).
tcf(c_7860,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X3,X1)),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X2,X0))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_7766]) ).
tcf(c_7862,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X2 )
| ( sK2(singleton(X3),X4,X2) = X3 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK1(singleton(X3),X4,X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_7766]) ).
tcf(c_7863,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK1(X2,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,singleton(X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_7766]) ).
tcf(c_7864,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X2 )
| ( sK3(X3,singleton(X4),X2) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,singleton(X4),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_7766]) ).
tcf(c_7865,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X2) = singleton(X4) )
| ( sK1(X3,X2,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,singleton(X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_7766]) ).
tcf(c_7866,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_7766]) ).
tcf(c_7867,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X2,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_7766]) ).
tcf(c_7868,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_7766]) ).
tcf(c_7869,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X2,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_7766]) ).
tcf(c_7870,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_7766]) ).
tcf(c_7871,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_7766]) ).
tcf(c_7872,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_7766]) ).
tcf(c_7873,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_7766]) ).
tcf(c_8027,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),cartesian_product2(singleton(X3),X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,X3),singleton(X3))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_1572]) ).
tcf(c_8028,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_1572]) ).
tcf(c_8029,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1572]) ).
tcf(c_8030,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1572]) ).
tcf(c_8031,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1572]) ).
tcf(c_8032,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1572]) ).
tcf(c_8033,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X1,X4),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(unordered_pair(X3,sK4(X1,X2,X0)),singleton(sK4(X1,X2,X0)))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_1572]) ).
tcf(c_8034,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X2,X4),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(unordered_pair(X3,sK5(X1,X2,X0)),singleton(sK5(X1,X2,X0)))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_1572]) ).
tcf(c_8035,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X3,X1),X5),unordered_pair(singleton(X6),unordered_pair(X6,unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_1572]) ).
tcf(c_8036,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X1,X3),X5),unordered_pair(singleton(X6),unordered_pair(X6,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))),singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_1572]) ).
tcf(c_8037,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X1,X3),X5),unordered_pair(singleton(X6),unordered_pair(X6,unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_1572]) ).
tcf(c_8038,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X1,X3),X5),unordered_pair(singleton(X6),unordered_pair(X6,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))),singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_1572]) ).
tcf(c_8039,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X3,X1),X5),unordered_pair(singleton(X6),unordered_pair(X6,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))),singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_1572]) ).
tcf(c_8040,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X3,X1),X5),unordered_pair(singleton(X6),unordered_pair(X6,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))),singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_1572]) ).
tcf(c_8042,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(singleton(X4),X5,X3)),singleton(sK1(singleton(X4),X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_1572]) ).
tcf(c_8043,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK2(X3,X4,singleton(X5))),singleton(sK2(X3,X4,singleton(X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_1572]) ).
tcf(c_8044,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,singleton(X5),X3)),singleton(sK1(X4,singleton(X5),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_1572]) ).
tcf(c_8045,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK3(X4,X3,singleton(X5))),singleton(sK3(X4,X3,singleton(X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_1572]) ).
tcf(c_8046,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_1572]) ).
tcf(c_8047,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_1572]) ).
tcf(c_8048,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_1572]) ).
tcf(c_8049,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_1572]) ).
tcf(c_8050,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_1572]) ).
tcf(c_8051,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_1572]) ).
tcf(c_8052,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_1572]) ).
tcf(c_8053,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_1572]) ).
tcf(c_8146,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X2),sK3(X3,X4,X2)),singleton(sK2(X3,X4,X2))) = sK1(X3,X4,X2) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_8027]) ).
tcf(c_8147,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X2),X4)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_8027]) ).
tcf(c_8148,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X2),X3)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_8027]) ).
tcf(c_8149,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X2,X3,X4),X4)
| ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_8027]) ).
tcf(c_8150,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X2,X4),X4)
| ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_8027]) ).
tcf(c_8151,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(singleton(X4),X1),unordered_pair(singleton(X3),unordered_pair(X3,unordered_pair(unordered_pair(sK4(X1,X2,X0),X4),singleton(X4))))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_8027]) ).
tcf(c_8152,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(singleton(X4),X2),unordered_pair(singleton(X3),unordered_pair(X3,unordered_pair(unordered_pair(sK5(X1,X2,X0),X4),singleton(X4))))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_8027]) ).
tcf(c_8153,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X3,X1)),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5),singleton(X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_8027]) ).
tcf(c_8154,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X1,X3)),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5),singleton(X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_8027]) ).
tcf(c_8155,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X1,X3)),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5),singleton(X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_8027]) ).
tcf(c_8156,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X1,X3)),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5),singleton(X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_8027]) ).
tcf(c_8157,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X3,X1)),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5),singleton(X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_8027]) ).
tcf(c_8158,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X3,X1)),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5),singleton(X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_8027]) ).
tcf(c_8160,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X2 )
| ( sK2(singleton(X3),X4,X2) = X3 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK1(singleton(X3),X4,X2),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_8027]) ).
tcf(c_8161,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK1(X2,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK2(X2,X3,singleton(X4)),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_8027]) ).
tcf(c_8162,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X2 )
| ( sK3(X3,singleton(X4),X2) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,singleton(X4),X2),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_8027]) ).
tcf(c_8163,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X2) = singleton(X4) )
| ( sK1(X3,X2,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK3(X3,X2,singleton(X4)),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_8027]) ).
tcf(c_8164,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_8027]) ).
tcf(c_8165,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X2,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_8027]) ).
tcf(c_8166,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_8027]) ).
tcf(c_8167,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X2,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_8027]) ).
tcf(c_8168,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_8027]) ).
tcf(c_8169,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_8027]) ).
tcf(c_8170,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_8027]) ).
tcf(c_8171,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_8027]) ).
tcf(c_8285,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),cartesian_product2(singleton(X3),X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X3),unordered_pair(X0,X3))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_1573]) ).
tcf(c_8286,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_1573]) ).
tcf(c_8287,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1573]) ).
tcf(c_8288,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1573]) ).
tcf(c_8289,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1573]) ).
tcf(c_8290,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1573]) ).
tcf(c_8291,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X1,X4),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(X3,sK4(X1,X2,X0)))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_1573]) ).
tcf(c_8292,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X2,X4),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(X3,sK5(X1,X2,X0)))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_1573]) ).
tcf(c_8293,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X3,X1),X5),unordered_pair(singleton(X6),unordered_pair(X6,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_1573]) ).
tcf(c_8294,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X1,X3),X5),unordered_pair(singleton(X6),unordered_pair(X6,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_1573]) ).
tcf(c_8295,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X1,X3),X5),unordered_pair(singleton(X6),unordered_pair(X6,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_1573]) ).
tcf(c_8296,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X1,X3),X5),unordered_pair(singleton(X6),unordered_pair(X6,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_1573]) ).
tcf(c_8297,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X3,X1),X5),unordered_pair(singleton(X6),unordered_pair(X6,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_1573]) ).
tcf(c_8298,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X3,X1),X5),unordered_pair(singleton(X6),unordered_pair(X6,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_1573]) ).
tcf(c_8300,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK1(singleton(X4),X5,X3)),unordered_pair(X0,sK1(singleton(X4),X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_1573]) ).
tcf(c_8301,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK2(X3,X4,singleton(X5))),unordered_pair(X0,sK2(X3,X4,singleton(X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_1573]) ).
tcf(c_8302,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK1(X4,singleton(X5),X3)),unordered_pair(X0,sK1(X4,singleton(X5),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_1573]) ).
tcf(c_8303,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK3(X4,X3,singleton(X5))),unordered_pair(X0,sK3(X4,X3,singleton(X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_1573]) ).
tcf(c_8304,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_1573]) ).
tcf(c_8305,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_1573]) ).
tcf(c_8306,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_1573]) ).
tcf(c_8307,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_1573]) ).
tcf(c_8308,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_1573]) ).
tcf(c_8309,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_1573]) ).
tcf(c_8310,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_1573]) ).
tcf(c_8311,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_1573]) ).
tcf(c_8452,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X2),sK3(X3,X4,X2)),singleton(sK2(X3,X4,X2))) = sK1(X3,X4,X2) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_8285]) ).
tcf(c_8453,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X2),X4)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_8285]) ).
tcf(c_8454,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X2),X3)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_8285]) ).
tcf(c_8455,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X2,X3,X4),X4)
| ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_8285]) ).
tcf(c_8456,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X2,X4),X4)
| ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_8285]) ).
tcf(c_8457,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(singleton(X4),X1),unordered_pair(singleton(X3),unordered_pair(X3,unordered_pair(singleton(X4),unordered_pair(sK4(X1,X2,X0),X4))))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_8285]) ).
tcf(c_8458,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(singleton(X4),X2),unordered_pair(singleton(X3),unordered_pair(X3,unordered_pair(singleton(X4),unordered_pair(sK5(X1,X2,X0),X4))))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_8285]) ).
tcf(c_8459,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X3,X1)),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_8285]) ).
tcf(c_8460,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X1,X3)),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_8285]) ).
tcf(c_8461,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X1,X3)),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_8285]) ).
tcf(c_8462,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X1,X3)),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_8285]) ).
tcf(c_8463,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X3,X1)),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_8285]) ).
tcf(c_8464,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X3,X1)),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_8285]) ).
tcf(c_8466,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X2 )
| ( sK2(singleton(X3),X4,X2) = X3 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK1(singleton(X3),X4,X2),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_8285]) ).
tcf(c_8467,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK1(X2,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,singleton(X4)),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_8285]) ).
tcf(c_8468,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X2 )
| ( sK3(X3,singleton(X4),X2) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK1(X3,singleton(X4),X2),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_8285]) ).
tcf(c_8469,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X2) = singleton(X4) )
| ( sK1(X3,X2,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,singleton(X4)),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_8285]) ).
tcf(c_8470,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_8285]) ).
tcf(c_8471,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X2,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_8285]) ).
tcf(c_8472,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_8285]) ).
tcf(c_8473,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X2,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_8285]) ).
tcf(c_8474,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_8285]) ).
tcf(c_8475,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_8285]) ).
tcf(c_8476,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_8285]) ).
tcf(c_8477,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_8285]) ).
tcf(c_8554,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),cartesian_product2(X1,singleton(X3)),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X3,X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_1574]) ).
tcf(c_8555,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_1574]) ).
tcf(c_8556,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1574]) ).
tcf(c_8557,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1574]) ).
tcf(c_8558,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1574]) ).
tcf(c_8559,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1574]) ).
tcf(c_8560,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X4,X1),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X3),unordered_pair(sK4(X1,X2,X0),X3))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_1574]) ).
tcf(c_8561,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X4,X2),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X3),unordered_pair(sK5(X1,X2,X0),X3))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_1574]) ).
tcf(c_8562,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X3,X1)),unordered_pair(singleton(X6),unordered_pair(X6,unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X4))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_1574]) ).
tcf(c_8563,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X1,X3)),unordered_pair(singleton(X6),unordered_pair(X6,unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X4))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_1574]) ).
tcf(c_8564,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X1,X3)),unordered_pair(singleton(X6),unordered_pair(X6,unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X4))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_1574]) ).
tcf(c_8565,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X1,X3)),unordered_pair(singleton(X6),unordered_pair(X6,unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X4))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_1574]) ).
tcf(c_8566,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X3,X1)),unordered_pair(singleton(X6),unordered_pair(X6,unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X4))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_1574]) ).
tcf(c_8567,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X3,X1)),unordered_pair(singleton(X6),unordered_pair(X6,unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X4))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_1574]) ).
tcf(c_8569,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK1(singleton(X4),X5,X3),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_1574]) ).
tcf(c_8570,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,singleton(X5)),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_1574]) ).
tcf(c_8571,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK1(X4,singleton(X5),X3),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_1574]) ).
tcf(c_8572,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,singleton(X5)),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_1574]) ).
tcf(c_8573,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_1574]) ).
tcf(c_8574,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_1574]) ).
tcf(c_8575,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_1574]) ).
tcf(c_8576,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_1574]) ).
tcf(c_8577,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_1574]) ).
tcf(c_8578,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_1574]) ).
tcf(c_8579,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_1574]) ).
tcf(c_8580,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_1574]) ).
tcf(c_8616,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X1),sK3(X3,X4,X1)),singleton(sK2(X3,X4,X1))) = sK1(X3,X4,X1) )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_8554]) ).
tcf(c_8617,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X1),X4)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_8554]) ).
tcf(c_8618,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X1),X3)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_8554]) ).
tcf(c_8619,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X1,X3,X4),X4)
| ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_8554]) ).
tcf(c_8620,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X1,X4),X4)
| ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_8554]) ).
tcf(c_8621,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(X1,singleton(X4)),unordered_pair(singleton(X3),unordered_pair(X3,unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(X4,sK4(X1,X2,X0)))))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_8554]) ).
tcf(c_8622,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(X2,singleton(X4)),unordered_pair(singleton(X3),unordered_pair(X3,unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(X4,sK5(X1,X2,X0)))))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_8554]) ).
tcf(c_8623,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X3,X1),singleton(X5)),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X2))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_8554]) ).
tcf(c_8624,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X1,X3),singleton(X5)),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X0,X2))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_8554]) ).
tcf(c_8625,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X1,X3),singleton(X5)),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X0))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_8554]) ).
tcf(c_8626,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X1,X3),singleton(X5)),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X2,X0))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_8554]) ).
tcf(c_8627,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X3,X1),singleton(X5)),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X0,X2))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_8554]) ).
tcf(c_8628,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X3,X1),singleton(X5)),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X2,X0))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_8554]) ).
tcf(c_8630,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X1 )
| ( sK2(singleton(X3),X4,X1) = X3 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK1(singleton(X3),X4,X1)),unordered_pair(X2,sK1(singleton(X3),X4,X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_8554]) ).
tcf(c_8631,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X3) = singleton(X4) )
| ( sK1(X1,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK2(X1,X3,singleton(X4))),unordered_pair(X2,sK2(X1,X3,singleton(X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_8554]) ).
tcf(c_8632,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X1 )
| ( sK3(X3,singleton(X4),X1) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK1(X3,singleton(X4),X1)),unordered_pair(X2,sK1(X3,singleton(X4),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_8554]) ).
tcf(c_8633,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X1) = singleton(X4) )
| ( sK1(X3,X1,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK3(X3,X1,singleton(X4))),unordered_pair(X2,sK3(X3,X1,singleton(X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_8554]) ).
tcf(c_8634,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_8554]) ).
tcf(c_8635,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X1,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_8554]) ).
tcf(c_8636,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_8554]) ).
tcf(c_8637,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X1,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_8554]) ).
tcf(c_8638,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_8554]) ).
tcf(c_8639,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_8554]) ).
tcf(c_8640,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_8554]) ).
tcf(c_8641,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_8554]) ).
tcf(c_8720,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),cartesian_product2(X1,singleton(X3)),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,X3))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_1575]) ).
tcf(c_8721,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_1575]) ).
tcf(c_8722,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1575]) ).
tcf(c_8723,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1575]) ).
tcf(c_8724,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1575]) ).
tcf(c_8725,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1575]) ).
tcf(c_8726,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X4,X1),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X3),unordered_pair(X3,sK4(X1,X2,X0)))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_1575]) ).
tcf(c_8727,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X4,X2),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X3),unordered_pair(X3,sK5(X1,X2,X0)))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_1575]) ).
tcf(c_8728,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X3,X1)),unordered_pair(singleton(X6),unordered_pair(X6,unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_1575]) ).
tcf(c_8729,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X1,X3)),unordered_pair(singleton(X6),unordered_pair(X6,unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_1575]) ).
tcf(c_8730,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X1,X3)),unordered_pair(singleton(X6),unordered_pair(X6,unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_1575]) ).
tcf(c_8731,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X1,X3)),unordered_pair(singleton(X6),unordered_pair(X6,unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_1575]) ).
tcf(c_8732,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X3,X1)),unordered_pair(singleton(X6),unordered_pair(X6,unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_1575]) ).
tcf(c_8733,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X3,X1)),unordered_pair(singleton(X6),unordered_pair(X6,unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_1575]) ).
tcf(c_8735,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK1(singleton(X4),X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_1575]) ).
tcf(c_8736,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,singleton(X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_1575]) ).
tcf(c_8737,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,singleton(X5),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_1575]) ).
tcf(c_8738,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,singleton(X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_1575]) ).
tcf(c_8739,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_1575]) ).
tcf(c_8740,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_1575]) ).
tcf(c_8741,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_1575]) ).
tcf(c_8742,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_1575]) ).
tcf(c_8743,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_1575]) ).
tcf(c_8744,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_1575]) ).
tcf(c_8745,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_1575]) ).
tcf(c_8746,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_1575]) ).
tcf(c_8780,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X1),sK3(X3,X4,X1)),singleton(sK2(X3,X4,X1))) = sK1(X3,X4,X1) )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_8720]) ).
tcf(c_8781,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X1),X4)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_8720]) ).
tcf(c_8782,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X1),X3)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_8720]) ).
tcf(c_8783,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X1,X3,X4),X4)
| ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_8720]) ).
tcf(c_8784,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X1,X4),X4)
| ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_8720]) ).
tcf(c_8785,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(X1,singleton(X4)),unordered_pair(singleton(X3),unordered_pair(X3,unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(sK4(X1,X2,X0),X4))))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_8720]) ).
tcf(c_8786,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(X2,singleton(X4)),unordered_pair(singleton(X3),unordered_pair(X3,unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(sK5(X1,X2,X0),X4))))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_8720]) ).
tcf(c_8787,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X3,X1),singleton(X5)),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_8720]) ).
tcf(c_8788,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X1,X3),singleton(X5)),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_8720]) ).
tcf(c_8789,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X1,X3),singleton(X5)),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_8720]) ).
tcf(c_8790,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X1,X3),singleton(X5)),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_8720]) ).
tcf(c_8791,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X3,X1),singleton(X5)),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_8720]) ).
tcf(c_8792,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X3,X1),singleton(X5)),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_8720]) ).
tcf(c_8794,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X1 )
| ( sK2(singleton(X3),X4,X1) = X3 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK1(singleton(X3),X4,X1)),unordered_pair(sK1(singleton(X3),X4,X1),X2))))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_8720]) ).
tcf(c_8795,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X3) = singleton(X4) )
| ( sK1(X1,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK2(X1,X3,singleton(X4))),unordered_pair(sK2(X1,X3,singleton(X4)),X2))))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_8720]) ).
tcf(c_8796,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X1 )
| ( sK3(X3,singleton(X4),X1) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK1(X3,singleton(X4),X1)),unordered_pair(sK1(X3,singleton(X4),X1),X2))))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_8720]) ).
tcf(c_8797,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X1) = singleton(X4) )
| ( sK1(X3,X1,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK3(X3,X1,singleton(X4))),unordered_pair(sK3(X3,X1,singleton(X4)),X2))))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_8720]) ).
tcf(c_8798,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_8720]) ).
tcf(c_8799,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X1,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_8720]) ).
tcf(c_8800,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_8720]) ).
tcf(c_8801,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X1,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_8720]) ).
tcf(c_8802,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_8720]) ).
tcf(c_8803,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_8720]) ).
tcf(c_8804,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_8720]) ).
tcf(c_8805,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_8720]) ).
tcf(c_8888,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X2,X3) )
| ( sK5(X1,singleton(X4),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X4),X5,sK1(X2,X3,cartesian_product2(singleton(X4),X5)))))) = X4 )
| ( unordered_pair(unordered_pair(sK2(X2,X3,cartesian_product2(singleton(X4),X5)),sK3(X2,X3,cartesian_product2(singleton(X4),X5))),singleton(sK2(X2,X3,cartesian_product2(singleton(X4),X5)))) = sK1(X2,X3,cartesian_product2(singleton(X4),X5)) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_1649]) ).
tcf(c_8889,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X5)
| ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X2),X3,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1649]) ).
tcf(c_8890,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X4)
| ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X2),X3,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1649]) ).
tcf(c_8891,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X2),X3,sK2(cartesian_product2(singleton(X2),X3),X4,X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1649]) ).
tcf(c_8892,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X2),X3,sK3(X4,cartesian_product2(singleton(X2),X3),X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1649]) ).
tcf(c_8893,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X1),unordered_pair(singleton(X4),unordered_pair(X4,sK4(singleton(X1),X2,sK4(cartesian_product2(singleton(X1),X2),X3,X0))))) = X1 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(cartesian_product2(singleton(X1),X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_1649]) ).
tcf(c_8894,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X2),unordered_pair(singleton(X4),unordered_pair(X4,sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),X0))))) = X2 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(X1,cartesian_product2(singleton(X2),X3))) ),
inference(superposition,[status(thm)],[c_61,c_1649]) ).
tcf(c_8895,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X1),unordered_pair(singleton(X4),unordered_pair(X4,sK4(singleton(X1),X3,unordered_pair(unordered_pair(X0,X2),singleton(X0)))))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_64,c_1649]) ).
tcf(c_8897,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X1),unordered_pair(singleton(X4),unordered_pair(X4,sK4(singleton(X1),X3,unordered_pair(unordered_pair(X2,X0),singleton(X0)))))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_809,c_1649]) ).
tcf(c_8898,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X1),unordered_pair(singleton(X4),unordered_pair(X4,sK4(singleton(X1),X3,unordered_pair(singleton(X0),unordered_pair(X2,X0)))))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_882,c_1649]) ).
tcf(c_8900,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X1),unordered_pair(singleton(X4),unordered_pair(X4,sK4(singleton(X1),X3,unordered_pair(singleton(X0),unordered_pair(X0,X2)))))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_900,c_1649]) ).
tcf(c_8901,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(singleton(X4),X5) )
| ( sK2(singleton(X4),X5,cartesian_product2(singleton(X2),X3)) = X4 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X2),X3,sK1(singleton(X4),X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_1649]) ).
tcf(c_8902,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = singleton(X5) )
| ( sK1(cartesian_product2(singleton(X2),X3),X4,singleton(X5)) = X5 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X2),X3,sK2(cartesian_product2(singleton(X2),X3),X4,singleton(X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_1649]) ).
tcf(c_8903,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,singleton(X5)) )
| ( sK3(X4,singleton(X5),cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X2),X3,sK1(X4,singleton(X5),cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_1649]) ).
tcf(c_8904,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(singleton(X2),X3),singleton(X5)) = X5 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X2),X3,sK3(X4,cartesian_product2(singleton(X2),X3),singleton(X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_1649]) ).
tcf(c_8905,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(singleton(X2),X3),X5)))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X2),X3,sK3(X4,cartesian_product2(singleton(X2),X3),X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_1649]) ).
tcf(c_8906,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(singleton(X2),X3),X5)),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X2),X3,sK3(X4,cartesian_product2(singleton(X2),X3),X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_1649]) ).
tcf(c_8907,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(singleton(X2),X3),X4,X5)))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X2),X3,sK2(cartesian_product2(singleton(X2),X3),X4,X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_1649]) ).
tcf(c_8908,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(singleton(X2),X3),X4,X5)),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X2),X3,sK2(cartesian_product2(singleton(X2),X3),X4,X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_1649]) ).
tcf(c_8909,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(singleton(X2),X3))))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X2),X3,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_1649]) ).
tcf(c_8910,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X2),X3,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_1649]) ).
tcf(c_8911,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(singleton(X2),X3))))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X2),X3,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_1649]) ).
tcf(c_8912,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X2),X3,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_1649]) ).
tcf(c_9030,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = cartesian_product2(X2,X3) )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X4,singleton(X5),sK1(X2,X3,cartesian_product2(X4,singleton(X5))))))) = X5 )
| ( unordered_pair(unordered_pair(sK2(X2,X3,cartesian_product2(X4,singleton(X5))),sK3(X2,X3,cartesian_product2(X4,singleton(X5)))),singleton(sK2(X2,X3,cartesian_product2(X4,singleton(X5))))) = sK1(X2,X3,cartesian_product2(X4,singleton(X5))) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_1650]) ).
tcf(c_9031,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X3,singleton(X2))),X5)
| ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,X5) )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X3,singleton(X2),sK1(X4,X5,cartesian_product2(X3,singleton(X2))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1650]) ).
tcf(c_9032,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X3,singleton(X2))),X4)
| ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,X5) )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X3,singleton(X2),sK1(X4,X5,cartesian_product2(X3,singleton(X2))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1650]) ).
tcf(c_9033,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X3,singleton(X2)),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X3,singleton(X2)),X4) = X5 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X3,singleton(X2),sK2(cartesian_product2(X3,singleton(X2)),X4,X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1650]) ).
tcf(c_9034,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X3,singleton(X2)),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X3,singleton(X2))) = X5 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X3,singleton(X2),sK3(X4,cartesian_product2(X3,singleton(X2)),X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1650]) ).
tcf(c_9035,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X2),unordered_pair(singleton(X4),unordered_pair(X4,sK5(X1,singleton(X2),sK4(cartesian_product2(X1,singleton(X2)),X3,X0))))) = X2 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(cartesian_product2(X1,singleton(X2)),X3)) ),
inference(superposition,[status(thm)],[c_60,c_1650]) ).
tcf(c_9036,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X3),unordered_pair(singleton(X4),unordered_pair(X4,sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),X0))))) = X3 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,singleton(X3)))) ),
inference(superposition,[status(thm)],[c_61,c_1650]) ).
tcf(c_9037,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X1),unordered_pair(singleton(X4),unordered_pair(X4,sK5(X3,singleton(X1),unordered_pair(unordered_pair(X2,X0),singleton(X2)))))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_64,c_1650]) ).
tcf(c_9039,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X1),unordered_pair(singleton(X4),unordered_pair(X4,sK5(X3,singleton(X1),unordered_pair(unordered_pair(X0,X2),singleton(X2)))))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_809,c_1650]) ).
tcf(c_9040,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X1),unordered_pair(singleton(X4),unordered_pair(X4,sK5(X3,singleton(X1),unordered_pair(singleton(X2),unordered_pair(X0,X2)))))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_882,c_1650]) ).
tcf(c_9042,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X1),unordered_pair(singleton(X4),unordered_pair(X4,sK5(X3,singleton(X1),unordered_pair(singleton(X2),unordered_pair(X2,X0)))))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_900,c_1650]) ).
tcf(c_9043,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X3,singleton(X2)) )
| ( sK2(singleton(X4),X5,cartesian_product2(X3,singleton(X2))) = X4 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X3,singleton(X2),sK1(singleton(X4),X5,cartesian_product2(X3,singleton(X2))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_1650]) ).
tcf(c_9044,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X3,singleton(X2)),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X3,singleton(X2)),X4,singleton(X5)) = X5 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X3,singleton(X2),sK2(cartesian_product2(X3,singleton(X2)),X4,singleton(X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_1650]) ).
tcf(c_9045,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,singleton(X5)) )
| ( sK3(X4,singleton(X5),cartesian_product2(X3,singleton(X2))) = X5 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X3,singleton(X2),sK1(X4,singleton(X5),cartesian_product2(X3,singleton(X2))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_1650]) ).
tcf(c_9046,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,singleton(X2))) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X3,singleton(X2)),singleton(X5)) = X5 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X3,singleton(X2),sK3(X4,cartesian_product2(X3,singleton(X2)),singleton(X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_1650]) ).
tcf(c_9047,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,singleton(X2))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X3,singleton(X2)),X5)))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X3,singleton(X2),sK3(X4,cartesian_product2(X3,singleton(X2)),X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_1650]) ).
tcf(c_9048,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,singleton(X2))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X3,singleton(X2)),X5)),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X3,singleton(X2),sK3(X4,cartesian_product2(X3,singleton(X2)),X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_1650]) ).
tcf(c_9049,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,singleton(X2)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X3,singleton(X2)),X4,X5)))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X3,singleton(X2),sK2(cartesian_product2(X3,singleton(X2)),X4,X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_1650]) ).
tcf(c_9050,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,singleton(X2)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X3,singleton(X2)),X4,X5)),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X3,singleton(X2),sK2(cartesian_product2(X3,singleton(X2)),X4,X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_1650]) ).
tcf(c_9051,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,singleton(X2)))))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X3,singleton(X2),sK1(X4,X5,cartesian_product2(X3,singleton(X2))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_1650]) ).
tcf(c_9052,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,singleton(X2)))),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X3,singleton(X2),sK1(X4,X5,cartesian_product2(X3,singleton(X2))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_1650]) ).
tcf(c_9053,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,singleton(X2)))))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X3,singleton(X2),sK1(X4,X5,cartesian_product2(X3,singleton(X2))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_1650]) ).
tcf(c_9054,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,singleton(X2)))),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X3,singleton(X2),sK1(X4,X5,cartesian_product2(X3,singleton(X2))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_1650]) ).
tcf(c_9262,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,singleton(X3))
| ( cartesian_product2(X2,singleton(X3)) = singleton(X1) )
| ( sK1(X2,singleton(X3),singleton(X1)) = X1 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK1(X2,singleton(X3),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1032,c_1852]) ).
tcf(c_9263,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_8720]) ).
tcf(c_9264,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_1575]) ).
tcf(c_9265,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_8554]) ).
tcf(c_9266,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_1574]) ).
tcf(c_9267,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_8285]) ).
tcf(c_9268,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_1573]) ).
tcf(c_9269,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_8027]) ).
tcf(c_9270,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_1572]) ).
tcf(c_9271,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_7766]) ).
tcf(c_9272,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_1571]) ).
tcf(c_9273,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_7495]) ).
tcf(c_9274,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_1570]) ).
tcf(c_9275,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_6164]) ).
tcf(c_9276,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_1156]) ).
tcf(c_9277,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_5987]) ).
tcf(c_9278,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_1155]) ).
tcf(c_9279,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_5758]) ).
tcf(c_9280,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_1154]) ).
tcf(c_9281,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_5518]) ).
tcf(c_9282,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_1153]) ).
tcf(c_9283,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_5291]) ).
tcf(c_9284,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_1152]) ).
tcf(c_9285,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_4798]) ).
tcf(c_9286,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_1151]) ).
tcf(c_9287,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X0) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(sK1(X2,X0,X3),X4),singleton(X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK3(X2,X0,X3)),unordered_pair(X1,sK3(X2,X0,X3)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1852,c_2539]) ).
tcf(c_9288,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X1 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(sK3(X2,X3,X1),X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK1(X2,X3,X1),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_2384]) ).
tcf(c_9289,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X0) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(sK1(X2,X0,X3),X4),singleton(X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK3(X2,X0,X3)),singleton(sK3(X2,X0,X3)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1852,c_1929]) ).
tcf(c_9290,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X1 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(sK3(X2,X3,X1),X4),singleton(X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK1(X2,X3,X1),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_1823]) ).
tcf(c_9291,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X0) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(sK1(X2,X0,X3),X4),singleton(X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK3(X2,X0,X3)),unordered_pair(sK3(X2,X0,X3),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1852,c_1643]) ).
tcf(c_9292,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X1 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(X4,sK3(X2,X3,X1)))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK1(X2,X3,X1),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_1524]) ).
tcf(c_9293,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X0) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(sK1(X2,X0,X3),X4),singleton(X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK3(X2,X0,X3),X1),singleton(sK3(X2,X0,X3)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1852,c_1306]) ).
tcf(c_9294,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X1 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(X4,sK3(X2,X3,X1)),singleton(X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK1(X2,X3,X1),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_1060]) ).
tcf(c_9295,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(sK3(X4,singleton(X5),X3),X0))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK1(X4,singleton(X5),X3),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_907]) ).
tcf(c_9296,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,singleton(X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,singleton(X2),X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK3(X3,singleton(X2),X4)),unordered_pair(X0,sK3(X3,singleton(X2),X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_906]) ).
tcf(c_9297,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(sK3(X4,singleton(X5),X3),X0),singleton(X0))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK1(X4,singleton(X5),X3),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_899]) ).
tcf(c_9298,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,singleton(X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,singleton(X2),X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X0,sK3(X3,singleton(X2),X4)),singleton(sK3(X3,singleton(X2),X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_898]) ).
tcf(c_9299,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,singleton(X5),X3)))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK1(X4,singleton(X5),X3),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_889]) ).
tcf(c_9300,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,singleton(X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,singleton(X2),X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK3(X3,singleton(X2),X4)),unordered_pair(sK3(X3,singleton(X2),X4),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_888]) ).
tcf(c_9301,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(X0,sK3(X4,singleton(X5),X3)),singleton(X0))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK1(X4,singleton(X5),X3),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_863]) ).
tcf(c_9302,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,singleton(X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,singleton(X2),X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK3(X3,singleton(X2),X4),X0),singleton(sK3(X3,singleton(X2),X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_837]) ).
tcf(c_9304,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X0)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,cartesian_product2(X2,X0),X4),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))),unordered_pair(X1,sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1852,c_2611]) ).
tcf(c_9305,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X0,X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,cartesian_product2(X0,X2),X4),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))),unordered_pair(X1,sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1852,c_2610]) ).
tcf(c_9306,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X0)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,cartesian_product2(X2,X0),X4),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))),singleton(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1852,c_2036]) ).
tcf(c_9307,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X0,X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,cartesian_product2(X0,X2),X4),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))),singleton(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1852,c_2035]) ).
tcf(c_9308,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X0)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,cartesian_product2(X2,X0),X4),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))),unordered_pair(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4)),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1852,c_1703]) ).
tcf(c_9309,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X0,X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,cartesian_product2(X0,X2),X4),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))),unordered_pair(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4)),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1852,c_1702]) ).
tcf(c_9310,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X0)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,cartesian_product2(X2,X0),X4),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4)),X1),singleton(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1852,c_1389]) ).
tcf(c_9311,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X0,X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,cartesian_product2(X0,X2),X4),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4)),X1),singleton(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1852,c_1388]) ).
tcf(c_9312,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,cartesian_product2(X2,X1),X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK3(X3,cartesian_product2(X2,X1),X4)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_2459]) ).
tcf(c_9313,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,cartesian_product2(X1,X2),X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK3(X3,cartesian_product2(X1,X2),X4)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_2458]) ).
tcf(c_9314,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,cartesian_product2(X2,X1),X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK3(X3,cartesian_product2(X2,X1),X4)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_1857]) ).
tcf(c_9315,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,cartesian_product2(X1,X2),X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK3(X3,cartesian_product2(X1,X2),X4)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_1856]) ).
tcf(c_9316,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,cartesian_product2(X2,X1),X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK3(X3,cartesian_product2(X2,X1),X4))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_1569]) ).
tcf(c_9317,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,cartesian_product2(X1,X2),X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK3(X3,cartesian_product2(X1,X2),X4))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_1568]) ).
tcf(c_9318,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,cartesian_product2(X2,X1),X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK3(X3,cartesian_product2(X2,X1),X4))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_1150]) ).
tcf(c_9319,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,cartesian_product2(X1,X2),X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK3(X3,cartesian_product2(X1,X2),X4))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_1149]) ).
tcf(c_9320,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,cartesian_product2(X0,X1)) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(sK1(X2,cartesian_product2(X0,X1),X3),X4),singleton(X4))) = X4 )
| ( unordered_pair(unordered_pair(sK4(X0,X1,sK3(X2,cartesian_product2(X0,X1),X3)),sK5(X0,X1,sK3(X2,cartesian_product2(X0,X1),X3))),singleton(sK4(X0,X1,sK3(X2,cartesian_product2(X0,X1),X3)))) = sK3(X2,cartesian_product2(X0,X1),X3) ) ),
inference(superposition,[status(thm)],[c_1852,c_62]) ).
tcf(c_9321,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X6),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X2),X3,sK3(X4,cartesian_product2(singleton(X2),X3),X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_1649]) ).
tcf(c_9322,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X6),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK4(singleton(X2),X3,sK3(X4,cartesian_product2(singleton(X2),X3),X5))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_1312]) ).
tcf(c_9323,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,cartesian_product2(singleton(X3),X4)) = X1 )
| ( sK4(singleton(X3),X4,sK3(X2,cartesian_product2(singleton(X3),X4),X1)) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK1(X2,cartesian_product2(singleton(X3),X4),X1),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_787]) ).
tcf(c_9324,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,singleton(X2))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,singleton(X2)),X5),X6),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X3,singleton(X2),sK3(X4,cartesian_product2(X3,singleton(X2)),X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_1650]) ).
tcf(c_9325,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,singleton(X2))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,singleton(X2)),X5),X6),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK5(X3,singleton(X2),sK3(X4,cartesian_product2(X3,singleton(X2)),X5))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_1313]) ).
tcf(c_9326,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,cartesian_product2(X3,singleton(X4))) = X1 )
| ( sK5(X3,singleton(X4),sK3(X2,cartesian_product2(X3,singleton(X4)),X1)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK1(X2,cartesian_product2(X3,singleton(X4)),X1),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_789]) ).
tcf(c_9327,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(cartesian_product2(singleton(X0),X1),X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,cartesian_product2(cartesian_product2(singleton(X0),X1),X2),X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,sK4(cartesian_product2(singleton(X0),X1),X2,sK3(X3,cartesian_product2(cartesian_product2(singleton(X0),X1),X2),X4))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_835]) ).
tcf(c_9328,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,cartesian_product2(singleton(X0),X1))) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,cartesian_product2(X2,cartesian_product2(singleton(X0),X1)),X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,sK5(X2,cartesian_product2(singleton(X0),X1),sK3(X3,cartesian_product2(X2,cartesian_product2(singleton(X0),X1)),X4))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_836]) ).
tcf(c_9329,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(cartesian_product2(X0,singleton(X1)),X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,cartesian_product2(cartesian_product2(X0,singleton(X1)),X2),X4),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),sK4(cartesian_product2(X0,singleton(X1)),X2,sK3(X3,cartesian_product2(cartesian_product2(X0,singleton(X1)),X2),X4))) = X1 ) ),
inference(superposition,[status(thm)],[c_1852,c_861]) ).
tcf(c_9330,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,cartesian_product2(X0,singleton(X1)))) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,cartesian_product2(X2,cartesian_product2(X0,singleton(X1))),X4),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),sK5(X2,cartesian_product2(X0,singleton(X1)),sK3(X3,cartesian_product2(X2,cartesian_product2(X0,singleton(X1))),X4))) = X1 ) ),
inference(superposition,[status(thm)],[c_1852,c_862]) ).
tcf(c_9532,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X2,singleton(X2))
| ( cartesian_product2(singleton(X2),X3) = singleton(X1) )
| ( sK1(singleton(X2),X3,singleton(X1)) = X1 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK1(singleton(X2),X3,singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1009,c_1853]) ).
tcf(c_9533,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_8720]) ).
tcf(c_9534,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_1575]) ).
tcf(c_9535,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_8554]) ).
tcf(c_9536,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_1574]) ).
tcf(c_9537,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_8285]) ).
tcf(c_9538,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_1573]) ).
tcf(c_9539,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_8027]) ).
tcf(c_9540,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_1572]) ).
tcf(c_9541,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_7766]) ).
tcf(c_9542,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_1571]) ).
tcf(c_9543,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_7495]) ).
tcf(c_9544,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_1570]) ).
tcf(c_9545,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_6164]) ).
tcf(c_9546,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_1156]) ).
tcf(c_9547,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_5987]) ).
tcf(c_9548,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_1155]) ).
tcf(c_9549,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_5758]) ).
tcf(c_9550,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_1154]) ).
tcf(c_9551,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_5518]) ).
tcf(c_9552,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_1153]) ).
tcf(c_9553,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_5291]) ).
tcf(c_9554,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_1152]) ).
tcf(c_9555,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_4798]) ).
tcf(c_9556,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_1151]) ).
tcf(c_9557,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X2) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(sK1(X0,X2,X3),X4),singleton(X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK2(X0,X2,X3)),unordered_pair(X1,sK2(X0,X2,X3)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1853,c_2539]) ).
tcf(c_9558,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X1 )
| ( sK4(singleton(X4),X2,unordered_pair(singleton(X4),unordered_pair(sK2(X2,X3,X1),X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK1(X2,X3,X1),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_2384]) ).
tcf(c_9559,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X2) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(sK1(X0,X2,X3),X4),singleton(X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK2(X0,X2,X3)),singleton(sK2(X0,X2,X3)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1853,c_1929]) ).
tcf(c_9560,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X1 )
| ( sK4(singleton(X4),X2,unordered_pair(unordered_pair(sK2(X2,X3,X1),X4),singleton(X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK1(X2,X3,X1),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_1823]) ).
tcf(c_9561,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X2) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(sK1(X0,X2,X3),X4),singleton(X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK2(X0,X2,X3)),unordered_pair(sK2(X0,X2,X3),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1853,c_1643]) ).
tcf(c_9562,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X1 )
| ( sK4(singleton(X4),X2,unordered_pair(singleton(X4),unordered_pair(X4,sK2(X2,X3,X1)))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK1(X2,X3,X1),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_1524]) ).
tcf(c_9563,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X2) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(sK1(X0,X2,X3),X4),singleton(X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK2(X0,X2,X3),X1),singleton(sK2(X0,X2,X3)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1853,c_1306]) ).
tcf(c_9564,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X1 )
| ( sK4(singleton(X4),X2,unordered_pair(unordered_pair(X4,sK2(X2,X3,X1)),singleton(X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK1(X2,X3,X1),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_1060]) ).
tcf(c_9565,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK5(X1,singleton(X4),unordered_pair(singleton(X0),unordered_pair(sK2(singleton(X4),X5,X3),X0))) = X4 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK1(singleton(X4),X5,X3),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_907]) ).
tcf(c_9566,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(singleton(X2),X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK2(singleton(X2),X3,X4)),unordered_pair(X0,sK2(singleton(X2),X3,X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_906]) ).
tcf(c_9567,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK5(X1,singleton(X4),unordered_pair(unordered_pair(sK2(singleton(X4),X5,X3),X0),singleton(X0))) = X4 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK1(singleton(X4),X5,X3),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_899]) ).
tcf(c_9568,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(singleton(X2),X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X0,sK2(singleton(X2),X3,X4)),singleton(sK2(singleton(X2),X3,X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_898]) ).
tcf(c_9569,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK5(X1,singleton(X4),unordered_pair(singleton(X0),unordered_pair(X0,sK2(singleton(X4),X5,X3)))) = X4 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK1(singleton(X4),X5,X3),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_889]) ).
tcf(c_9570,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(singleton(X2),X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK2(singleton(X2),X3,X4)),unordered_pair(sK2(singleton(X2),X3,X4),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_888]) ).
tcf(c_9571,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK5(X1,singleton(X4),unordered_pair(unordered_pair(X0,sK2(singleton(X4),X5,X3)),singleton(X0))) = X4 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK1(singleton(X4),X5,X3),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_863]) ).
tcf(c_9572,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(singleton(X2),X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK2(singleton(X2),X3,X4),X0),singleton(sK2(singleton(X2),X3,X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_837]) ).
tcf(c_9574,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X0),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X0),X3,X4),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))),unordered_pair(X1,sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1853,c_2611]) ).
tcf(c_9575,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X0,X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(cartesian_product2(X0,X2),X3,X4),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))),unordered_pair(X1,sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1853,c_2610]) ).
tcf(c_9576,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X0),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X0),X3,X4),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))),singleton(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1853,c_2036]) ).
tcf(c_9577,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X0,X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(cartesian_product2(X0,X2),X3,X4),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))),singleton(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1853,c_2035]) ).
tcf(c_9578,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X0),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X0),X3,X4),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))),unordered_pair(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4)),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1853,c_1703]) ).
tcf(c_9579,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X0,X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(cartesian_product2(X0,X2),X3,X4),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))),unordered_pair(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4)),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1853,c_1702]) ).
tcf(c_9580,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X0),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X0),X3,X4),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4)),X1),singleton(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1853,c_1389]) ).
tcf(c_9581,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X0,X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(cartesian_product2(X0,X2),X3,X4),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4)),X1),singleton(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1853,c_1388]) ).
tcf(c_9582,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X1),X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK2(cartesian_product2(X2,X1),X3,X4)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_2459]) ).
tcf(c_9583,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(cartesian_product2(X1,X2),X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK2(cartesian_product2(X1,X2),X3,X4)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_2458]) ).
tcf(c_9584,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X1),X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK2(cartesian_product2(X2,X1),X3,X4)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_1857]) ).
tcf(c_9585,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(cartesian_product2(X1,X2),X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK2(cartesian_product2(X1,X2),X3,X4)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_1856]) ).
tcf(c_9586,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X1),X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK2(cartesian_product2(X2,X1),X3,X4))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_1569]) ).
tcf(c_9587,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(cartesian_product2(X1,X2),X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK2(cartesian_product2(X1,X2),X3,X4))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_1568]) ).
tcf(c_9588,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X1),X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK2(cartesian_product2(X2,X1),X3,X4))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_1150]) ).
tcf(c_9589,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(cartesian_product2(X1,X2),X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK2(cartesian_product2(X1,X2),X3,X4))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_1149]) ).
tcf(c_9590,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(X0,X1),X2) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(sK1(cartesian_product2(X0,X1),X2,X3),X4),singleton(X4))) = X4 )
| ( unordered_pair(unordered_pair(sK4(X0,X1,sK2(cartesian_product2(X0,X1),X2,X3)),sK5(X0,X1,sK2(cartesian_product2(X0,X1),X2,X3))),singleton(sK4(X0,X1,sK2(cartesian_product2(X0,X1),X2,X3)))) = sK2(cartesian_product2(X0,X1),X2,X3) ) ),
inference(superposition,[status(thm)],[c_1853,c_62]) ).
tcf(c_9591,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X6),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X2),X3,sK2(cartesian_product2(singleton(X2),X3),X4,X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_1649]) ).
tcf(c_9592,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X6),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK4(singleton(X2),X3,sK2(cartesian_product2(singleton(X2),X3),X4,X5))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_1312]) ).
tcf(c_9593,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X1 )
| ( sK4(singleton(X2),X3,sK2(cartesian_product2(singleton(X2),X3),X4,X1)) = X2 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X1),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_787]) ).
tcf(c_9594,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,singleton(X2)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X3,singleton(X2)),X4,X5),X6),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X3,singleton(X2),sK2(cartesian_product2(X3,singleton(X2)),X4,X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_1650]) ).
tcf(c_9595,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,singleton(X2)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X3,singleton(X2)),X4,X5),X6),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK5(X3,singleton(X2),sK2(cartesian_product2(X3,singleton(X2)),X4,X5))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_1313]) ).
tcf(c_9596,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X1 )
| ( sK5(X2,singleton(X3),sK2(cartesian_product2(X2,singleton(X3)),X4,X1)) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK1(cartesian_product2(X2,singleton(X3)),X4,X1),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_789]) ).
tcf(c_9597,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(singleton(X0),X1),X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(cartesian_product2(cartesian_product2(singleton(X0),X1),X2),X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,sK4(cartesian_product2(singleton(X0),X1),X2,sK2(cartesian_product2(cartesian_product2(singleton(X0),X1),X2),X3,X4))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_835]) ).
tcf(c_9598,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,cartesian_product2(singleton(X0),X1)),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(cartesian_product2(X2,cartesian_product2(singleton(X0),X1)),X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,sK5(X2,cartesian_product2(singleton(X0),X1),sK2(cartesian_product2(X2,cartesian_product2(singleton(X0),X1)),X3,X4))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_836]) ).
tcf(c_9599,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X0,singleton(X1)),X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(cartesian_product2(cartesian_product2(X0,singleton(X1)),X2),X3,X4),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),sK4(cartesian_product2(X0,singleton(X1)),X2,sK2(cartesian_product2(cartesian_product2(X0,singleton(X1)),X2),X3,X4))) = X1 ) ),
inference(superposition,[status(thm)],[c_1853,c_861]) ).
tcf(c_9600,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,cartesian_product2(X0,singleton(X1))),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(cartesian_product2(X2,cartesian_product2(X0,singleton(X1))),X3,X4),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),sK5(X2,cartesian_product2(X0,singleton(X1)),sK2(cartesian_product2(X2,cartesian_product2(X0,singleton(X1))),X3,X4))) = X1 ) ),
inference(superposition,[status(thm)],[c_1853,c_862]) ).
tcf(c_9809,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_8720]) ).
tcf(c_9810,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_1575]) ).
tcf(c_9811,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_8554]) ).
tcf(c_9812,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_1574]) ).
tcf(c_9813,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_8285]) ).
tcf(c_9814,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_1573]) ).
tcf(c_9815,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_8027]) ).
tcf(c_9816,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_1572]) ).
tcf(c_9817,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_7766]) ).
tcf(c_9818,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_1571]) ).
tcf(c_9819,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_7495]) ).
tcf(c_9820,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_1570]) ).
tcf(c_9821,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_6164]) ).
tcf(c_9822,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_1156]) ).
tcf(c_9823,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_5987]) ).
tcf(c_9824,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_1155]) ).
tcf(c_9825,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_5758]) ).
tcf(c_9826,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_1154]) ).
tcf(c_9827,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_5518]) ).
tcf(c_9828,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_1153]) ).
tcf(c_9829,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_5291]) ).
tcf(c_9830,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_1152]) ).
tcf(c_9831,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_4798]) ).
tcf(c_9832,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_1151]) ).
tcf(c_9833,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK4(singleton(X4),X2,unordered_pair(unordered_pair(sK2(X2,X3,X0),X4),singleton(X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,X3,X0)),unordered_pair(X1,sK1(X2,X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1854,c_2539]) ).
tcf(c_9834,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X2) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(sK1(X1,X2,X3),X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK2(X1,X2,X3),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_2384]) ).
tcf(c_9835,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK4(singleton(X4),X2,unordered_pair(unordered_pair(sK2(X2,X3,X0),X4),singleton(X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK1(X2,X3,X0)),singleton(sK1(X2,X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1854,c_1929]) ).
tcf(c_9836,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X2) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(sK1(X1,X2,X3),X4),singleton(X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK2(X1,X2,X3),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_1823]) ).
tcf(c_9837,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK4(singleton(X4),X2,unordered_pair(unordered_pair(sK2(X2,X3,X0),X4),singleton(X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,X3,X0)),unordered_pair(sK1(X2,X3,X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1854,c_1643]) ).
tcf(c_9838,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X2) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(X4,sK1(X1,X2,X3)))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK2(X1,X2,X3),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_1524]) ).
tcf(c_9839,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK4(singleton(X4),X2,unordered_pair(unordered_pair(sK2(X2,X3,X0),X4),singleton(X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(X2,X3,X0),X1),singleton(sK1(X2,X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1854,c_1306]) ).
tcf(c_9840,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X2) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(X4,sK1(X1,X2,X3)),singleton(X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK2(X1,X2,X3),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_1060]) ).
tcf(c_9841,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(sK1(X3,X4,singleton(X5)),X0))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK2(X3,X4,singleton(X5)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_907]) ).
tcf(c_9842,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,singleton(X2)),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK1(X3,X4,singleton(X2))),unordered_pair(X0,sK1(X3,X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_906]) ).
tcf(c_9843,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X4,singleton(X5)),X0),singleton(X0))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK2(X3,X4,singleton(X5)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_899]) ).
tcf(c_9844,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,singleton(X2)),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X0,sK1(X3,X4,singleton(X2))),singleton(sK1(X3,X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_898]) ).
tcf(c_9845,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X3,X4,singleton(X5))))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK2(X3,X4,singleton(X5)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_889]) ).
tcf(c_9846,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,singleton(X2)),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK1(X3,X4,singleton(X2))),unordered_pair(sK1(X3,X4,singleton(X2)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_888]) ).
tcf(c_9847,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(X0,sK1(X3,X4,singleton(X5))),singleton(X0))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK2(X3,X4,singleton(X5)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_863]) ).
tcf(c_9848,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,singleton(X2)),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,singleton(X2)),X0),singleton(sK1(X3,X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_837]) ).
tcf(c_9850,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,cartesian_product2(X2,X0)),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))),unordered_pair(X1,sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1854,c_2611]) ).
tcf(c_9851,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,cartesian_product2(X0,X2)),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))),unordered_pair(X1,sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1854,c_2610]) ).
tcf(c_9852,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,cartesian_product2(X2,X0)),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))),singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1854,c_2036]) ).
tcf(c_9853,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,cartesian_product2(X0,X2)),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))),singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1854,c_2035]) ).
tcf(c_9854,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,cartesian_product2(X2,X0)),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))),unordered_pair(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0))),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1854,c_1703]) ).
tcf(c_9855,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,cartesian_product2(X0,X2)),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))),unordered_pair(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2))),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1854,c_1702]) ).
tcf(c_9856,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,cartesian_product2(X2,X0)),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0))),X1),singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1854,c_1389]) ).
tcf(c_9857,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,cartesian_product2(X0,X2)),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2))),X1),singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1854,c_1388]) ).
tcf(c_9858,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X1) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,cartesian_product2(X2,X1)),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK1(X3,X4,cartesian_product2(X2,X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_2459]) ).
tcf(c_9859,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,cartesian_product2(X1,X2)),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK1(X3,X4,cartesian_product2(X1,X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_2458]) ).
tcf(c_9860,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X1) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,cartesian_product2(X2,X1)),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK1(X3,X4,cartesian_product2(X2,X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_1857]) ).
tcf(c_9861,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,cartesian_product2(X1,X2)),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK1(X3,X4,cartesian_product2(X1,X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_1856]) ).
tcf(c_9862,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X1) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,cartesian_product2(X2,X1)),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK1(X3,X4,cartesian_product2(X2,X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_1569]) ).
tcf(c_9863,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,cartesian_product2(X1,X2)),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK1(X3,X4,cartesian_product2(X1,X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_1568]) ).
tcf(c_9864,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X1) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,cartesian_product2(X2,X1)),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK1(X3,X4,cartesian_product2(X2,X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_1150]) ).
tcf(c_9865,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,cartesian_product2(X1,X2)),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK1(X3,X4,cartesian_product2(X1,X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_1149]) ).
tcf(c_9866,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( sK4(singleton(X4),X2,unordered_pair(unordered_pair(sK2(X2,X3,cartesian_product2(X0,X1)),X4),singleton(X4))) = X4 )
| ( unordered_pair(unordered_pair(sK4(X0,X1,sK1(X2,X3,cartesian_product2(X0,X1))),sK5(X0,X1,sK1(X2,X3,cartesian_product2(X0,X1)))),singleton(sK4(X0,X1,sK1(X2,X3,cartesian_product2(X0,X1))))) = sK1(X2,X3,cartesian_product2(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_1854,c_62]) ).
tcf(c_9867,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X6),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X2),X3,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_1649]) ).
tcf(c_9868,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X6),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK4(singleton(X2),X3,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_1312]) ).
tcf(c_9869,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = cartesian_product2(X1,X2) )
| ( sK4(singleton(X3),X4,sK1(X1,X2,cartesian_product2(singleton(X3),X4))) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK2(X1,X2,cartesian_product2(singleton(X3),X4)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_787]) ).
tcf(c_9870,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,singleton(X2))),X6),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X3,singleton(X2),sK1(X4,X5,cartesian_product2(X3,singleton(X2))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_1650]) ).
tcf(c_9871,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,singleton(X2))),X6),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK5(X3,singleton(X2),sK1(X4,X5,cartesian_product2(X3,singleton(X2))))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_1313]) ).
tcf(c_9872,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = cartesian_product2(X1,X2) )
| ( sK5(X3,singleton(X4),sK1(X1,X2,cartesian_product2(X3,singleton(X4)))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK2(X1,X2,cartesian_product2(X3,singleton(X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_789]) ).
tcf(c_9873,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X0),X1),X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,cartesian_product2(cartesian_product2(singleton(X0),X1),X2)),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,sK4(cartesian_product2(singleton(X0),X1),X2,sK1(X3,X4,cartesian_product2(cartesian_product2(singleton(X0),X1),X2)))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_835]) ).
tcf(c_9874,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(singleton(X0),X1)) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,cartesian_product2(X2,cartesian_product2(singleton(X0),X1))),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,sK5(X2,cartesian_product2(singleton(X0),X1),sK1(X3,X4,cartesian_product2(X2,cartesian_product2(singleton(X0),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_836]) ).
tcf(c_9875,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X0,singleton(X1)),X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,cartesian_product2(cartesian_product2(X0,singleton(X1)),X2)),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),sK4(cartesian_product2(X0,singleton(X1)),X2,sK1(X3,X4,cartesian_product2(cartesian_product2(X0,singleton(X1)),X2)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1854,c_861]) ).
tcf(c_9876,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(X0,singleton(X1))) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,cartesian_product2(X2,cartesian_product2(X0,singleton(X1)))),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),sK5(X2,cartesian_product2(X0,singleton(X1)),sK1(X3,X4,cartesian_product2(X2,cartesian_product2(X0,singleton(X1)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1854,c_862]) ).
tcf(c_10052,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_8720]) ).
tcf(c_10053,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_1575]) ).
tcf(c_10054,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_8554]) ).
tcf(c_10055,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_1574]) ).
tcf(c_10056,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_8285]) ).
tcf(c_10057,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_1573]) ).
tcf(c_10058,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_8027]) ).
tcf(c_10059,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_1572]) ).
tcf(c_10060,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_7766]) ).
tcf(c_10061,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_1571]) ).
tcf(c_10062,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_7495]) ).
tcf(c_10063,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_1570]) ).
tcf(c_10064,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_6164]) ).
tcf(c_10065,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_1156]) ).
tcf(c_10066,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_5987]) ).
tcf(c_10067,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_1155]) ).
tcf(c_10068,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_5758]) ).
tcf(c_10069,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_1154]) ).
tcf(c_10070,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_5518]) ).
tcf(c_10071,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_1153]) ).
tcf(c_10072,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_5291]) ).
tcf(c_10073,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_1152]) ).
tcf(c_10074,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_4798]) ).
tcf(c_10075,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_1151]) ).
tcf(c_10076,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(sK3(X2,X3,X0),X4),singleton(X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,X3,X0)),unordered_pair(X1,sK1(X2,X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1855,c_2539]) ).
tcf(c_10077,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X1) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(sK1(X2,X1,X3),X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK3(X2,X1,X3),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_2384]) ).
tcf(c_10078,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(sK3(X2,X3,X0),X4),singleton(X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK1(X2,X3,X0)),singleton(sK1(X2,X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1855,c_1929]) ).
tcf(c_10079,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X1) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(sK1(X2,X1,X3),X4),singleton(X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK3(X2,X1,X3),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_1823]) ).
tcf(c_10080,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(sK3(X2,X3,X0),X4),singleton(X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,X3,X0)),unordered_pair(sK1(X2,X3,X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1855,c_1643]) ).
tcf(c_10081,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X1) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(X4,sK1(X2,X1,X3)))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK3(X2,X1,X3),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_1524]) ).
tcf(c_10082,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(sK3(X2,X3,X0),X4),singleton(X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(X2,X3,X0),X1),singleton(sK1(X2,X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1855,c_1306]) ).
tcf(c_10083,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X1) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(X4,sK1(X2,X1,X3)),singleton(X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK3(X2,X1,X3),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_1060]) ).
tcf(c_10084,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(sK1(X4,X3,singleton(X5)),X0))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK3(X4,X3,singleton(X5)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_907]) ).
tcf(c_10085,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,singleton(X2)),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK1(X3,X4,singleton(X2))),unordered_pair(X0,sK1(X3,X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_906]) ).
tcf(c_10086,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(sK1(X4,X3,singleton(X5)),X0),singleton(X0))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK3(X4,X3,singleton(X5)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_899]) ).
tcf(c_10087,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,singleton(X2)),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X0,sK1(X3,X4,singleton(X2))),singleton(sK1(X3,X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_898]) ).
tcf(c_10088,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X3,singleton(X5))))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK3(X4,X3,singleton(X5)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_889]) ).
tcf(c_10089,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,singleton(X2)),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK1(X3,X4,singleton(X2))),unordered_pair(sK1(X3,X4,singleton(X2)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_888]) ).
tcf(c_10090,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(X0,sK1(X4,X3,singleton(X5))),singleton(X0))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK3(X4,X3,singleton(X5)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_863]) ).
tcf(c_10091,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,singleton(X2)),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,singleton(X2)),X0),singleton(sK1(X3,X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_837]) ).
tcf(c_10093,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,cartesian_product2(X2,X0)),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))),unordered_pair(X1,sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1855,c_2611]) ).
tcf(c_10094,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,cartesian_product2(X0,X2)),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))),unordered_pair(X1,sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1855,c_2610]) ).
tcf(c_10095,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,cartesian_product2(X2,X0)),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))),singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1855,c_2036]) ).
tcf(c_10096,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,cartesian_product2(X0,X2)),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))),singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1855,c_2035]) ).
tcf(c_10097,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,cartesian_product2(X2,X0)),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))),unordered_pair(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0))),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1855,c_1703]) ).
tcf(c_10098,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,cartesian_product2(X0,X2)),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))),unordered_pair(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2))),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1855,c_1702]) ).
tcf(c_10099,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,cartesian_product2(X2,X0)),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0))),X1),singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1855,c_1389]) ).
tcf(c_10100,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,cartesian_product2(X0,X2)),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2))),X1),singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1855,c_1388]) ).
tcf(c_10101,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X1) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,cartesian_product2(X2,X1)),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK1(X3,X4,cartesian_product2(X2,X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_2459]) ).
tcf(c_10102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,cartesian_product2(X1,X2)),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK1(X3,X4,cartesian_product2(X1,X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_2458]) ).
tcf(c_10103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X1) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,cartesian_product2(X2,X1)),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK1(X3,X4,cartesian_product2(X2,X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_1857]) ).
tcf(c_10104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,cartesian_product2(X1,X2)),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK1(X3,X4,cartesian_product2(X1,X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_1856]) ).
tcf(c_10105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X1) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,cartesian_product2(X2,X1)),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK1(X3,X4,cartesian_product2(X2,X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_1569]) ).
tcf(c_10106,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,cartesian_product2(X1,X2)),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK1(X3,X4,cartesian_product2(X1,X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_1568]) ).
tcf(c_10107,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X1) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,cartesian_product2(X2,X1)),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK1(X3,X4,cartesian_product2(X2,X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_1150]) ).
tcf(c_10108,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,cartesian_product2(X1,X2)),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK1(X3,X4,cartesian_product2(X1,X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_1149]) ).
tcf(c_10109,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(sK3(X2,X3,cartesian_product2(X0,X1)),X4),singleton(X4))) = X4 )
| ( unordered_pair(unordered_pair(sK4(X0,X1,sK1(X2,X3,cartesian_product2(X0,X1))),sK5(X0,X1,sK1(X2,X3,cartesian_product2(X0,X1)))),singleton(sK4(X0,X1,sK1(X2,X3,cartesian_product2(X0,X1))))) = sK1(X2,X3,cartesian_product2(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_1855,c_62]) ).
tcf(c_10110,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X6),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X2),X3,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_1649]) ).
tcf(c_10111,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X6),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK4(singleton(X2),X3,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_1312]) ).
tcf(c_10112,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = cartesian_product2(X2,X1) )
| ( sK4(singleton(X3),X4,sK1(X2,X1,cartesian_product2(singleton(X3),X4))) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK3(X2,X1,cartesian_product2(singleton(X3),X4)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_787]) ).
tcf(c_10113,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,singleton(X2))),X6),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X3,singleton(X2),sK1(X4,X5,cartesian_product2(X3,singleton(X2))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_1650]) ).
tcf(c_10114,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,singleton(X2))),X6),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK5(X3,singleton(X2),sK1(X4,X5,cartesian_product2(X3,singleton(X2))))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_1313]) ).
tcf(c_10115,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = cartesian_product2(X2,X1) )
| ( sK5(X3,singleton(X4),sK1(X2,X1,cartesian_product2(X3,singleton(X4)))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK3(X2,X1,cartesian_product2(X3,singleton(X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_789]) ).
tcf(c_10116,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X0),X1),X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,cartesian_product2(cartesian_product2(singleton(X0),X1),X2)),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,sK4(cartesian_product2(singleton(X0),X1),X2,sK1(X3,X4,cartesian_product2(cartesian_product2(singleton(X0),X1),X2)))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_835]) ).
tcf(c_10117,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(singleton(X0),X1)) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,cartesian_product2(X2,cartesian_product2(singleton(X0),X1))),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,sK5(X2,cartesian_product2(singleton(X0),X1),sK1(X3,X4,cartesian_product2(X2,cartesian_product2(singleton(X0),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_836]) ).
tcf(c_10118,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X0,singleton(X1)),X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,cartesian_product2(cartesian_product2(X0,singleton(X1)),X2)),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),sK4(cartesian_product2(X0,singleton(X1)),X2,sK1(X3,X4,cartesian_product2(cartesian_product2(X0,singleton(X1)),X2)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1855,c_861]) ).
tcf(c_10119,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(X0,singleton(X1))) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,cartesian_product2(X2,cartesian_product2(X0,singleton(X1)))),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),sK5(X2,cartesian_product2(X0,singleton(X1)),sK1(X3,X4,cartesian_product2(X2,cartesian_product2(X0,singleton(X1)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1855,c_862]) ).
tcf(c_10535,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),cartesian_product2(X1,singleton(X3)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X3),singleton(X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_1858]) ).
tcf(c_10536,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_1858]) ).
tcf(c_10537,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1858]) ).
tcf(c_10538,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1858]) ).
tcf(c_10539,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1858]) ).
tcf(c_10540,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1858]) ).
tcf(c_10541,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X4,X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,sK4(X1,X2,X0)),singleton(X3)),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_1858]) ).
tcf(c_10542,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X4,X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,sK5(X1,X2,X0)),singleton(X3)),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_1858]) ).
tcf(c_10543,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X3,X1)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))),singleton(X4)),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_1858]) ).
tcf(c_10544,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X1,X3)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))),singleton(X4)),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_1858]) ).
tcf(c_10545,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X1,X3)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))),singleton(X4)),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_1858]) ).
tcf(c_10546,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X1,X3)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))),singleton(X4)),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_1858]) ).
tcf(c_10547,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X3,X1)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))),singleton(X4)),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_1858]) ).
tcf(c_10548,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X3,X1)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))),singleton(X4)),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_1858]) ).
tcf(c_10550,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK1(singleton(X4),X5,X3)),singleton(X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_1858]) ).
tcf(c_10551,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK2(X3,X4,singleton(X5))),singleton(X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_1858]) ).
tcf(c_10552,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,singleton(X5),X3)),singleton(X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_1858]) ).
tcf(c_10553,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK3(X4,X3,singleton(X5))),singleton(X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_1858]) ).
tcf(c_10554,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_1858]) ).
tcf(c_10555,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_1858]) ).
tcf(c_10556,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_1858]) ).
tcf(c_10557,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_1858]) ).
tcf(c_10558,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_1858]) ).
tcf(c_10559,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_1858]) ).
tcf(c_10560,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_1858]) ).
tcf(c_10561,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_1858]) ).
tcf(c_10562,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_1858]) ).
tcf(c_10563,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_1858]) ).
tcf(c_10564,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_1858]) ).
tcf(c_10565,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_1858]) ).
tcf(c_10741,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X1),sK3(X3,X4,X1)),singleton(sK2(X3,X4,X1))) = sK1(X3,X4,X1) )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_10535]) ).
tcf(c_10742,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X1),X4)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_10535]) ).
tcf(c_10743,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X1),X3)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_10535]) ).
tcf(c_10744,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X1,X3,X4),X4)
| ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_10535]) ).
tcf(c_10745,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X1,X4),X4)
| ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_10535]) ).
tcf(c_10746,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(X1,singleton(X4)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK4(X1,X2,X0),X4),singleton(sK4(X1,X2,X0))),X3),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_10535]) ).
tcf(c_10747,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(X2,singleton(X4)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK5(X1,X2,X0),X4),singleton(sK5(X1,X2,X0))),X3),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_10535]) ).
tcf(c_10748,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X3,X1),singleton(X5)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2)))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_10535]) ).
tcf(c_10749,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X1,X3),singleton(X5)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5),singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2)))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_10535]) ).
tcf(c_10750,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X1,X3),singleton(X5)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0)))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_10535]) ).
tcf(c_10751,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X1,X3),singleton(X5)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5),singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0)))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_10535]) ).
tcf(c_10752,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X3,X1),singleton(X5)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5),singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2)))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_10535]) ).
tcf(c_10753,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X3,X1),singleton(X5)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5),singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0)))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_10535]) ).
tcf(c_10755,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X1 )
| ( sK2(singleton(X3),X4,X1) = X3 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1(singleton(X3),X4,X1),X2),singleton(sK1(singleton(X3),X4,X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_10535]) ).
tcf(c_10756,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X3) = singleton(X4) )
| ( sK1(X1,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK2(X1,X3,singleton(X4)),X2),singleton(sK2(X1,X3,singleton(X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_10535]) ).
tcf(c_10757,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X1 )
| ( sK3(X3,singleton(X4),X1) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1(X3,singleton(X4),X1),X2),singleton(sK1(X3,singleton(X4),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_10535]) ).
tcf(c_10758,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X1) = singleton(X4) )
| ( sK1(X3,X1,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK3(X3,X1,singleton(X4)),X2),singleton(sK3(X3,X1,singleton(X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_10535]) ).
tcf(c_10759,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_10535]) ).
tcf(c_10760,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_10535]) ).
tcf(c_10761,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X1,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_10535]) ).
tcf(c_10762,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_10535]) ).
tcf(c_10763,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_10535]) ).
tcf(c_10764,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X1,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_10535]) ).
tcf(c_10765,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_10535]) ).
tcf(c_10766,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_10535]) ).
tcf(c_10767,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_10535]) ).
tcf(c_10768,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_10535]) ).
tcf(c_10769,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_10535]) ).
tcf(c_10770,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_10535]) ).
tcf(c_10829,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),cartesian_product2(singleton(X3),X1),unordered_pair(unordered_pair(unordered_pair(singleton(X3),unordered_pair(X3,X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_1859]) ).
tcf(c_10830,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_1859]) ).
tcf(c_10831,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1859]) ).
tcf(c_10832,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1859]) ).
tcf(c_10833,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1859]) ).
tcf(c_10834,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1859]) ).
tcf(c_10835,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X1,X4),unordered_pair(unordered_pair(unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(sK4(X1,X2,X0),X3)),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_1859]) ).
tcf(c_10836,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X2,X4),unordered_pair(unordered_pair(unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(sK5(X1,X2,X0),X3)),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_1859]) ).
tcf(c_10837,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X3,X1),X5),unordered_pair(unordered_pair(unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X4)),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_1859]) ).
tcf(c_10838,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X1,X3),X5),unordered_pair(unordered_pair(unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X4)),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_1859]) ).
tcf(c_10839,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X1,X3),X5),unordered_pair(unordered_pair(unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X4)),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_1859]) ).
tcf(c_10840,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X1,X3),X5),unordered_pair(unordered_pair(unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X4)),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_1859]) ).
tcf(c_10841,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X3,X1),X5),unordered_pair(unordered_pair(unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X4)),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_1859]) ).
tcf(c_10842,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X3,X1),X5),unordered_pair(unordered_pair(unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X4)),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_1859]) ).
tcf(c_10844,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(singleton(X4),X5,X3)),unordered_pair(sK1(singleton(X4),X5,X3),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_1859]) ).
tcf(c_10845,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK2(X3,X4,singleton(X5))),unordered_pair(sK2(X3,X4,singleton(X5)),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_1859]) ).
tcf(c_10846,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X4,singleton(X5),X3)),unordered_pair(sK1(X4,singleton(X5),X3),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_1859]) ).
tcf(c_10847,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK3(X4,X3,singleton(X5))),unordered_pair(sK3(X4,X3,singleton(X5)),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_1859]) ).
tcf(c_10848,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_1859]) ).
tcf(c_10849,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_1859]) ).
tcf(c_10850,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_1859]) ).
tcf(c_10851,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_1859]) ).
tcf(c_10852,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_1859]) ).
tcf(c_10853,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_1859]) ).
tcf(c_10854,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_1859]) ).
tcf(c_10855,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_1859]) ).
tcf(c_10856,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_1859]) ).
tcf(c_10857,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_1859]) ).
tcf(c_10858,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_1859]) ).
tcf(c_10859,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_1859]) ).
tcf(c_11087,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X2),sK3(X3,X4,X2)),singleton(sK2(X3,X4,X2))) = sK1(X3,X4,X2) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_10829]) ).
tcf(c_11088,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X2),X4)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_10829]) ).
tcf(c_11089,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X2),X3)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_10829]) ).
tcf(c_11090,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X2,X3,X4),X4)
| ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_10829]) ).
tcf(c_11091,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X2,X4),X4)
| ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_10829]) ).
tcf(c_11092,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(singleton(X4),X1),unordered_pair(unordered_pair(unordered_pair(singleton(X4),unordered_pair(X4,sK4(X1,X2,X0))),X3),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_10829]) ).
tcf(c_11093,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(singleton(X4),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X4),unordered_pair(X4,sK5(X1,X2,X0))),X3),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_10829]) ).
tcf(c_11094,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X3,X1)),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X2)))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_10829]) ).
tcf(c_11095,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X1,X3)),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X0,X2)))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_10829]) ).
tcf(c_11096,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X1,X3)),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X0)))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_10829]) ).
tcf(c_11097,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X1,X3)),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X2,X0)))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_10829]) ).
tcf(c_11098,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X3,X1)),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X0,X2)))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_10829]) ).
tcf(c_11099,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X3,X1)),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X2,X0)))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_10829]) ).
tcf(c_11101,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X2 )
| ( sK2(singleton(X3),X4,X2) = X3 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK1(singleton(X3),X4,X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_10829]) ).
tcf(c_11102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK1(X2,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,singleton(X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_10829]) ).
tcf(c_11103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X2 )
| ( sK3(X3,singleton(X4),X2) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,singleton(X4),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_10829]) ).
tcf(c_11104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X2) = singleton(X4) )
| ( sK1(X3,X2,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,singleton(X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_10829]) ).
tcf(c_11105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_10829]) ).
tcf(c_11106,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_10829]) ).
tcf(c_11107,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X2,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_10829]) ).
tcf(c_11108,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_10829]) ).
tcf(c_11109,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_10829]) ).
tcf(c_11110,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X2,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_10829]) ).
tcf(c_11111,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_10829]) ).
tcf(c_11112,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_10829]) ).
tcf(c_11113,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_10829]) ).
tcf(c_11114,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_10829]) ).
tcf(c_11115,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_10829]) ).
tcf(c_11116,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_10829]) ).
tcf(c_11410,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),cartesian_product2(singleton(X3),X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X3),singleton(X3)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_1860]) ).
tcf(c_11411,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_1860]) ).
tcf(c_11412,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1860]) ).
tcf(c_11413,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1860]) ).
tcf(c_11414,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1860]) ).
tcf(c_11415,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1860]) ).
tcf(c_11416,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X1,X4),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,sK4(X1,X2,X0)),singleton(sK4(X1,X2,X0))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_1860]) ).
tcf(c_11417,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X2,X4),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,sK5(X1,X2,X0)),singleton(sK5(X1,X2,X0))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_1860]) ).
tcf(c_11418,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X3,X1),X5),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2)))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_1860]) ).
tcf(c_11419,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X1,X3),X5),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))),singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2)))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_1860]) ).
tcf(c_11420,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X1,X3),X5),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0)))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_1860]) ).
tcf(c_11421,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X1,X3),X5),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))),singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0)))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_1860]) ).
tcf(c_11422,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X3,X1),X5),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))),singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2)))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_1860]) ).
tcf(c_11423,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X3,X1),X5),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))),singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0)))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_1860]) ).
tcf(c_11425,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK1(singleton(X4),X5,X3)),singleton(sK1(singleton(X4),X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_1860]) ).
tcf(c_11426,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK2(X3,X4,singleton(X5))),singleton(sK2(X3,X4,singleton(X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_1860]) ).
tcf(c_11427,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,singleton(X5),X3)),singleton(sK1(X4,singleton(X5),X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_1860]) ).
tcf(c_11428,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK3(X4,X3,singleton(X5))),singleton(sK3(X4,X3,singleton(X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_1860]) ).
tcf(c_11429,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_1860]) ).
tcf(c_11430,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_1860]) ).
tcf(c_11431,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_1860]) ).
tcf(c_11432,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_1860]) ).
tcf(c_11433,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_1860]) ).
tcf(c_11434,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_1860]) ).
tcf(c_11435,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_1860]) ).
tcf(c_11436,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_1860]) ).
tcf(c_11437,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_1860]) ).
tcf(c_11438,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_1860]) ).
tcf(c_11439,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_1860]) ).
tcf(c_11440,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_1860]) ).
tcf(c_11512,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X2),sK3(X3,X4,X2)),singleton(sK2(X3,X4,X2))) = sK1(X3,X4,X2) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_11410]) ).
tcf(c_11513,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X2),X4)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_11410]) ).
tcf(c_11514,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X2),X3)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_11410]) ).
tcf(c_11515,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X2,X3,X4),X4)
| ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_11410]) ).
tcf(c_11516,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X2,X4),X4)
| ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_11410]) ).
tcf(c_11517,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(singleton(X4),X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK4(X1,X2,X0),X4),singleton(X4)),X3),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_11410]) ).
tcf(c_11518,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(singleton(X4),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK5(X1,X2,X0),X4),singleton(X4)),X3),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_11410]) ).
tcf(c_11519,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X3,X1)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5),singleton(X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_11410]) ).
tcf(c_11520,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X1,X3)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5),singleton(X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_11410]) ).
tcf(c_11521,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X1,X3)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5),singleton(X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_11410]) ).
tcf(c_11522,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X1,X3)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5),singleton(X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_11410]) ).
tcf(c_11523,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X3,X1)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5),singleton(X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_11410]) ).
tcf(c_11524,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X3,X1)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5),singleton(X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_11410]) ).
tcf(c_11526,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X2 )
| ( sK2(singleton(X3),X4,X2) = X3 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1(singleton(X3),X4,X2),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_11410]) ).
tcf(c_11527,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK1(X2,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK2(X2,X3,singleton(X4)),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_11410]) ).
tcf(c_11528,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X2 )
| ( sK3(X3,singleton(X4),X2) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1(X3,singleton(X4),X2),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_11410]) ).
tcf(c_11529,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X2) = singleton(X4) )
| ( sK1(X3,X2,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK3(X3,X2,singleton(X4)),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_11410]) ).
tcf(c_11530,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_11410]) ).
tcf(c_11531,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_11410]) ).
tcf(c_11532,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X2,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_11410]) ).
tcf(c_11533,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_11410]) ).
tcf(c_11534,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_11410]) ).
tcf(c_11535,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X2,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_11410]) ).
tcf(c_11536,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_11410]) ).
tcf(c_11537,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_11410]) ).
tcf(c_11538,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_11410]) ).
tcf(c_11539,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_11410]) ).
tcf(c_11540,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_11410]) ).
tcf(c_11541,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_11410]) ).
tcf(c_11834,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),cartesian_product2(singleton(X3),X1),unordered_pair(unordered_pair(unordered_pair(singleton(X3),unordered_pair(X0,X3)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_1861]) ).
tcf(c_11835,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_1861]) ).
tcf(c_11836,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1861]) ).
tcf(c_11837,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1861]) ).
tcf(c_11838,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1861]) ).
tcf(c_11839,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1861]) ).
tcf(c_11840,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X1,X4),unordered_pair(unordered_pair(unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(X3,sK4(X1,X2,X0))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_1861]) ).
tcf(c_11841,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X2,X4),unordered_pair(unordered_pair(unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(X3,sK5(X1,X2,X0))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_1861]) ).
tcf(c_11842,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X3,X1),X5),unordered_pair(unordered_pair(unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2)))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_1861]) ).
tcf(c_11843,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X1,X3),X5),unordered_pair(unordered_pair(unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2)))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_1861]) ).
tcf(c_11844,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X1,X3),X5),unordered_pair(unordered_pair(unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0)))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_1861]) ).
tcf(c_11845,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X1,X3),X5),unordered_pair(unordered_pair(unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0)))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_1861]) ).
tcf(c_11846,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X3,X1),X5),unordered_pair(unordered_pair(unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2)))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_1861]) ).
tcf(c_11847,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X3,X1),X5),unordered_pair(unordered_pair(unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0)))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_1861]) ).
tcf(c_11849,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(singleton(X4),X5,X3)),unordered_pair(X0,sK1(singleton(X4),X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_1861]) ).
tcf(c_11850,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK2(X3,X4,singleton(X5))),unordered_pair(X0,sK2(X3,X4,singleton(X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_1861]) ).
tcf(c_11851,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X4,singleton(X5),X3)),unordered_pair(X0,sK1(X4,singleton(X5),X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_1861]) ).
tcf(c_11852,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK3(X4,X3,singleton(X5))),unordered_pair(X0,sK3(X4,X3,singleton(X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_1861]) ).
tcf(c_11853,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_1861]) ).
tcf(c_11854,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_1861]) ).
tcf(c_11855,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_1861]) ).
tcf(c_11856,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_1861]) ).
tcf(c_11857,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_1861]) ).
tcf(c_11858,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_1861]) ).
tcf(c_11859,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_1861]) ).
tcf(c_11860,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_1861]) ).
tcf(c_11861,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_1861]) ).
tcf(c_11862,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_1861]) ).
tcf(c_11863,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_1861]) ).
tcf(c_11864,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_1861]) ).
tcf(c_12043,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X2),sK3(X3,X4,X2)),singleton(sK2(X3,X4,X2))) = sK1(X3,X4,X2) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_11834]) ).
tcf(c_12044,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X2),X4)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_11834]) ).
tcf(c_12045,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X2),X3)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_11834]) ).
tcf(c_12046,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X2,X3,X4),X4)
| ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_11834]) ).
tcf(c_12047,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X2,X4),X4)
| ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_11834]) ).
tcf(c_12048,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(singleton(X4),X1),unordered_pair(unordered_pair(unordered_pair(singleton(X4),unordered_pair(sK4(X1,X2,X0),X4)),X3),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_11834]) ).
tcf(c_12049,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(singleton(X4),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X4),unordered_pair(sK5(X1,X2,X0),X4)),X3),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_11834]) ).
tcf(c_12050,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X3,X1)),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_11834]) ).
tcf(c_12051,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X1,X3)),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_11834]) ).
tcf(c_12052,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X1,X3)),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_11834]) ).
tcf(c_12053,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X1,X3)),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_11834]) ).
tcf(c_12054,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X3,X1)),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_11834]) ).
tcf(c_12055,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X3,X1)),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_11834]) ).
tcf(c_12057,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X2 )
| ( sK2(singleton(X3),X4,X2) = X3 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK1(singleton(X3),X4,X2),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_11834]) ).
tcf(c_12058,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK1(X2,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,singleton(X4)),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_11834]) ).
tcf(c_12059,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X2 )
| ( sK3(X3,singleton(X4),X2) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK1(X3,singleton(X4),X2),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_11834]) ).
tcf(c_12060,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X2) = singleton(X4) )
| ( sK1(X3,X2,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,singleton(X4)),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_11834]) ).
tcf(c_12061,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_11834]) ).
tcf(c_12062,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_11834]) ).
tcf(c_12063,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X2,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_11834]) ).
tcf(c_12064,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_11834]) ).
tcf(c_12065,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_11834]) ).
tcf(c_12066,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X2,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_11834]) ).
tcf(c_12067,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_11834]) ).
tcf(c_12068,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_11834]) ).
tcf(c_12069,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_11834]) ).
tcf(c_12070,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_11834]) ).
tcf(c_12071,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_11834]) ).
tcf(c_12072,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_11834]) ).
tcf(c_12125,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),cartesian_product2(X1,singleton(X3)),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X3,X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_1862]) ).
tcf(c_12126,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_1862]) ).
tcf(c_12127,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1862]) ).
tcf(c_12128,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1862]) ).
tcf(c_12129,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1862]) ).
tcf(c_12130,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1862]) ).
tcf(c_12131,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X4,X1),unordered_pair(unordered_pair(unordered_pair(singleton(X3),unordered_pair(sK4(X1,X2,X0),X3)),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_1862]) ).
tcf(c_12132,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X4,X2),unordered_pair(unordered_pair(unordered_pair(singleton(X3),unordered_pair(sK5(X1,X2,X0),X3)),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_1862]) ).
tcf(c_12133,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X3,X1)),unordered_pair(unordered_pair(unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X4)),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_1862]) ).
tcf(c_12134,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X1,X3)),unordered_pair(unordered_pair(unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X4)),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_1862]) ).
tcf(c_12135,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X1,X3)),unordered_pair(unordered_pair(unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X4)),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_1862]) ).
tcf(c_12136,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X1,X3)),unordered_pair(unordered_pair(unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X4)),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_1862]) ).
tcf(c_12137,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X3,X1)),unordered_pair(unordered_pair(unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X4)),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_1862]) ).
tcf(c_12138,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X3,X1)),unordered_pair(unordered_pair(unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X4)),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_1862]) ).
tcf(c_12140,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK1(singleton(X4),X5,X3),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_1862]) ).
tcf(c_12141,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,singleton(X5)),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_1862]) ).
tcf(c_12142,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK1(X4,singleton(X5),X3),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_1862]) ).
tcf(c_12143,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,singleton(X5)),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_1862]) ).
tcf(c_12144,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_1862]) ).
tcf(c_12145,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_1862]) ).
tcf(c_12146,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_1862]) ).
tcf(c_12147,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_1862]) ).
tcf(c_12148,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_1862]) ).
tcf(c_12149,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_1862]) ).
tcf(c_12150,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_1862]) ).
tcf(c_12151,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_1862]) ).
tcf(c_12152,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_1862]) ).
tcf(c_12153,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_1862]) ).
tcf(c_12154,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_1862]) ).
tcf(c_12155,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_1862]) ).
tcf(c_12254,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X1),sK3(X3,X4,X1)),singleton(sK2(X3,X4,X1))) = sK1(X3,X4,X1) )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_12125]) ).
tcf(c_12255,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X1),X4)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_12125]) ).
tcf(c_12256,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X1),X3)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_12125]) ).
tcf(c_12257,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X1,X3,X4),X4)
| ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_12125]) ).
tcf(c_12258,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X1,X4),X4)
| ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_12125]) ).
tcf(c_12259,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(X1,singleton(X4)),unordered_pair(unordered_pair(unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(X4,sK4(X1,X2,X0))),X3),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_12125]) ).
tcf(c_12260,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(X2,singleton(X4)),unordered_pair(unordered_pair(unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(X4,sK5(X1,X2,X0))),X3),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_12125]) ).
tcf(c_12261,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X3,X1),singleton(X5)),unordered_pair(unordered_pair(unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X2)))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_12125]) ).
tcf(c_12262,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X1,X3),singleton(X5)),unordered_pair(unordered_pair(unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X0,X2)))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_12125]) ).
tcf(c_12263,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X1,X3),singleton(X5)),unordered_pair(unordered_pair(unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X0)))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_12125]) ).
tcf(c_12264,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X1,X3),singleton(X5)),unordered_pair(unordered_pair(unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X2,X0)))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_12125]) ).
tcf(c_12265,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X3,X1),singleton(X5)),unordered_pair(unordered_pair(unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X0,X2)))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_12125]) ).
tcf(c_12266,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X3,X1),singleton(X5)),unordered_pair(unordered_pair(unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X2,X0)))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_12125]) ).
tcf(c_12268,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X1 )
| ( sK2(singleton(X3),X4,X1) = X3 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(singleton(X3),X4,X1)),unordered_pair(X2,sK1(singleton(X3),X4,X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_12125]) ).
tcf(c_12269,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X3) = singleton(X4) )
| ( sK1(X1,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK2(X1,X3,singleton(X4))),unordered_pair(X2,sK2(X1,X3,singleton(X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_12125]) ).
tcf(c_12270,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X1 )
| ( sK3(X3,singleton(X4),X1) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X3,singleton(X4),X1)),unordered_pair(X2,sK1(X3,singleton(X4),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_12125]) ).
tcf(c_12271,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X1) = singleton(X4) )
| ( sK1(X3,X1,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK3(X3,X1,singleton(X4))),unordered_pair(X2,sK3(X3,X1,singleton(X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_12125]) ).
tcf(c_12272,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_12125]) ).
tcf(c_12273,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_12125]) ).
tcf(c_12274,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X1,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_12125]) ).
tcf(c_12275,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_12125]) ).
tcf(c_12276,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_12125]) ).
tcf(c_12277,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X1,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_12125]) ).
tcf(c_12278,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_12125]) ).
tcf(c_12279,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_12125]) ).
tcf(c_12280,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_12125]) ).
tcf(c_12281,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_12125]) ).
tcf(c_12282,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_12125]) ).
tcf(c_12283,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_12125]) ).
tcf(c_12397,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X2,X3) )
| ( sK5(X1,singleton(X4),unordered_pair(unordered_pair(sK4(singleton(X4),X5,sK1(X2,X3,cartesian_product2(singleton(X4),X5))),X0),singleton(X0))) = X4 )
| ( unordered_pair(unordered_pair(sK2(X2,X3,cartesian_product2(singleton(X4),X5)),sK3(X2,X3,cartesian_product2(singleton(X4),X5))),singleton(sK2(X2,X3,cartesian_product2(singleton(X4),X5)))) = sK1(X2,X3,cartesian_product2(singleton(X4),X5)) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_1935]) ).
tcf(c_12398,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X5)
| ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK4(singleton(X2),X3,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1935]) ).
tcf(c_12399,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X4)
| ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK4(singleton(X2),X3,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1935]) ).
tcf(c_12400,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK4(singleton(X2),X3,sK2(cartesian_product2(singleton(X2),X3),X4,X5)),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1935]) ).
tcf(c_12401,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK4(singleton(X2),X3,sK3(X4,cartesian_product2(singleton(X2),X3),X5)),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1935]) ).
tcf(c_12402,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,sK4(cartesian_product2(singleton(X1),X2),X3,X0)),X4),singleton(X4))) = X1 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(cartesian_product2(singleton(X1),X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_1935]) ).
tcf(c_12403,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X2),unordered_pair(unordered_pair(sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),X0)),X4),singleton(X4))) = X2 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(X1,cartesian_product2(singleton(X2),X3))) ),
inference(superposition,[status(thm)],[c_61,c_1935]) ).
tcf(c_12404,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X3,unordered_pair(unordered_pair(X0,X2),singleton(X0))),X4),singleton(X4))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_64,c_1935]) ).
tcf(c_12406,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X3,unordered_pair(unordered_pair(X2,X0),singleton(X0))),X4),singleton(X4))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_809,c_1935]) ).
tcf(c_12407,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X3,unordered_pair(singleton(X0),unordered_pair(X2,X0))),X4),singleton(X4))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_882,c_1935]) ).
tcf(c_12409,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X3,unordered_pair(singleton(X0),unordered_pair(X0,X2))),X4),singleton(X4))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_900,c_1935]) ).
tcf(c_12410,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(singleton(X4),X5) )
| ( sK2(singleton(X4),X5,cartesian_product2(singleton(X2),X3)) = X4 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK4(singleton(X2),X3,sK1(singleton(X4),X5,cartesian_product2(singleton(X2),X3))),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_1935]) ).
tcf(c_12411,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = singleton(X5) )
| ( sK1(cartesian_product2(singleton(X2),X3),X4,singleton(X5)) = X5 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK4(singleton(X2),X3,sK2(cartesian_product2(singleton(X2),X3),X4,singleton(X5))),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_1935]) ).
tcf(c_12412,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,singleton(X5)) )
| ( sK3(X4,singleton(X5),cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK4(singleton(X2),X3,sK1(X4,singleton(X5),cartesian_product2(singleton(X2),X3))),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_1935]) ).
tcf(c_12413,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(singleton(X2),X3),singleton(X5)) = X5 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK4(singleton(X2),X3,sK3(X4,cartesian_product2(singleton(X2),X3),singleton(X5))),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_1935]) ).
tcf(c_12414,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X6),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK4(singleton(X2),X3,sK3(X4,cartesian_product2(singleton(X2),X3),X5)),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_1935]) ).
tcf(c_12415,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(singleton(X2),X3),X5)))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK4(singleton(X2),X3,sK3(X4,cartesian_product2(singleton(X2),X3),X5)),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_1935]) ).
tcf(c_12416,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(singleton(X2),X3),X5)),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK4(singleton(X2),X3,sK3(X4,cartesian_product2(singleton(X2),X3),X5)),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_1935]) ).
tcf(c_12417,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X6),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK4(singleton(X2),X3,sK2(cartesian_product2(singleton(X2),X3),X4,X5)),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_1935]) ).
tcf(c_12418,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(singleton(X2),X3),X4,X5)))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK4(singleton(X2),X3,sK2(cartesian_product2(singleton(X2),X3),X4,X5)),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_1935]) ).
tcf(c_12419,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(singleton(X2),X3),X4,X5)),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK4(singleton(X2),X3,sK2(cartesian_product2(singleton(X2),X3),X4,X5)),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_1935]) ).
tcf(c_12420,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X6),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK4(singleton(X2),X3,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_1935]) ).
tcf(c_12421,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(singleton(X2),X3))))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK4(singleton(X2),X3,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_1935]) ).
tcf(c_12422,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK4(singleton(X2),X3,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_1935]) ).
tcf(c_12423,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X6),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK4(singleton(X2),X3,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_1935]) ).
tcf(c_12424,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(singleton(X2),X3))))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK4(singleton(X2),X3,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_1935]) ).
tcf(c_12425,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK4(singleton(X2),X3,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_1935]) ).
tcf(c_12508,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = cartesian_product2(X2,X3) )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(sK5(X4,singleton(X5),sK1(X2,X3,cartesian_product2(X4,singleton(X5)))),X0),singleton(X0))) = X5 )
| ( unordered_pair(unordered_pair(sK2(X2,X3,cartesian_product2(X4,singleton(X5))),sK3(X2,X3,cartesian_product2(X4,singleton(X5)))),singleton(sK2(X2,X3,cartesian_product2(X4,singleton(X5))))) = sK1(X2,X3,cartesian_product2(X4,singleton(X5))) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_1936]) ).
tcf(c_12509,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X3,singleton(X2))),X5)
| ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,X5) )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK5(X3,singleton(X2),sK1(X4,X5,cartesian_product2(X3,singleton(X2)))),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1936]) ).
tcf(c_12510,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X3,singleton(X2))),X4)
| ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,X5) )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK5(X3,singleton(X2),sK1(X4,X5,cartesian_product2(X3,singleton(X2)))),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1936]) ).
tcf(c_12511,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X3,singleton(X2)),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X3,singleton(X2)),X4) = X5 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK5(X3,singleton(X2),sK2(cartesian_product2(X3,singleton(X2)),X4,X5)),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1936]) ).
tcf(c_12512,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X3,singleton(X2)),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X3,singleton(X2))) = X5 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK5(X3,singleton(X2),sK3(X4,cartesian_product2(X3,singleton(X2)),X5)),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1936]) ).
tcf(c_12513,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X2),unordered_pair(unordered_pair(sK5(X1,singleton(X2),sK4(cartesian_product2(X1,singleton(X2)),X3,X0)),X4),singleton(X4))) = X2 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(cartesian_product2(X1,singleton(X2)),X3)) ),
inference(superposition,[status(thm)],[c_60,c_1936]) ).
tcf(c_12514,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X3),unordered_pair(unordered_pair(sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),X0)),X4),singleton(X4))) = X3 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,singleton(X3)))) ),
inference(superposition,[status(thm)],[c_61,c_1936]) ).
tcf(c_12515,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X1),unordered_pair(unordered_pair(sK5(X3,singleton(X1),unordered_pair(unordered_pair(X2,X0),singleton(X2))),X4),singleton(X4))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_64,c_1936]) ).
tcf(c_12517,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X1),unordered_pair(unordered_pair(sK5(X3,singleton(X1),unordered_pair(unordered_pair(X0,X2),singleton(X2))),X4),singleton(X4))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_809,c_1936]) ).
tcf(c_12518,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X1),unordered_pair(unordered_pair(sK5(X3,singleton(X1),unordered_pair(singleton(X2),unordered_pair(X0,X2))),X4),singleton(X4))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_882,c_1936]) ).
tcf(c_12520,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X1),unordered_pair(unordered_pair(sK5(X3,singleton(X1),unordered_pair(singleton(X2),unordered_pair(X2,X0))),X4),singleton(X4))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_900,c_1936]) ).
tcf(c_12521,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X3,singleton(X2)) )
| ( sK2(singleton(X4),X5,cartesian_product2(X3,singleton(X2))) = X4 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK5(X3,singleton(X2),sK1(singleton(X4),X5,cartesian_product2(X3,singleton(X2)))),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_1936]) ).
tcf(c_12522,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X3,singleton(X2)),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X3,singleton(X2)),X4,singleton(X5)) = X5 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK5(X3,singleton(X2),sK2(cartesian_product2(X3,singleton(X2)),X4,singleton(X5))),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_1936]) ).
tcf(c_12523,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,singleton(X5)) )
| ( sK3(X4,singleton(X5),cartesian_product2(X3,singleton(X2))) = X5 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK5(X3,singleton(X2),sK1(X4,singleton(X5),cartesian_product2(X3,singleton(X2)))),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_1936]) ).
tcf(c_12524,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,singleton(X2))) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X3,singleton(X2)),singleton(X5)) = X5 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK5(X3,singleton(X2),sK3(X4,cartesian_product2(X3,singleton(X2)),singleton(X5))),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_1936]) ).
tcf(c_12525,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,singleton(X2))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,singleton(X2)),X5),X6),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK5(X3,singleton(X2),sK3(X4,cartesian_product2(X3,singleton(X2)),X5)),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_1936]) ).
tcf(c_12526,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,singleton(X2))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X3,singleton(X2)),X5)))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK5(X3,singleton(X2),sK3(X4,cartesian_product2(X3,singleton(X2)),X5)),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_1936]) ).
tcf(c_12527,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,singleton(X2))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X3,singleton(X2)),X5)),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK5(X3,singleton(X2),sK3(X4,cartesian_product2(X3,singleton(X2)),X5)),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_1936]) ).
tcf(c_12528,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,singleton(X2)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X3,singleton(X2)),X4,X5),X6),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK5(X3,singleton(X2),sK2(cartesian_product2(X3,singleton(X2)),X4,X5)),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_1936]) ).
tcf(c_12529,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,singleton(X2)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X3,singleton(X2)),X4,X5)))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK5(X3,singleton(X2),sK2(cartesian_product2(X3,singleton(X2)),X4,X5)),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_1936]) ).
tcf(c_12530,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,singleton(X2)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X3,singleton(X2)),X4,X5)),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK5(X3,singleton(X2),sK2(cartesian_product2(X3,singleton(X2)),X4,X5)),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_1936]) ).
tcf(c_12531,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,singleton(X2))),X6),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK5(X3,singleton(X2),sK1(X4,X5,cartesian_product2(X3,singleton(X2)))),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_1936]) ).
tcf(c_12532,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,singleton(X2)))))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK5(X3,singleton(X2),sK1(X4,X5,cartesian_product2(X3,singleton(X2)))),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_1936]) ).
tcf(c_12533,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,singleton(X2)))),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK5(X3,singleton(X2),sK1(X4,X5,cartesian_product2(X3,singleton(X2)))),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_1936]) ).
tcf(c_12534,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,singleton(X2))),X6),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK5(X3,singleton(X2),sK1(X4,X5,cartesian_product2(X3,singleton(X2)))),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_1936]) ).
tcf(c_12535,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,singleton(X2)))))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK5(X3,singleton(X2),sK1(X4,X5,cartesian_product2(X3,singleton(X2)))),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_1936]) ).
tcf(c_12536,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,singleton(X2)))),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK5(X3,singleton(X2),sK1(X4,X5,cartesian_product2(X3,singleton(X2)))),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_1936]) ).
tcf(c_12723,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,singleton(X3))
| ( cartesian_product2(X2,singleton(X3)) = singleton(X1) )
| ( sK1(X2,singleton(X3),singleton(X1)) = X1 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK1(X2,singleton(X3),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1032,c_2454]) ).
tcf(c_12724,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_12125]) ).
tcf(c_12725,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_1862]) ).
tcf(c_12726,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_11834]) ).
tcf(c_12727,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_1861]) ).
tcf(c_12728,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_11410]) ).
tcf(c_12729,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_1860]) ).
tcf(c_12730,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_10829]) ).
tcf(c_12731,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_1859]) ).
tcf(c_12732,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_10535]) ).
tcf(c_12733,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_1858]) ).
tcf(c_12734,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_8720]) ).
tcf(c_12735,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_1575]) ).
tcf(c_12736,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_8554]) ).
tcf(c_12737,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_1574]) ).
tcf(c_12738,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_8285]) ).
tcf(c_12739,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_1573]) ).
tcf(c_12740,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_8027]) ).
tcf(c_12741,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_1572]) ).
tcf(c_12742,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_7766]) ).
tcf(c_12743,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_1571]) ).
tcf(c_12744,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_7495]) ).
tcf(c_12745,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_1570]) ).
tcf(c_12746,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_6164]) ).
tcf(c_12747,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_1156]) ).
tcf(c_12748,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_5987]) ).
tcf(c_12749,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_1155]) ).
tcf(c_12750,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_5758]) ).
tcf(c_12751,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_1154]) ).
tcf(c_12752,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_5518]) ).
tcf(c_12753,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_1153]) ).
tcf(c_12754,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_5291]) ).
tcf(c_12755,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_1152]) ).
tcf(c_12756,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_4798]) ).
tcf(c_12757,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_1151]) ).
tcf(c_12758,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X0) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(sK1(X2,X0,X3),X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK3(X2,X0,X3)),unordered_pair(X1,sK3(X2,X0,X3)))) = X1 ) ),
inference(superposition,[status(thm)],[c_2454,c_2539]) ).
tcf(c_12759,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X1 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(sK3(X2,X3,X1),X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK1(X2,X3,X1),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_2384]) ).
tcf(c_12760,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X0) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(sK1(X2,X0,X3),X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK3(X2,X0,X3)),singleton(sK3(X2,X0,X3)))) = X1 ) ),
inference(superposition,[status(thm)],[c_2454,c_1929]) ).
tcf(c_12761,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X1 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(sK3(X2,X3,X1),X4),singleton(X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK1(X2,X3,X1),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_1823]) ).
tcf(c_12762,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X0) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(sK1(X2,X0,X3),X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK3(X2,X0,X3)),unordered_pair(sK3(X2,X0,X3),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_2454,c_1643]) ).
tcf(c_12763,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X1 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(X4,sK3(X2,X3,X1)))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK1(X2,X3,X1),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_1524]) ).
tcf(c_12764,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X0) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(sK1(X2,X0,X3),X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK3(X2,X0,X3),X1),singleton(sK3(X2,X0,X3)))) = X1 ) ),
inference(superposition,[status(thm)],[c_2454,c_1306]) ).
tcf(c_12765,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X1 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(X4,sK3(X2,X3,X1)),singleton(X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK1(X2,X3,X1),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_1060]) ).
tcf(c_12766,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(sK3(X4,singleton(X5),X3),X0))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK1(X4,singleton(X5),X3),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_907]) ).
tcf(c_12767,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,singleton(X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,singleton(X2),X4),X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK3(X3,singleton(X2),X4)),unordered_pair(X0,sK3(X3,singleton(X2),X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_906]) ).
tcf(c_12768,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(sK3(X4,singleton(X5),X3),X0),singleton(X0))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK1(X4,singleton(X5),X3),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_899]) ).
tcf(c_12769,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,singleton(X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,singleton(X2),X4),X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X0,sK3(X3,singleton(X2),X4)),singleton(sK3(X3,singleton(X2),X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_898]) ).
tcf(c_12770,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,singleton(X5),X3)))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK1(X4,singleton(X5),X3),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_889]) ).
tcf(c_12771,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,singleton(X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,singleton(X2),X4),X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK3(X3,singleton(X2),X4)),unordered_pair(sK3(X3,singleton(X2),X4),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_888]) ).
tcf(c_12772,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(X0,sK3(X4,singleton(X5),X3)),singleton(X0))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK1(X4,singleton(X5),X3),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_863]) ).
tcf(c_12773,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,singleton(X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,singleton(X2),X4),X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK3(X3,singleton(X2),X4),X0),singleton(sK3(X3,singleton(X2),X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_837]) ).
tcf(c_12775,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X0)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,cartesian_product2(X2,X0),X4),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))),unordered_pair(X1,sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_2454,c_2611]) ).
tcf(c_12776,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X0,X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,cartesian_product2(X0,X2),X4),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))),unordered_pair(X1,sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_2454,c_2610]) ).
tcf(c_12777,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X0)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,cartesian_product2(X2,X0),X4),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))),singleton(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_2454,c_2036]) ).
tcf(c_12778,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X0,X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,cartesian_product2(X0,X2),X4),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))),singleton(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_2454,c_2035]) ).
tcf(c_12779,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X0)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,cartesian_product2(X2,X0),X4),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))),unordered_pair(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4)),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_2454,c_1703]) ).
tcf(c_12780,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X0,X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,cartesian_product2(X0,X2),X4),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))),unordered_pair(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4)),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_2454,c_1702]) ).
tcf(c_12781,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X0)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,cartesian_product2(X2,X0),X4),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4)),X1),singleton(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_2454,c_1389]) ).
tcf(c_12782,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X0,X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,cartesian_product2(X0,X2),X4),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4)),X1),singleton(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_2454,c_1388]) ).
tcf(c_12783,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,cartesian_product2(X2,X1),X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK3(X3,cartesian_product2(X2,X1),X4)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_2459]) ).
tcf(c_12784,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,cartesian_product2(X1,X2),X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK3(X3,cartesian_product2(X1,X2),X4)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_2458]) ).
tcf(c_12785,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,cartesian_product2(X2,X1),X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK3(X3,cartesian_product2(X2,X1),X4)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_1857]) ).
tcf(c_12786,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,cartesian_product2(X1,X2),X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK3(X3,cartesian_product2(X1,X2),X4)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_1856]) ).
tcf(c_12787,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,cartesian_product2(X2,X1),X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK3(X3,cartesian_product2(X2,X1),X4))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_1569]) ).
tcf(c_12788,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,cartesian_product2(X1,X2),X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK3(X3,cartesian_product2(X1,X2),X4))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_1568]) ).
tcf(c_12789,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,cartesian_product2(X2,X1),X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK3(X3,cartesian_product2(X2,X1),X4))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_1150]) ).
tcf(c_12790,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,cartesian_product2(X1,X2),X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK3(X3,cartesian_product2(X1,X2),X4))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_1149]) ).
tcf(c_12791,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,cartesian_product2(X0,X1)) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(sK1(X2,cartesian_product2(X0,X1),X3),X4))) = X4 )
| ( unordered_pair(unordered_pair(sK4(X0,X1,sK3(X2,cartesian_product2(X0,X1),X3)),sK5(X0,X1,sK3(X2,cartesian_product2(X0,X1),X3))),singleton(sK4(X0,X1,sK3(X2,cartesian_product2(X0,X1),X3)))) = sK3(X2,cartesian_product2(X0,X1),X3) ) ),
inference(superposition,[status(thm)],[c_2454,c_62]) ).
tcf(c_12792,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK4(singleton(X2),X3,sK3(X4,cartesian_product2(singleton(X2),X3),X5)),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_1935]) ).
tcf(c_12793,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X2),X3,sK3(X4,cartesian_product2(singleton(X2),X3),X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_1649]) ).
tcf(c_12794,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK4(singleton(X2),X3,sK3(X4,cartesian_product2(singleton(X2),X3),X5))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_1312]) ).
tcf(c_12795,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,cartesian_product2(singleton(X3),X4)) = X1 )
| ( sK4(singleton(X3),X4,sK3(X2,cartesian_product2(singleton(X3),X4),X1)) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK1(X2,cartesian_product2(singleton(X3),X4),X1),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_787]) ).
tcf(c_12796,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,singleton(X2))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X3,singleton(X2)),X5),X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK5(X3,singleton(X2),sK3(X4,cartesian_product2(X3,singleton(X2)),X5)),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_1936]) ).
tcf(c_12797,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,singleton(X2))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X3,singleton(X2)),X5),X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X3,singleton(X2),sK3(X4,cartesian_product2(X3,singleton(X2)),X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_1650]) ).
tcf(c_12798,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,singleton(X2))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X3,singleton(X2)),X5),X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK5(X3,singleton(X2),sK3(X4,cartesian_product2(X3,singleton(X2)),X5))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_1313]) ).
tcf(c_12799,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,cartesian_product2(X3,singleton(X4))) = X1 )
| ( sK5(X3,singleton(X4),sK3(X2,cartesian_product2(X3,singleton(X4)),X1)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK1(X2,cartesian_product2(X3,singleton(X4)),X1),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_789]) ).
tcf(c_12800,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(cartesian_product2(singleton(X0),X1),X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,cartesian_product2(cartesian_product2(singleton(X0),X1),X2),X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,sK4(cartesian_product2(singleton(X0),X1),X2,sK3(X3,cartesian_product2(cartesian_product2(singleton(X0),X1),X2),X4))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_835]) ).
tcf(c_12801,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,cartesian_product2(singleton(X0),X1))) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,cartesian_product2(X2,cartesian_product2(singleton(X0),X1)),X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,sK5(X2,cartesian_product2(singleton(X0),X1),sK3(X3,cartesian_product2(X2,cartesian_product2(singleton(X0),X1)),X4))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_836]) ).
tcf(c_12802,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(cartesian_product2(X0,singleton(X1)),X2)) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,cartesian_product2(cartesian_product2(X0,singleton(X1)),X2),X4),X5))) = X5 )
| ( sK5(X0,singleton(X1),sK4(cartesian_product2(X0,singleton(X1)),X2,sK3(X3,cartesian_product2(cartesian_product2(X0,singleton(X1)),X2),X4))) = X1 ) ),
inference(superposition,[status(thm)],[c_2454,c_861]) ).
tcf(c_12803,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,cartesian_product2(X0,singleton(X1)))) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,cartesian_product2(X2,cartesian_product2(X0,singleton(X1))),X4),X5))) = X5 )
| ( sK5(X0,singleton(X1),sK5(X2,cartesian_product2(X0,singleton(X1)),sK3(X3,cartesian_product2(X2,cartesian_product2(X0,singleton(X1))),X4))) = X1 ) ),
inference(superposition,[status(thm)],[c_2454,c_862]) ).
tcf(c_13234,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),cartesian_product2(X1,singleton(X3)),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X3)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_1863]) ).
tcf(c_13235,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_1863]) ).
tcf(c_13236,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1863]) ).
tcf(c_13237,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1863]) ).
tcf(c_13238,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1863]) ).
tcf(c_13239,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_1863]) ).
tcf(c_13240,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X4,X1),unordered_pair(unordered_pair(unordered_pair(singleton(X3),unordered_pair(X3,sK4(X1,X2,X0))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_1863]) ).
tcf(c_13241,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X4,X2),unordered_pair(unordered_pair(unordered_pair(singleton(X3),unordered_pair(X3,sK5(X1,X2,X0))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_1863]) ).
tcf(c_13242,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X3,X1)),unordered_pair(unordered_pair(unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2)))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_1863]) ).
tcf(c_13243,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X1,X3)),unordered_pair(unordered_pair(unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2)))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_1863]) ).
tcf(c_13244,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X1,X3)),unordered_pair(unordered_pair(unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0)))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_1863]) ).
tcf(c_13245,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X1,X3)),unordered_pair(unordered_pair(unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0)))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_1863]) ).
tcf(c_13246,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X3,X1)),unordered_pair(unordered_pair(unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2)))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_1863]) ).
tcf(c_13247,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X3,X1)),unordered_pair(unordered_pair(unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0)))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_1863]) ).
tcf(c_13249,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK1(singleton(X4),X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_1863]) ).
tcf(c_13250,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,singleton(X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_1863]) ).
tcf(c_13251,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,singleton(X5),X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_1863]) ).
tcf(c_13252,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,singleton(X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_1863]) ).
tcf(c_13253,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_1863]) ).
tcf(c_13254,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_1863]) ).
tcf(c_13255,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_1863]) ).
tcf(c_13256,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_1863]) ).
tcf(c_13257,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_1863]) ).
tcf(c_13258,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_1863]) ).
tcf(c_13259,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_1863]) ).
tcf(c_13260,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_1863]) ).
tcf(c_13261,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_1863]) ).
tcf(c_13262,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_1863]) ).
tcf(c_13263,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_1863]) ).
tcf(c_13264,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_1863]) ).
tcf(c_13265,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_1863]) ).
tcf(c_13396,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X1),sK3(X3,X4,X1)),singleton(sK2(X3,X4,X1))) = sK1(X3,X4,X1) )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_13234]) ).
tcf(c_13397,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X1),X4)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_13234]) ).
tcf(c_13398,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X1),X3)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_13234]) ).
tcf(c_13399,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X1,X3,X4),X4)
| ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_13234]) ).
tcf(c_13400,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X1,X4),X4)
| ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_13234]) ).
tcf(c_13401,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(X1,singleton(X4)),unordered_pair(unordered_pair(unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(sK4(X1,X2,X0),X4)),X3),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_13234]) ).
tcf(c_13402,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(X2,singleton(X4)),unordered_pair(unordered_pair(unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(sK5(X1,X2,X0),X4)),X3),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_13234]) ).
tcf(c_13403,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X3,X1),singleton(X5)),unordered_pair(unordered_pair(unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_13234]) ).
tcf(c_13404,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X1,X3),singleton(X5)),unordered_pair(unordered_pair(unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_13234]) ).
tcf(c_13405,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X1,X3),singleton(X5)),unordered_pair(unordered_pair(unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_13234]) ).
tcf(c_13406,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X1,X3),singleton(X5)),unordered_pair(unordered_pair(unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_13234]) ).
tcf(c_13407,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X3,X1),singleton(X5)),unordered_pair(unordered_pair(unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_13234]) ).
tcf(c_13408,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X3,X1),singleton(X5)),unordered_pair(unordered_pair(unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_13234]) ).
tcf(c_13410,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X1 )
| ( sK2(singleton(X3),X4,X1) = X3 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(singleton(X3),X4,X1)),unordered_pair(sK1(singleton(X3),X4,X1),X2)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_13234]) ).
tcf(c_13411,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X3) = singleton(X4) )
| ( sK1(X1,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK2(X1,X3,singleton(X4))),unordered_pair(sK2(X1,X3,singleton(X4)),X2)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_13234]) ).
tcf(c_13412,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X1 )
| ( sK3(X3,singleton(X4),X1) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X3,singleton(X4),X1)),unordered_pair(sK1(X3,singleton(X4),X1),X2)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_13234]) ).
tcf(c_13413,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X1) = singleton(X4) )
| ( sK1(X3,X1,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK3(X3,X1,singleton(X4))),unordered_pair(sK3(X3,X1,singleton(X4)),X2)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_13234]) ).
tcf(c_13414,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_13234]) ).
tcf(c_13415,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_13234]) ).
tcf(c_13416,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_13234]) ).
tcf(c_13417,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X1,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_13234]) ).
tcf(c_13418,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_13234]) ).
tcf(c_13419,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_13234]) ).
tcf(c_13420,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X1,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_13234]) ).
tcf(c_13421,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_13234]) ).
tcf(c_13422,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_13234]) ).
tcf(c_13423,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_13234]) ).
tcf(c_13424,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_13234]) ).
tcf(c_13425,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_13234]) ).
tcf(c_13426,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_13234]) ).
tcf(c_13536,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X2,singleton(X2))
| ( cartesian_product2(singleton(X2),X3) = singleton(X1) )
| ( sK1(singleton(X2),X3,singleton(X1)) = X1 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK1(singleton(X2),X3,singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1009,c_2455]) ).
tcf(c_13537,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_13234]) ).
tcf(c_13538,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_1863]) ).
tcf(c_13539,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_12125]) ).
tcf(c_13540,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_1862]) ).
tcf(c_13541,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_11834]) ).
tcf(c_13542,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_1861]) ).
tcf(c_13543,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_11410]) ).
tcf(c_13544,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_1860]) ).
tcf(c_13545,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_10829]) ).
tcf(c_13546,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_1859]) ).
tcf(c_13547,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_10535]) ).
tcf(c_13548,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_1858]) ).
tcf(c_13549,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_8720]) ).
tcf(c_13550,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_1575]) ).
tcf(c_13551,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_8554]) ).
tcf(c_13552,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_1574]) ).
tcf(c_13553,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_8285]) ).
tcf(c_13554,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_1573]) ).
tcf(c_13555,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_8027]) ).
tcf(c_13556,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_1572]) ).
tcf(c_13557,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_7766]) ).
tcf(c_13558,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_1571]) ).
tcf(c_13559,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_7495]) ).
tcf(c_13560,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_1570]) ).
tcf(c_13561,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_6164]) ).
tcf(c_13562,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_1156]) ).
tcf(c_13563,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_5987]) ).
tcf(c_13564,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_1155]) ).
tcf(c_13565,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_5758]) ).
tcf(c_13566,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_1154]) ).
tcf(c_13567,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_5518]) ).
tcf(c_13568,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_1153]) ).
tcf(c_13569,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_5291]) ).
tcf(c_13570,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_1152]) ).
tcf(c_13571,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_4798]) ).
tcf(c_13572,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_1151]) ).
tcf(c_13573,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X2) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(sK1(X0,X2,X3),X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK2(X0,X2,X3)),unordered_pair(X1,sK2(X0,X2,X3)))) = X1 ) ),
inference(superposition,[status(thm)],[c_2455,c_2539]) ).
tcf(c_13574,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X1 )
| ( sK4(singleton(X4),X2,unordered_pair(singleton(X4),unordered_pair(sK2(X2,X3,X1),X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK1(X2,X3,X1),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_2384]) ).
tcf(c_13575,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X2) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(sK1(X0,X2,X3),X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK2(X0,X2,X3)),singleton(sK2(X0,X2,X3)))) = X1 ) ),
inference(superposition,[status(thm)],[c_2455,c_1929]) ).
tcf(c_13576,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X1 )
| ( sK4(singleton(X4),X2,unordered_pair(unordered_pair(sK2(X2,X3,X1),X4),singleton(X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK1(X2,X3,X1),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_1823]) ).
tcf(c_13577,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X2) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(sK1(X0,X2,X3),X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK2(X0,X2,X3)),unordered_pair(sK2(X0,X2,X3),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_2455,c_1643]) ).
tcf(c_13578,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X1 )
| ( sK4(singleton(X4),X2,unordered_pair(singleton(X4),unordered_pair(X4,sK2(X2,X3,X1)))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK1(X2,X3,X1),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_1524]) ).
tcf(c_13579,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X2) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(sK1(X0,X2,X3),X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK2(X0,X2,X3),X1),singleton(sK2(X0,X2,X3)))) = X1 ) ),
inference(superposition,[status(thm)],[c_2455,c_1306]) ).
tcf(c_13580,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X1 )
| ( sK4(singleton(X4),X2,unordered_pair(unordered_pair(X4,sK2(X2,X3,X1)),singleton(X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK1(X2,X3,X1),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_1060]) ).
tcf(c_13581,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK5(X1,singleton(X4),unordered_pair(singleton(X0),unordered_pair(sK2(singleton(X4),X5,X3),X0))) = X4 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK1(singleton(X4),X5,X3),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_907]) ).
tcf(c_13582,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(singleton(X2),X3,X4),X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK2(singleton(X2),X3,X4)),unordered_pair(X0,sK2(singleton(X2),X3,X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_906]) ).
tcf(c_13583,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK5(X1,singleton(X4),unordered_pair(unordered_pair(sK2(singleton(X4),X5,X3),X0),singleton(X0))) = X4 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK1(singleton(X4),X5,X3),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_899]) ).
tcf(c_13584,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(singleton(X2),X3,X4),X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X0,sK2(singleton(X2),X3,X4)),singleton(sK2(singleton(X2),X3,X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_898]) ).
tcf(c_13585,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK5(X1,singleton(X4),unordered_pair(singleton(X0),unordered_pair(X0,sK2(singleton(X4),X5,X3)))) = X4 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK1(singleton(X4),X5,X3),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_889]) ).
tcf(c_13586,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(singleton(X2),X3,X4),X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK2(singleton(X2),X3,X4)),unordered_pair(sK2(singleton(X2),X3,X4),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_888]) ).
tcf(c_13587,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK5(X1,singleton(X4),unordered_pair(unordered_pair(X0,sK2(singleton(X4),X5,X3)),singleton(X0))) = X4 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK1(singleton(X4),X5,X3),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_863]) ).
tcf(c_13588,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(singleton(X2),X3,X4),X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK2(singleton(X2),X3,X4),X0),singleton(sK2(singleton(X2),X3,X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_837]) ).
tcf(c_13590,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X0),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(cartesian_product2(X2,X0),X3,X4),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))),unordered_pair(X1,sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_2455,c_2611]) ).
tcf(c_13591,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X0,X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(cartesian_product2(X0,X2),X3,X4),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))),unordered_pair(X1,sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_2455,c_2610]) ).
tcf(c_13592,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X0),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(cartesian_product2(X2,X0),X3,X4),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))),singleton(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_2455,c_2036]) ).
tcf(c_13593,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X0,X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(cartesian_product2(X0,X2),X3,X4),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))),singleton(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_2455,c_2035]) ).
tcf(c_13594,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X0),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(cartesian_product2(X2,X0),X3,X4),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))),unordered_pair(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4)),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_2455,c_1703]) ).
tcf(c_13595,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X0,X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(cartesian_product2(X0,X2),X3,X4),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))),unordered_pair(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4)),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_2455,c_1702]) ).
tcf(c_13596,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X0),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(cartesian_product2(X2,X0),X3,X4),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4)),X1),singleton(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_2455,c_1389]) ).
tcf(c_13597,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X0,X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(cartesian_product2(X0,X2),X3,X4),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4)),X1),singleton(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_2455,c_1388]) ).
tcf(c_13598,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(cartesian_product2(X2,X1),X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK2(cartesian_product2(X2,X1),X3,X4)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_2459]) ).
tcf(c_13599,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(cartesian_product2(X1,X2),X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK2(cartesian_product2(X1,X2),X3,X4)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_2458]) ).
tcf(c_13600,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(cartesian_product2(X2,X1),X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK2(cartesian_product2(X2,X1),X3,X4)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_1857]) ).
tcf(c_13601,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(cartesian_product2(X1,X2),X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK2(cartesian_product2(X1,X2),X3,X4)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_1856]) ).
tcf(c_13602,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(cartesian_product2(X2,X1),X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK2(cartesian_product2(X2,X1),X3,X4))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_1569]) ).
tcf(c_13603,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(cartesian_product2(X1,X2),X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK2(cartesian_product2(X1,X2),X3,X4))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_1568]) ).
tcf(c_13604,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(cartesian_product2(X2,X1),X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK2(cartesian_product2(X2,X1),X3,X4))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_1150]) ).
tcf(c_13605,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(cartesian_product2(X1,X2),X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK2(cartesian_product2(X1,X2),X3,X4))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_1149]) ).
tcf(c_13606,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(X0,X1),X2) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(sK1(cartesian_product2(X0,X1),X2,X3),X4))) = X4 )
| ( unordered_pair(unordered_pair(sK4(X0,X1,sK2(cartesian_product2(X0,X1),X2,X3)),sK5(X0,X1,sK2(cartesian_product2(X0,X1),X2,X3))),singleton(sK4(X0,X1,sK2(cartesian_product2(X0,X1),X2,X3)))) = sK2(cartesian_product2(X0,X1),X2,X3) ) ),
inference(superposition,[status(thm)],[c_2455,c_62]) ).
tcf(c_13607,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK4(singleton(X2),X3,sK2(cartesian_product2(singleton(X2),X3),X4,X5)),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_1935]) ).
tcf(c_13608,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X2),X3,sK2(cartesian_product2(singleton(X2),X3),X4,X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_1649]) ).
tcf(c_13609,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK4(singleton(X2),X3,sK2(cartesian_product2(singleton(X2),X3),X4,X5))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_1312]) ).
tcf(c_13610,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X1 )
| ( sK4(singleton(X2),X3,sK2(cartesian_product2(singleton(X2),X3),X4,X1)) = X2 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X1),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_787]) ).
tcf(c_13611,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,singleton(X2)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X3,singleton(X2)),X4,X5),X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK5(X3,singleton(X2),sK2(cartesian_product2(X3,singleton(X2)),X4,X5)),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_1936]) ).
tcf(c_13612,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,singleton(X2)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X3,singleton(X2)),X4,X5),X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X3,singleton(X2),sK2(cartesian_product2(X3,singleton(X2)),X4,X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_1650]) ).
tcf(c_13613,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,singleton(X2)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X3,singleton(X2)),X4,X5),X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK5(X3,singleton(X2),sK2(cartesian_product2(X3,singleton(X2)),X4,X5))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_1313]) ).
tcf(c_13614,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X1 )
| ( sK5(X2,singleton(X3),sK2(cartesian_product2(X2,singleton(X3)),X4,X1)) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK1(cartesian_product2(X2,singleton(X3)),X4,X1),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_789]) ).
tcf(c_13615,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(singleton(X0),X1),X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(cartesian_product2(cartesian_product2(singleton(X0),X1),X2),X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,sK4(cartesian_product2(singleton(X0),X1),X2,sK2(cartesian_product2(cartesian_product2(singleton(X0),X1),X2),X3,X4))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_835]) ).
tcf(c_13616,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,cartesian_product2(singleton(X0),X1)),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(cartesian_product2(X2,cartesian_product2(singleton(X0),X1)),X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,sK5(X2,cartesian_product2(singleton(X0),X1),sK2(cartesian_product2(X2,cartesian_product2(singleton(X0),X1)),X3,X4))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_836]) ).
tcf(c_13617,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X0,singleton(X1)),X2),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(cartesian_product2(cartesian_product2(X0,singleton(X1)),X2),X3,X4),X5))) = X5 )
| ( sK5(X0,singleton(X1),sK4(cartesian_product2(X0,singleton(X1)),X2,sK2(cartesian_product2(cartesian_product2(X0,singleton(X1)),X2),X3,X4))) = X1 ) ),
inference(superposition,[status(thm)],[c_2455,c_861]) ).
tcf(c_13618,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,cartesian_product2(X0,singleton(X1))),X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(cartesian_product2(X2,cartesian_product2(X0,singleton(X1))),X3,X4),X5))) = X5 )
| ( sK5(X0,singleton(X1),sK5(X2,cartesian_product2(X0,singleton(X1)),sK2(cartesian_product2(X2,cartesian_product2(X0,singleton(X1))),X3,X4))) = X1 ) ),
inference(superposition,[status(thm)],[c_2455,c_862]) ).
tcf(c_13907,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_13234]) ).
tcf(c_13908,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_1863]) ).
tcf(c_13909,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_12125]) ).
tcf(c_13910,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_1862]) ).
tcf(c_13911,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_11834]) ).
tcf(c_13912,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_1861]) ).
tcf(c_13913,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_11410]) ).
tcf(c_13914,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_1860]) ).
tcf(c_13915,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_10829]) ).
tcf(c_13916,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_1859]) ).
tcf(c_13917,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_10535]) ).
tcf(c_13918,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_1858]) ).
tcf(c_13919,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_8720]) ).
tcf(c_13920,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_1575]) ).
tcf(c_13921,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_8554]) ).
tcf(c_13922,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_1574]) ).
tcf(c_13923,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_8285]) ).
tcf(c_13924,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_1573]) ).
tcf(c_13925,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_8027]) ).
tcf(c_13926,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_1572]) ).
tcf(c_13927,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_7766]) ).
tcf(c_13928,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_1571]) ).
tcf(c_13929,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_7495]) ).
tcf(c_13930,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_1570]) ).
tcf(c_13931,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_6164]) ).
tcf(c_13932,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_1156]) ).
tcf(c_13933,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_5987]) ).
tcf(c_13934,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_1155]) ).
tcf(c_13935,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_5758]) ).
tcf(c_13936,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_1154]) ).
tcf(c_13937,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_5518]) ).
tcf(c_13938,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_1153]) ).
tcf(c_13939,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_5291]) ).
tcf(c_13940,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_1152]) ).
tcf(c_13941,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_4798]) ).
tcf(c_13942,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_1151]) ).
tcf(c_13943,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK4(singleton(X4),X2,unordered_pair(singleton(X4),unordered_pair(sK2(X2,X3,X0),X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,X3,X0)),unordered_pair(X1,sK1(X2,X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_2456,c_2539]) ).
tcf(c_13944,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X2) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(sK1(X1,X2,X3),X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK2(X1,X2,X3),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_2384]) ).
tcf(c_13945,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK4(singleton(X4),X2,unordered_pair(singleton(X4),unordered_pair(sK2(X2,X3,X0),X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK1(X2,X3,X0)),singleton(sK1(X2,X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_2456,c_1929]) ).
tcf(c_13946,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X2) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(sK1(X1,X2,X3),X4),singleton(X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK2(X1,X2,X3),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_1823]) ).
tcf(c_13947,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK4(singleton(X4),X2,unordered_pair(singleton(X4),unordered_pair(sK2(X2,X3,X0),X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,X3,X0)),unordered_pair(sK1(X2,X3,X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_2456,c_1643]) ).
tcf(c_13948,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X2) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(X4,sK1(X1,X2,X3)))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK2(X1,X2,X3),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_1524]) ).
tcf(c_13949,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK4(singleton(X4),X2,unordered_pair(singleton(X4),unordered_pair(sK2(X2,X3,X0),X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(X2,X3,X0),X1),singleton(sK1(X2,X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_2456,c_1306]) ).
tcf(c_13950,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X2) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(X4,sK1(X1,X2,X3)),singleton(X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK2(X1,X2,X3),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_1060]) ).
tcf(c_13951,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(sK1(X3,X4,singleton(X5)),X0))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK2(X3,X4,singleton(X5)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_907]) ).
tcf(c_13952,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,singleton(X2)),X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK1(X3,X4,singleton(X2))),unordered_pair(X0,sK1(X3,X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_906]) ).
tcf(c_13953,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X4,singleton(X5)),X0),singleton(X0))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK2(X3,X4,singleton(X5)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_899]) ).
tcf(c_13954,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,singleton(X2)),X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X0,sK1(X3,X4,singleton(X2))),singleton(sK1(X3,X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_898]) ).
tcf(c_13955,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X3,X4,singleton(X5))))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK2(X3,X4,singleton(X5)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_889]) ).
tcf(c_13956,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,singleton(X2)),X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK1(X3,X4,singleton(X2))),unordered_pair(sK1(X3,X4,singleton(X2)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_888]) ).
tcf(c_13957,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(X0,sK1(X3,X4,singleton(X5))),singleton(X0))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK2(X3,X4,singleton(X5)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_863]) ).
tcf(c_13958,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,singleton(X2)),X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,singleton(X2)),X0),singleton(sK1(X3,X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_837]) ).
tcf(c_13960,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,cartesian_product2(X2,X0)),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))),unordered_pair(X1,sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_2456,c_2611]) ).
tcf(c_13961,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,cartesian_product2(X0,X2)),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))),unordered_pair(X1,sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_2456,c_2610]) ).
tcf(c_13962,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,cartesian_product2(X2,X0)),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))),singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_2456,c_2036]) ).
tcf(c_13963,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,cartesian_product2(X0,X2)),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))),singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_2456,c_2035]) ).
tcf(c_13964,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,cartesian_product2(X2,X0)),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))),unordered_pair(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0))),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_2456,c_1703]) ).
tcf(c_13965,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,cartesian_product2(X0,X2)),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))),unordered_pair(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2))),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_2456,c_1702]) ).
tcf(c_13966,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,cartesian_product2(X2,X0)),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0))),X1),singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_2456,c_1389]) ).
tcf(c_13967,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,cartesian_product2(X0,X2)),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2))),X1),singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_2456,c_1388]) ).
tcf(c_13968,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X1) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,cartesian_product2(X2,X1)),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK1(X3,X4,cartesian_product2(X2,X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_2459]) ).
tcf(c_13969,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,cartesian_product2(X1,X2)),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK1(X3,X4,cartesian_product2(X1,X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_2458]) ).
tcf(c_13970,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X1) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,cartesian_product2(X2,X1)),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK1(X3,X4,cartesian_product2(X2,X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_1857]) ).
tcf(c_13971,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,cartesian_product2(X1,X2)),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK1(X3,X4,cartesian_product2(X1,X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_1856]) ).
tcf(c_13972,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X1) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,cartesian_product2(X2,X1)),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK1(X3,X4,cartesian_product2(X2,X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_1569]) ).
tcf(c_13973,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,cartesian_product2(X1,X2)),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK1(X3,X4,cartesian_product2(X1,X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_1568]) ).
tcf(c_13974,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X1) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,cartesian_product2(X2,X1)),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK1(X3,X4,cartesian_product2(X2,X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_1150]) ).
tcf(c_13975,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,cartesian_product2(X1,X2)),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK1(X3,X4,cartesian_product2(X1,X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_1149]) ).
tcf(c_13976,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( sK4(singleton(X4),X2,unordered_pair(singleton(X4),unordered_pair(sK2(X2,X3,cartesian_product2(X0,X1)),X4))) = X4 )
| ( unordered_pair(unordered_pair(sK4(X0,X1,sK1(X2,X3,cartesian_product2(X0,X1))),sK5(X0,X1,sK1(X2,X3,cartesian_product2(X0,X1)))),singleton(sK4(X0,X1,sK1(X2,X3,cartesian_product2(X0,X1))))) = sK1(X2,X3,cartesian_product2(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_2456,c_62]) ).
tcf(c_13977,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK4(singleton(X2),X3,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_1935]) ).
tcf(c_13978,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X2),X3,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_1649]) ).
tcf(c_13979,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK4(singleton(X2),X3,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_1312]) ).
tcf(c_13980,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = cartesian_product2(X1,X2) )
| ( sK4(singleton(X3),X4,sK1(X1,X2,cartesian_product2(singleton(X3),X4))) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK2(X1,X2,cartesian_product2(singleton(X3),X4)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_787]) ).
tcf(c_13981,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X3,singleton(X2))),X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK5(X3,singleton(X2),sK1(X4,X5,cartesian_product2(X3,singleton(X2)))),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_1936]) ).
tcf(c_13982,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X3,singleton(X2))),X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X3,singleton(X2),sK1(X4,X5,cartesian_product2(X3,singleton(X2))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_1650]) ).
tcf(c_13983,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X3,singleton(X2))),X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK5(X3,singleton(X2),sK1(X4,X5,cartesian_product2(X3,singleton(X2))))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_1313]) ).
tcf(c_13984,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = cartesian_product2(X1,X2) )
| ( sK5(X3,singleton(X4),sK1(X1,X2,cartesian_product2(X3,singleton(X4)))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK2(X1,X2,cartesian_product2(X3,singleton(X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_789]) ).
tcf(c_13985,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X0),X1),X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,cartesian_product2(cartesian_product2(singleton(X0),X1),X2)),X5))) = X5 )
| ( sK4(singleton(X0),X1,sK4(cartesian_product2(singleton(X0),X1),X2,sK1(X3,X4,cartesian_product2(cartesian_product2(singleton(X0),X1),X2)))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_835]) ).
tcf(c_13986,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(singleton(X0),X1)) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,cartesian_product2(X2,cartesian_product2(singleton(X0),X1))),X5))) = X5 )
| ( sK4(singleton(X0),X1,sK5(X2,cartesian_product2(singleton(X0),X1),sK1(X3,X4,cartesian_product2(X2,cartesian_product2(singleton(X0),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_836]) ).
tcf(c_13987,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X0,singleton(X1)),X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,cartesian_product2(cartesian_product2(X0,singleton(X1)),X2)),X5))) = X5 )
| ( sK5(X0,singleton(X1),sK4(cartesian_product2(X0,singleton(X1)),X2,sK1(X3,X4,cartesian_product2(cartesian_product2(X0,singleton(X1)),X2)))) = X1 ) ),
inference(superposition,[status(thm)],[c_2456,c_861]) ).
tcf(c_13988,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(X0,singleton(X1))) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,cartesian_product2(X2,cartesian_product2(X0,singleton(X1)))),X5))) = X5 )
| ( sK5(X0,singleton(X1),sK5(X2,cartesian_product2(X0,singleton(X1)),sK1(X3,X4,cartesian_product2(X2,cartesian_product2(X0,singleton(X1)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_2456,c_862]) ).
tcf(c_14342,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_13234]) ).
tcf(c_14343,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_1863]) ).
tcf(c_14344,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_12125]) ).
tcf(c_14345,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_1862]) ).
tcf(c_14346,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_11834]) ).
tcf(c_14347,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_1861]) ).
tcf(c_14348,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_11410]) ).
tcf(c_14349,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_1860]) ).
tcf(c_14350,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_10829]) ).
tcf(c_14351,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_1859]) ).
tcf(c_14352,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_10535]) ).
tcf(c_14353,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_1858]) ).
tcf(c_14354,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_8720]) ).
tcf(c_14355,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_1575]) ).
tcf(c_14356,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_8554]) ).
tcf(c_14357,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_1574]) ).
tcf(c_14358,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_8285]) ).
tcf(c_14359,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_1573]) ).
tcf(c_14360,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_8027]) ).
tcf(c_14361,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_1572]) ).
tcf(c_14362,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_7766]) ).
tcf(c_14363,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_1571]) ).
tcf(c_14364,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_7495]) ).
tcf(c_14365,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_1570]) ).
tcf(c_14366,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_6164]) ).
tcf(c_14367,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_1156]) ).
tcf(c_14368,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_5987]) ).
tcf(c_14369,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_1155]) ).
tcf(c_14370,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_5758]) ).
tcf(c_14371,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_1154]) ).
tcf(c_14372,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_5518]) ).
tcf(c_14373,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_1153]) ).
tcf(c_14374,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_5291]) ).
tcf(c_14375,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_1152]) ).
tcf(c_14376,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_4798]) ).
tcf(c_14377,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_1151]) ).
tcf(c_14378,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(sK3(X2,X3,X0),X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,X3,X0)),unordered_pair(X1,sK1(X2,X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_2457,c_2539]) ).
tcf(c_14379,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X1) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(sK1(X2,X1,X3),X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK3(X2,X1,X3),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_2384]) ).
tcf(c_14380,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(sK3(X2,X3,X0),X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK1(X2,X3,X0)),singleton(sK1(X2,X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_2457,c_1929]) ).
tcf(c_14381,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X1) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(sK1(X2,X1,X3),X4),singleton(X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK3(X2,X1,X3),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_1823]) ).
tcf(c_14382,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(sK3(X2,X3,X0),X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,X3,X0)),unordered_pair(sK1(X2,X3,X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_2457,c_1643]) ).
tcf(c_14383,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X1) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(X4,sK1(X2,X1,X3)))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK3(X2,X1,X3),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_1524]) ).
tcf(c_14384,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(sK3(X2,X3,X0),X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(X2,X3,X0),X1),singleton(sK1(X2,X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_2457,c_1306]) ).
tcf(c_14385,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X1) = X3 )
| ( sK4(singleton(X4),X3,unordered_pair(unordered_pair(X4,sK1(X2,X1,X3)),singleton(X4))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK3(X2,X1,X3),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_1060]) ).
tcf(c_14386,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(sK1(X4,X3,singleton(X5)),X0))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK3(X4,X3,singleton(X5)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_907]) ).
tcf(c_14387,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,singleton(X2)),X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK1(X3,X4,singleton(X2))),unordered_pair(X0,sK1(X3,X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_906]) ).
tcf(c_14388,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(sK1(X4,X3,singleton(X5)),X0),singleton(X0))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK3(X4,X3,singleton(X5)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_899]) ).
tcf(c_14389,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,singleton(X2)),X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X0,sK1(X3,X4,singleton(X2))),singleton(sK1(X3,X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_898]) ).
tcf(c_14390,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X3,singleton(X5))))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK3(X4,X3,singleton(X5)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_889]) ).
tcf(c_14391,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,singleton(X2)),X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK1(X3,X4,singleton(X2))),unordered_pair(sK1(X3,X4,singleton(X2)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_888]) ).
tcf(c_14392,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(X0,sK1(X4,X3,singleton(X5))),singleton(X0))) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK3(X4,X3,singleton(X5)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_863]) ).
tcf(c_14393,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,singleton(X2)),X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,singleton(X2)),X0),singleton(sK1(X3,X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_837]) ).
tcf(c_14395,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,cartesian_product2(X2,X0)),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))),unordered_pair(X1,sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_2457,c_2611]) ).
tcf(c_14396,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,cartesian_product2(X0,X2)),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))),unordered_pair(X1,sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_2457,c_2610]) ).
tcf(c_14397,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,cartesian_product2(X2,X0)),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))),singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_2457,c_2036]) ).
tcf(c_14398,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,cartesian_product2(X0,X2)),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))),singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_2457,c_2035]) ).
tcf(c_14399,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,cartesian_product2(X2,X0)),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))),unordered_pair(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0))),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_2457,c_1703]) ).
tcf(c_14400,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,cartesian_product2(X0,X2)),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))),unordered_pair(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2))),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_2457,c_1702]) ).
tcf(c_14401,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,cartesian_product2(X2,X0)),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0))),X1),singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_2457,c_1389]) ).
tcf(c_14402,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,cartesian_product2(X0,X2)),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2))),X1),singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_2457,c_1388]) ).
tcf(c_14403,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X1) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,cartesian_product2(X2,X1)),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK1(X3,X4,cartesian_product2(X2,X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_2459]) ).
tcf(c_14404,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,cartesian_product2(X1,X2)),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK1(X3,X4,cartesian_product2(X1,X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_2458]) ).
tcf(c_14405,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X1) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,cartesian_product2(X2,X1)),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK1(X3,X4,cartesian_product2(X2,X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_1857]) ).
tcf(c_14406,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,cartesian_product2(X1,X2)),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK1(X3,X4,cartesian_product2(X1,X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_1856]) ).
tcf(c_14407,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X1) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,cartesian_product2(X2,X1)),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK1(X3,X4,cartesian_product2(X2,X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_1569]) ).
tcf(c_14408,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,cartesian_product2(X1,X2)),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK1(X3,X4,cartesian_product2(X1,X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_1568]) ).
tcf(c_14409,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X1) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,cartesian_product2(X2,X1)),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK1(X3,X4,cartesian_product2(X2,X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_1150]) ).
tcf(c_14410,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,cartesian_product2(X1,X2)),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK1(X3,X4,cartesian_product2(X1,X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_1149]) ).
tcf(c_14411,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( sK4(singleton(X4),X3,unordered_pair(singleton(X4),unordered_pair(sK3(X2,X3,cartesian_product2(X0,X1)),X4))) = X4 )
| ( unordered_pair(unordered_pair(sK4(X0,X1,sK1(X2,X3,cartesian_product2(X0,X1))),sK5(X0,X1,sK1(X2,X3,cartesian_product2(X0,X1)))),singleton(sK4(X0,X1,sK1(X2,X3,cartesian_product2(X0,X1))))) = sK1(X2,X3,cartesian_product2(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_2457,c_62]) ).
tcf(c_14412,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK4(singleton(X2),X3,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_1935]) ).
tcf(c_14413,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X2),X3,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_1649]) ).
tcf(c_14414,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK4(singleton(X2),X3,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_1312]) ).
tcf(c_14415,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = cartesian_product2(X2,X1) )
| ( sK4(singleton(X3),X4,sK1(X2,X1,cartesian_product2(singleton(X3),X4))) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK3(X2,X1,cartesian_product2(singleton(X3),X4)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_787]) ).
tcf(c_14416,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X3,singleton(X2))),X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(sK5(X3,singleton(X2),sK1(X4,X5,cartesian_product2(X3,singleton(X2)))),X0),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_1936]) ).
tcf(c_14417,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X3,singleton(X2))),X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X3,singleton(X2),sK1(X4,X5,cartesian_product2(X3,singleton(X2))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_1650]) ).
tcf(c_14418,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X3,singleton(X2))),X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(unordered_pair(X0,sK5(X3,singleton(X2),sK1(X4,X5,cartesian_product2(X3,singleton(X2))))),singleton(X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_1313]) ).
tcf(c_14419,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = cartesian_product2(X2,X1) )
| ( sK5(X3,singleton(X4),sK1(X2,X1,cartesian_product2(X3,singleton(X4)))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK3(X2,X1,cartesian_product2(X3,singleton(X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_789]) ).
tcf(c_14420,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X0),X1),X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,cartesian_product2(cartesian_product2(singleton(X0),X1),X2)),X5))) = X5 )
| ( sK4(singleton(X0),X1,sK4(cartesian_product2(singleton(X0),X1),X2,sK1(X3,X4,cartesian_product2(cartesian_product2(singleton(X0),X1),X2)))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_835]) ).
tcf(c_14421,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(singleton(X0),X1)) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,cartesian_product2(X2,cartesian_product2(singleton(X0),X1))),X5))) = X5 )
| ( sK4(singleton(X0),X1,sK5(X2,cartesian_product2(singleton(X0),X1),sK1(X3,X4,cartesian_product2(X2,cartesian_product2(singleton(X0),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_836]) ).
tcf(c_14422,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X0,singleton(X1)),X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,cartesian_product2(cartesian_product2(X0,singleton(X1)),X2)),X5))) = X5 )
| ( sK5(X0,singleton(X1),sK4(cartesian_product2(X0,singleton(X1)),X2,sK1(X3,X4,cartesian_product2(cartesian_product2(X0,singleton(X1)),X2)))) = X1 ) ),
inference(superposition,[status(thm)],[c_2457,c_861]) ).
tcf(c_14423,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(X0,singleton(X1))) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,cartesian_product2(X2,cartesian_product2(X0,singleton(X1)))),X5))) = X5 )
| ( sK5(X0,singleton(X1),sK5(X2,cartesian_product2(X0,singleton(X1)),sK1(X3,X4,cartesian_product2(X2,cartesian_product2(X0,singleton(X1)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_2457,c_862]) ).
tcf(c_14882,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),cartesian_product2(X1,singleton(X3)),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,X3),singleton(X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2460]) ).
tcf(c_14883,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2460]) ).
tcf(c_14884,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2460]) ).
tcf(c_14885,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2460]) ).
tcf(c_14886,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2460]) ).
tcf(c_14887,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2460]) ).
tcf(c_14888,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X4,X1),unordered_pair(singleton(X5),unordered_pair(unordered_pair(unordered_pair(X3,sK4(X1,X2,X0)),singleton(X3)),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2460]) ).
tcf(c_14889,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X4,X2),unordered_pair(singleton(X5),unordered_pair(unordered_pair(unordered_pair(X3,sK5(X1,X2,X0)),singleton(X3)),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2460]) ).
tcf(c_14890,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X3,X1)),unordered_pair(singleton(X6),unordered_pair(unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))),singleton(X4)),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2460]) ).
tcf(c_14891,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X1,X3)),unordered_pair(singleton(X6),unordered_pair(unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))),singleton(X4)),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2460]) ).
tcf(c_14892,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X1,X3)),unordered_pair(singleton(X6),unordered_pair(unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))),singleton(X4)),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2460]) ).
tcf(c_14893,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X1,X3)),unordered_pair(singleton(X6),unordered_pair(unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))),singleton(X4)),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2460]) ).
tcf(c_14894,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X3,X1)),unordered_pair(singleton(X6),unordered_pair(unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))),singleton(X4)),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2460]) ).
tcf(c_14895,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X3,X1)),unordered_pair(singleton(X6),unordered_pair(unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))),singleton(X4)),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2460]) ).
tcf(c_14897,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK1(singleton(X4),X5,X3)),singleton(X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2460]) ).
tcf(c_14898,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK2(X3,X4,singleton(X5))),singleton(X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2460]) ).
tcf(c_14899,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,singleton(X5),X3)),singleton(X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2460]) ).
tcf(c_14900,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK3(X4,X3,singleton(X5))),singleton(X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2460]) ).
tcf(c_14901,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2460]) ).
tcf(c_14902,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2460]) ).
tcf(c_14903,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2460]) ).
tcf(c_14904,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2460]) ).
tcf(c_14905,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2460]) ).
tcf(c_14906,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2460]) ).
tcf(c_14907,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2460]) ).
tcf(c_14908,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2460]) ).
tcf(c_14909,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2460]) ).
tcf(c_14910,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2460]) ).
tcf(c_14911,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2460]) ).
tcf(c_14912,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2460]) ).
tcf(c_14913,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2460]) ).
tcf(c_14914,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2460]) ).
tcf(c_14915,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2460]) ).
tcf(c_14916,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2460]) ).
tcf(c_15083,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X1),sK3(X3,X4,X1)),singleton(sK2(X3,X4,X1))) = sK1(X3,X4,X1) )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_14882]) ).
tcf(c_15084,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X1),X4)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_14882]) ).
tcf(c_15085,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X1),X3)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_14882]) ).
tcf(c_15086,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X1,X3,X4),X4)
| ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_14882]) ).
tcf(c_15087,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X1,X4),X4)
| ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_14882]) ).
tcf(c_15088,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(X1,singleton(X4)),unordered_pair(singleton(X3),unordered_pair(unordered_pair(unordered_pair(sK4(X1,X2,X0),X4),singleton(sK4(X1,X2,X0))),X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_14882]) ).
tcf(c_15089,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(X2,singleton(X4)),unordered_pair(singleton(X3),unordered_pair(unordered_pair(unordered_pair(sK5(X1,X2,X0),X4),singleton(sK5(X1,X2,X0))),X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_14882]) ).
tcf(c_15090,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X3,X1),singleton(X5)),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2)))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_14882]) ).
tcf(c_15091,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X1,X3),singleton(X5)),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5),singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2)))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_14882]) ).
tcf(c_15092,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X1,X3),singleton(X5)),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0)))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_14882]) ).
tcf(c_15093,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X1,X3),singleton(X5)),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5),singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0)))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_14882]) ).
tcf(c_15094,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X3,X1),singleton(X5)),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5),singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2)))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_14882]) ).
tcf(c_15095,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X3,X1),singleton(X5)),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5),singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0)))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_14882]) ).
tcf(c_15097,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X1 )
| ( sK2(singleton(X3),X4,X1) = X3 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK1(singleton(X3),X4,X1),X2),singleton(sK1(singleton(X3),X4,X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_14882]) ).
tcf(c_15098,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X3) = singleton(X4) )
| ( sK1(X1,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK2(X1,X3,singleton(X4)),X2),singleton(sK2(X1,X3,singleton(X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_14882]) ).
tcf(c_15099,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X1 )
| ( sK3(X3,singleton(X4),X1) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK1(X3,singleton(X4),X1),X2),singleton(sK1(X3,singleton(X4),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_14882]) ).
tcf(c_15100,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X1) = singleton(X4) )
| ( sK1(X3,X1,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK3(X3,X1,singleton(X4)),X2),singleton(sK3(X3,X1,singleton(X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_14882]) ).
tcf(c_15101,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_14882]) ).
tcf(c_15102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_14882]) ).
tcf(c_15103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_14882]) ).
tcf(c_15104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X1,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_14882]) ).
tcf(c_15105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_14882]) ).
tcf(c_15106,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_14882]) ).
tcf(c_15107,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_14882]) ).
tcf(c_15108,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X1,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_14882]) ).
tcf(c_15109,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_14882]) ).
tcf(c_15110,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_14882]) ).
tcf(c_15111,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_14882]) ).
tcf(c_15112,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_14882]) ).
tcf(c_15113,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_14882]) ).
tcf(c_15114,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_14882]) ).
tcf(c_15115,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_14882]) ).
tcf(c_15116,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_14882]) ).
tcf(c_15187,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),cartesian_product2(singleton(X3),X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X3),unordered_pair(X3,X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2461]) ).
tcf(c_15188,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2461]) ).
tcf(c_15189,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2461]) ).
tcf(c_15190,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2461]) ).
tcf(c_15191,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2461]) ).
tcf(c_15192,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2461]) ).
tcf(c_15193,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X1,X4),unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(sK4(X1,X2,X0),X3)),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2461]) ).
tcf(c_15194,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X2,X4),unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(sK5(X1,X2,X0),X3)),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2461]) ).
tcf(c_15195,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X3,X1),X5),unordered_pair(singleton(X6),unordered_pair(unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X4)),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2461]) ).
tcf(c_15196,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X1,X3),X5),unordered_pair(singleton(X6),unordered_pair(unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X4)),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2461]) ).
tcf(c_15197,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X1,X3),X5),unordered_pair(singleton(X6),unordered_pair(unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X4)),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2461]) ).
tcf(c_15198,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X1,X3),X5),unordered_pair(singleton(X6),unordered_pair(unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X4)),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2461]) ).
tcf(c_15199,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X3,X1),X5),unordered_pair(singleton(X6),unordered_pair(unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X4)),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2461]) ).
tcf(c_15200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X3,X1),X5),unordered_pair(singleton(X6),unordered_pair(unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X4)),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2461]) ).
tcf(c_15202,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK1(singleton(X4),X5,X3)),unordered_pair(sK1(singleton(X4),X5,X3),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2461]) ).
tcf(c_15203,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK2(X3,X4,singleton(X5))),unordered_pair(sK2(X3,X4,singleton(X5)),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2461]) ).
tcf(c_15204,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK1(X4,singleton(X5),X3)),unordered_pair(sK1(X4,singleton(X5),X3),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2461]) ).
tcf(c_15205,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK3(X4,X3,singleton(X5))),unordered_pair(sK3(X4,X3,singleton(X5)),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2461]) ).
tcf(c_15206,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2461]) ).
tcf(c_15207,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2461]) ).
tcf(c_15208,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2461]) ).
tcf(c_15209,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2461]) ).
tcf(c_15210,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2461]) ).
tcf(c_15211,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2461]) ).
tcf(c_15212,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2461]) ).
tcf(c_15213,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2461]) ).
tcf(c_15214,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2461]) ).
tcf(c_15215,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2461]) ).
tcf(c_15216,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2461]) ).
tcf(c_15217,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2461]) ).
tcf(c_15218,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2461]) ).
tcf(c_15219,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2461]) ).
tcf(c_15220,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2461]) ).
tcf(c_15221,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2461]) ).
tcf(c_15371,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X2),sK3(X3,X4,X2)),singleton(sK2(X3,X4,X2))) = sK1(X3,X4,X2) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_15187]) ).
tcf(c_15372,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X2),X4)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_15187]) ).
tcf(c_15373,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X2),X3)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_15187]) ).
tcf(c_15374,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X2,X3,X4),X4)
| ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_15187]) ).
tcf(c_15375,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X2,X4),X4)
| ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_15187]) ).
tcf(c_15376,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(singleton(X4),X1),unordered_pair(singleton(X3),unordered_pair(unordered_pair(singleton(X4),unordered_pair(X4,sK4(X1,X2,X0))),X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_15187]) ).
tcf(c_15377,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(singleton(X4),X2),unordered_pair(singleton(X3),unordered_pair(unordered_pair(singleton(X4),unordered_pair(X4,sK5(X1,X2,X0))),X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_15187]) ).
tcf(c_15378,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X3,X1)),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X2)))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_15187]) ).
tcf(c_15379,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X1,X3)),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X0,X2)))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_15187]) ).
tcf(c_15380,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X1,X3)),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X0)))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_15187]) ).
tcf(c_15381,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X1,X3)),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X2,X0)))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_15187]) ).
tcf(c_15382,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X3,X1)),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X0,X2)))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_15187]) ).
tcf(c_15383,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X3,X1)),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X2,X0)))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_15187]) ).
tcf(c_15385,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X2 )
| ( sK2(singleton(X3),X4,X2) = X3 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK1(singleton(X3),X4,X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_15187]) ).
tcf(c_15386,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK1(X2,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,singleton(X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_15187]) ).
tcf(c_15387,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X2 )
| ( sK3(X3,singleton(X4),X2) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,singleton(X4),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_15187]) ).
tcf(c_15388,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X2) = singleton(X4) )
| ( sK1(X3,X2,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,singleton(X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_15187]) ).
tcf(c_15389,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_15187]) ).
tcf(c_15390,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_15187]) ).
tcf(c_15391,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_15187]) ).
tcf(c_15392,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X2,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_15187]) ).
tcf(c_15393,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_15187]) ).
tcf(c_15394,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_15187]) ).
tcf(c_15395,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_15187]) ).
tcf(c_15396,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X2,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_15187]) ).
tcf(c_15397,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_15187]) ).
tcf(c_15398,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_15187]) ).
tcf(c_15399,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_15187]) ).
tcf(c_15400,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_15187]) ).
tcf(c_15401,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_15187]) ).
tcf(c_15402,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_15187]) ).
tcf(c_15403,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_15187]) ).
tcf(c_15404,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_15187]) ).
tcf(c_15658,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),cartesian_product2(singleton(X3),X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,X3),singleton(X3)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2462]) ).
tcf(c_15659,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2462]) ).
tcf(c_15660,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2462]) ).
tcf(c_15661,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2462]) ).
tcf(c_15662,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2462]) ).
tcf(c_15663,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2462]) ).
tcf(c_15664,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X1,X4),unordered_pair(singleton(X5),unordered_pair(unordered_pair(unordered_pair(X3,sK4(X1,X2,X0)),singleton(sK4(X1,X2,X0))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2462]) ).
tcf(c_15665,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X2,X4),unordered_pair(singleton(X5),unordered_pair(unordered_pair(unordered_pair(X3,sK5(X1,X2,X0)),singleton(sK5(X1,X2,X0))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2462]) ).
tcf(c_15666,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X3,X1),X5),unordered_pair(singleton(X6),unordered_pair(unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2)))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2462]) ).
tcf(c_15667,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X1,X3),X5),unordered_pair(singleton(X6),unordered_pair(unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))),singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2)))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2462]) ).
tcf(c_15668,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X1,X3),X5),unordered_pair(singleton(X6),unordered_pair(unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0)))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2462]) ).
tcf(c_15669,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X1,X3),X5),unordered_pair(singleton(X6),unordered_pair(unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))),singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0)))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2462]) ).
tcf(c_15670,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X3,X1),X5),unordered_pair(singleton(X6),unordered_pair(unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))),singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2)))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2462]) ).
tcf(c_15671,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X3,X1),X5),unordered_pair(singleton(X6),unordered_pair(unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))),singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0)))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2462]) ).
tcf(c_15673,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK1(singleton(X4),X5,X3)),singleton(sK1(singleton(X4),X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2462]) ).
tcf(c_15674,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK2(X3,X4,singleton(X5))),singleton(sK2(X3,X4,singleton(X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2462]) ).
tcf(c_15675,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,singleton(X5),X3)),singleton(sK1(X4,singleton(X5),X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2462]) ).
tcf(c_15676,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK3(X4,X3,singleton(X5))),singleton(sK3(X4,X3,singleton(X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2462]) ).
tcf(c_15677,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2462]) ).
tcf(c_15678,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2462]) ).
tcf(c_15679,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2462]) ).
tcf(c_15680,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2462]) ).
tcf(c_15681,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2462]) ).
tcf(c_15682,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2462]) ).
tcf(c_15683,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2462]) ).
tcf(c_15684,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2462]) ).
tcf(c_15685,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2462]) ).
tcf(c_15686,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2462]) ).
tcf(c_15687,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2462]) ).
tcf(c_15688,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2462]) ).
tcf(c_15689,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2462]) ).
tcf(c_15690,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2462]) ).
tcf(c_15691,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2462]) ).
tcf(c_15692,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2462]) ).
tcf(c_15717,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X2),sK3(X3,X4,X2)),singleton(sK2(X3,X4,X2))) = sK1(X3,X4,X2) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_15658]) ).
tcf(c_15718,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X2),X4)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_15658]) ).
tcf(c_15719,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X2),X3)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_15658]) ).
tcf(c_15720,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X2,X3,X4),X4)
| ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_15658]) ).
tcf(c_15721,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X2,X4),X4)
| ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_15658]) ).
tcf(c_15722,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(singleton(X4),X1),unordered_pair(singleton(X3),unordered_pair(unordered_pair(unordered_pair(sK4(X1,X2,X0),X4),singleton(X4)),X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_15658]) ).
tcf(c_15723,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(singleton(X4),X2),unordered_pair(singleton(X3),unordered_pair(unordered_pair(unordered_pair(sK5(X1,X2,X0),X4),singleton(X4)),X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_15658]) ).
tcf(c_15724,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X3,X1)),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5),singleton(X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_15658]) ).
tcf(c_15725,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X1,X3)),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5),singleton(X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_15658]) ).
tcf(c_15726,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X1,X3)),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5),singleton(X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_15658]) ).
tcf(c_15727,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X1,X3)),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5),singleton(X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_15658]) ).
tcf(c_15728,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X3,X1)),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5),singleton(X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_15658]) ).
tcf(c_15729,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X3,X1)),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5),singleton(X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_15658]) ).
tcf(c_15731,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X2 )
| ( sK2(singleton(X3),X4,X2) = X3 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK1(singleton(X3),X4,X2),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_15658]) ).
tcf(c_15732,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK1(X2,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK2(X2,X3,singleton(X4)),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_15658]) ).
tcf(c_15733,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X2 )
| ( sK3(X3,singleton(X4),X2) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK1(X3,singleton(X4),X2),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_15658]) ).
tcf(c_15734,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X2) = singleton(X4) )
| ( sK1(X3,X2,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK3(X3,X2,singleton(X4)),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_15658]) ).
tcf(c_15735,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_15658]) ).
tcf(c_15736,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_15658]) ).
tcf(c_15737,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_15658]) ).
tcf(c_15738,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X2,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_15658]) ).
tcf(c_15739,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_15658]) ).
tcf(c_15740,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_15658]) ).
tcf(c_15741,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_15658]) ).
tcf(c_15742,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X2,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_15658]) ).
tcf(c_15743,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_15658]) ).
tcf(c_15744,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_15658]) ).
tcf(c_15745,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_15658]) ).
tcf(c_15746,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_15658]) ).
tcf(c_15747,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_15658]) ).
tcf(c_15748,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_15658]) ).
tcf(c_15749,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_15658]) ).
tcf(c_15750,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_15658]) ).
tcf(c_16125,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),cartesian_product2(singleton(X3),X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X3),unordered_pair(X0,X3)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2463]) ).
tcf(c_16126,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2463]) ).
tcf(c_16127,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2463]) ).
tcf(c_16128,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2463]) ).
tcf(c_16129,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2463]) ).
tcf(c_16130,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2463]) ).
tcf(c_16131,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X1,X4),unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(X3,sK4(X1,X2,X0))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2463]) ).
tcf(c_16132,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X2,X4),unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(X3,sK5(X1,X2,X0))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2463]) ).
tcf(c_16133,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X3,X1),X5),unordered_pair(singleton(X6),unordered_pair(unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2)))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2463]) ).
tcf(c_16134,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X1,X3),X5),unordered_pair(singleton(X6),unordered_pair(unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2)))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2463]) ).
tcf(c_16135,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X1,X3),X5),unordered_pair(singleton(X6),unordered_pair(unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0)))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2463]) ).
tcf(c_16136,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X1,X3),X5),unordered_pair(singleton(X6),unordered_pair(unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0)))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2463]) ).
tcf(c_16137,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X3,X1),X5),unordered_pair(singleton(X6),unordered_pair(unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2)))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2463]) ).
tcf(c_16138,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(cartesian_product2(X3,X1),X5),unordered_pair(singleton(X6),unordered_pair(unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0)))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2463]) ).
tcf(c_16140,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK1(singleton(X4),X5,X3)),unordered_pair(X0,sK1(singleton(X4),X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2463]) ).
tcf(c_16141,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK2(X3,X4,singleton(X5))),unordered_pair(X0,sK2(X3,X4,singleton(X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2463]) ).
tcf(c_16142,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK1(X4,singleton(X5),X3)),unordered_pair(X0,sK1(X4,singleton(X5),X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2463]) ).
tcf(c_16143,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK3(X4,X3,singleton(X5))),unordered_pair(X0,sK3(X4,X3,singleton(X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2463]) ).
tcf(c_16144,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2463]) ).
tcf(c_16145,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2463]) ).
tcf(c_16146,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2463]) ).
tcf(c_16147,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2463]) ).
tcf(c_16148,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2463]) ).
tcf(c_16149,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2463]) ).
tcf(c_16150,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2463]) ).
tcf(c_16151,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2463]) ).
tcf(c_16152,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2463]) ).
tcf(c_16153,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2463]) ).
tcf(c_16154,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2463]) ).
tcf(c_16155,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2463]) ).
tcf(c_16156,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2463]) ).
tcf(c_16157,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2463]) ).
tcf(c_16158,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2463]) ).
tcf(c_16159,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2463]) ).
tcf(c_16261,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X2),sK3(X3,X4,X2)),singleton(sK2(X3,X4,X2))) = sK1(X3,X4,X2) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_16125]) ).
tcf(c_16262,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X2),X4)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_16125]) ).
tcf(c_16263,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X2),X3)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_16125]) ).
tcf(c_16264,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X2,X3,X4),X4)
| ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_16125]) ).
tcf(c_16265,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X2,X4),X4)
| ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_16125]) ).
tcf(c_16266,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(singleton(X4),X1),unordered_pair(singleton(X3),unordered_pair(unordered_pair(singleton(X4),unordered_pair(sK4(X1,X2,X0),X4)),X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_16125]) ).
tcf(c_16267,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(singleton(X4),X2),unordered_pair(singleton(X3),unordered_pair(unordered_pair(singleton(X4),unordered_pair(sK5(X1,X2,X0),X4)),X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_16125]) ).
tcf(c_16268,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X3,X1)),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_16125]) ).
tcf(c_16269,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X1,X3)),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_16125]) ).
tcf(c_16270,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X1,X3)),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_16125]) ).
tcf(c_16271,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X1,X3)),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_16125]) ).
tcf(c_16272,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X3,X1)),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_16125]) ).
tcf(c_16273,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),cartesian_product2(X3,X1)),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_16125]) ).
tcf(c_16275,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X2 )
| ( sK2(singleton(X3),X4,X2) = X3 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK1(singleton(X3),X4,X2),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_16125]) ).
tcf(c_16276,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK1(X2,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,singleton(X4)),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_16125]) ).
tcf(c_16277,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X2 )
| ( sK3(X3,singleton(X4),X2) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK1(X3,singleton(X4),X2),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_16125]) ).
tcf(c_16278,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X2) = singleton(X4) )
| ( sK1(X3,X2,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,singleton(X4)),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_16125]) ).
tcf(c_16279,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_16125]) ).
tcf(c_16280,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_16125]) ).
tcf(c_16281,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_16125]) ).
tcf(c_16282,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X2,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_16125]) ).
tcf(c_16283,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_16125]) ).
tcf(c_16284,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_16125]) ).
tcf(c_16285,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_16125]) ).
tcf(c_16286,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X2,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_16125]) ).
tcf(c_16287,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_16125]) ).
tcf(c_16288,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_16125]) ).
tcf(c_16289,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_16125]) ).
tcf(c_16290,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_16125]) ).
tcf(c_16291,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_16125]) ).
tcf(c_16292,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_16125]) ).
tcf(c_16293,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_16125]) ).
tcf(c_16294,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_16125]) ).
tcf(c_16411,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X2,X3) )
| ( sK5(X1,singleton(X4),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X4),X5,sK1(X2,X3,cartesian_product2(singleton(X4),X5))),X0))) = X4 )
| ( unordered_pair(unordered_pair(sK2(X2,X3,cartesian_product2(singleton(X4),X5)),sK3(X2,X3,cartesian_product2(singleton(X4),X5))),singleton(sK2(X2,X3,cartesian_product2(singleton(X4),X5)))) = sK1(X2,X3,cartesian_product2(singleton(X4),X5)) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2545]) ).
tcf(c_16412,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X5)
| ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X2),X3,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2545]) ).
tcf(c_16413,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X4)
| ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X2),X3,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2545]) ).
tcf(c_16414,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X2),X3,sK2(cartesian_product2(singleton(X2),X3),X4,X5)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2545]) ).
tcf(c_16415,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X2),X3,sK3(X4,cartesian_product2(singleton(X2),X3),X5)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2545]) ).
tcf(c_16416,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X1),unordered_pair(singleton(X4),unordered_pair(sK4(singleton(X1),X2,sK4(cartesian_product2(singleton(X1),X2),X3,X0)),X4))) = X1 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(cartesian_product2(singleton(X1),X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_2545]) ).
tcf(c_16417,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X2),unordered_pair(singleton(X4),unordered_pair(sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),X0)),X4))) = X2 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(X1,cartesian_product2(singleton(X2),X3))) ),
inference(superposition,[status(thm)],[c_61,c_2545]) ).
tcf(c_16418,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X1),unordered_pair(singleton(X4),unordered_pair(sK4(singleton(X1),X3,unordered_pair(unordered_pair(X0,X2),singleton(X0))),X4))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_64,c_2545]) ).
tcf(c_16420,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X1),unordered_pair(singleton(X4),unordered_pair(sK4(singleton(X1),X3,unordered_pair(unordered_pair(X2,X0),singleton(X0))),X4))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_809,c_2545]) ).
tcf(c_16421,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X1),unordered_pair(singleton(X4),unordered_pair(sK4(singleton(X1),X3,unordered_pair(singleton(X0),unordered_pair(X2,X0))),X4))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_882,c_2545]) ).
tcf(c_16423,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X1),unordered_pair(singleton(X4),unordered_pair(sK4(singleton(X1),X3,unordered_pair(singleton(X0),unordered_pair(X0,X2))),X4))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_900,c_2545]) ).
tcf(c_16424,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(singleton(X4),X5) )
| ( sK2(singleton(X4),X5,cartesian_product2(singleton(X2),X3)) = X4 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X2),X3,sK1(singleton(X4),X5,cartesian_product2(singleton(X2),X3))),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2545]) ).
tcf(c_16425,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = singleton(X5) )
| ( sK1(cartesian_product2(singleton(X2),X3),X4,singleton(X5)) = X5 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X2),X3,sK2(cartesian_product2(singleton(X2),X3),X4,singleton(X5))),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2545]) ).
tcf(c_16426,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,singleton(X5)) )
| ( sK3(X4,singleton(X5),cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X2),X3,sK1(X4,singleton(X5),cartesian_product2(singleton(X2),X3))),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2545]) ).
tcf(c_16427,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(singleton(X2),X3),singleton(X5)) = X5 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X2),X3,sK3(X4,cartesian_product2(singleton(X2),X3),singleton(X5))),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2545]) ).
tcf(c_16428,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X2),X3,sK3(X4,cartesian_product2(singleton(X2),X3),X5)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2545]) ).
tcf(c_16429,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X6),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X2),X3,sK3(X4,cartesian_product2(singleton(X2),X3),X5)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2545]) ).
tcf(c_16430,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(singleton(X2),X3),X5)))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X2),X3,sK3(X4,cartesian_product2(singleton(X2),X3),X5)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2545]) ).
tcf(c_16431,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(singleton(X2),X3),X5)),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X2),X3,sK3(X4,cartesian_product2(singleton(X2),X3),X5)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2545]) ).
tcf(c_16432,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X2),X3,sK2(cartesian_product2(singleton(X2),X3),X4,X5)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2545]) ).
tcf(c_16433,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X6),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X2),X3,sK2(cartesian_product2(singleton(X2),X3),X4,X5)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2545]) ).
tcf(c_16434,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(singleton(X2),X3),X4,X5)))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X2),X3,sK2(cartesian_product2(singleton(X2),X3),X4,X5)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2545]) ).
tcf(c_16435,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(singleton(X2),X3),X4,X5)),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X2),X3,sK2(cartesian_product2(singleton(X2),X3),X4,X5)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2545]) ).
tcf(c_16436,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X2),X3,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2545]) ).
tcf(c_16437,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X6),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X2),X3,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2545]) ).
tcf(c_16438,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(singleton(X2),X3))))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X2),X3,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2545]) ).
tcf(c_16439,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X2),X3,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2545]) ).
tcf(c_16440,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X2),X3,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2545]) ).
tcf(c_16441,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X6),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X2),X3,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2545]) ).
tcf(c_16442,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(singleton(X2),X3))))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X2),X3,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2545]) ).
tcf(c_16443,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X2),X3,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2545]) ).
tcf(c_16486,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = cartesian_product2(X2,X3) )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(sK5(X4,singleton(X5),sK1(X2,X3,cartesian_product2(X4,singleton(X5)))),X0))) = X5 )
| ( unordered_pair(unordered_pair(sK2(X2,X3,cartesian_product2(X4,singleton(X5))),sK3(X2,X3,cartesian_product2(X4,singleton(X5)))),singleton(sK2(X2,X3,cartesian_product2(X4,singleton(X5))))) = sK1(X2,X3,cartesian_product2(X4,singleton(X5))) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2546]) ).
tcf(c_16487,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X3,singleton(X2))),X5)
| ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,X5) )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK5(X3,singleton(X2),sK1(X4,X5,cartesian_product2(X3,singleton(X2)))),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2546]) ).
tcf(c_16488,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X3,singleton(X2))),X4)
| ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,X5) )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK5(X3,singleton(X2),sK1(X4,X5,cartesian_product2(X3,singleton(X2)))),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2546]) ).
tcf(c_16489,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X3,singleton(X2)),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X3,singleton(X2)),X4) = X5 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK5(X3,singleton(X2),sK2(cartesian_product2(X3,singleton(X2)),X4,X5)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2546]) ).
tcf(c_16490,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X3,singleton(X2)),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X3,singleton(X2))) = X5 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK5(X3,singleton(X2),sK3(X4,cartesian_product2(X3,singleton(X2)),X5)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2546]) ).
tcf(c_16491,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X2),unordered_pair(singleton(X4),unordered_pair(sK5(X1,singleton(X2),sK4(cartesian_product2(X1,singleton(X2)),X3,X0)),X4))) = X2 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(cartesian_product2(X1,singleton(X2)),X3)) ),
inference(superposition,[status(thm)],[c_60,c_2546]) ).
tcf(c_16492,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X3),unordered_pair(singleton(X4),unordered_pair(sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),X0)),X4))) = X3 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,singleton(X3)))) ),
inference(superposition,[status(thm)],[c_61,c_2546]) ).
tcf(c_16493,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X1),unordered_pair(singleton(X4),unordered_pair(sK5(X3,singleton(X1),unordered_pair(unordered_pair(X2,X0),singleton(X2))),X4))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_64,c_2546]) ).
tcf(c_16495,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X1),unordered_pair(singleton(X4),unordered_pair(sK5(X3,singleton(X1),unordered_pair(unordered_pair(X0,X2),singleton(X2))),X4))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_809,c_2546]) ).
tcf(c_16496,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X1),unordered_pair(singleton(X4),unordered_pair(sK5(X3,singleton(X1),unordered_pair(singleton(X2),unordered_pair(X0,X2))),X4))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_882,c_2546]) ).
tcf(c_16498,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X5,singleton(X1),unordered_pair(singleton(X4),unordered_pair(sK5(X3,singleton(X1),unordered_pair(singleton(X2),unordered_pair(X2,X0))),X4))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_900,c_2546]) ).
tcf(c_16499,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X3,singleton(X2)) )
| ( sK2(singleton(X4),X5,cartesian_product2(X3,singleton(X2))) = X4 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK5(X3,singleton(X2),sK1(singleton(X4),X5,cartesian_product2(X3,singleton(X2)))),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2546]) ).
tcf(c_16500,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X3,singleton(X2)),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X3,singleton(X2)),X4,singleton(X5)) = X5 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK5(X3,singleton(X2),sK2(cartesian_product2(X3,singleton(X2)),X4,singleton(X5))),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2546]) ).
tcf(c_16501,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,singleton(X5)) )
| ( sK3(X4,singleton(X5),cartesian_product2(X3,singleton(X2))) = X5 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK5(X3,singleton(X2),sK1(X4,singleton(X5),cartesian_product2(X3,singleton(X2)))),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2546]) ).
tcf(c_16502,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,singleton(X2))) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X3,singleton(X2)),singleton(X5)) = X5 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK5(X3,singleton(X2),sK3(X4,cartesian_product2(X3,singleton(X2)),singleton(X5))),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2546]) ).
tcf(c_16503,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,singleton(X2))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X3,singleton(X2)),X5),X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK5(X3,singleton(X2),sK3(X4,cartesian_product2(X3,singleton(X2)),X5)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2546]) ).
tcf(c_16504,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,singleton(X2))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,singleton(X2)),X5),X6),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK5(X3,singleton(X2),sK3(X4,cartesian_product2(X3,singleton(X2)),X5)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2546]) ).
tcf(c_16505,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,singleton(X2))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X3,singleton(X2)),X5)))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK5(X3,singleton(X2),sK3(X4,cartesian_product2(X3,singleton(X2)),X5)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2546]) ).
tcf(c_16506,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,singleton(X2))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X3,singleton(X2)),X5)),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK5(X3,singleton(X2),sK3(X4,cartesian_product2(X3,singleton(X2)),X5)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2546]) ).
tcf(c_16507,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,singleton(X2)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X3,singleton(X2)),X4,X5),X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK5(X3,singleton(X2),sK2(cartesian_product2(X3,singleton(X2)),X4,X5)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2546]) ).
tcf(c_16508,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,singleton(X2)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X3,singleton(X2)),X4,X5),X6),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK5(X3,singleton(X2),sK2(cartesian_product2(X3,singleton(X2)),X4,X5)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2546]) ).
tcf(c_16509,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,singleton(X2)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X3,singleton(X2)),X4,X5)))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK5(X3,singleton(X2),sK2(cartesian_product2(X3,singleton(X2)),X4,X5)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2546]) ).
tcf(c_16510,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,singleton(X2)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X3,singleton(X2)),X4,X5)),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK5(X3,singleton(X2),sK2(cartesian_product2(X3,singleton(X2)),X4,X5)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2546]) ).
tcf(c_16511,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X3,singleton(X2))),X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK5(X3,singleton(X2),sK1(X4,X5,cartesian_product2(X3,singleton(X2)))),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2546]) ).
tcf(c_16512,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,singleton(X2))),X6),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK5(X3,singleton(X2),sK1(X4,X5,cartesian_product2(X3,singleton(X2)))),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2546]) ).
tcf(c_16513,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,singleton(X2)))))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK5(X3,singleton(X2),sK1(X4,X5,cartesian_product2(X3,singleton(X2)))),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2546]) ).
tcf(c_16514,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,singleton(X2)))),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK5(X3,singleton(X2),sK1(X4,X5,cartesian_product2(X3,singleton(X2)))),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2546]) ).
tcf(c_16515,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X3,singleton(X2))),X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK5(X3,singleton(X2),sK1(X4,X5,cartesian_product2(X3,singleton(X2)))),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2546]) ).
tcf(c_16516,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,singleton(X2))),X6),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK5(X3,singleton(X2),sK1(X4,X5,cartesian_product2(X3,singleton(X2)))),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2546]) ).
tcf(c_16517,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,singleton(X2)))))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK5(X3,singleton(X2),sK1(X4,X5,cartesian_product2(X3,singleton(X2)))),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2546]) ).
tcf(c_16518,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,singleton(X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,singleton(X2)))),singleton(X6))) = X6 )
| ( sK5(X1,singleton(X2),unordered_pair(singleton(X0),unordered_pair(sK5(X3,singleton(X2),sK1(X4,X5,cartesian_product2(X3,singleton(X2)))),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2546]) ).
tcf(c_16631,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = cartesian_product2(X0,X1) )
| ( sK4(singleton(X5),X2,unordered_pair(unordered_pair(X5,sK4(X2,X3,sK4(cartesian_product2(X2,X3),X4,sK1(X0,X1,cartesian_product2(cartesian_product2(X2,X3),X4))))),singleton(X5))) = X5 )
| ( unordered_pair(unordered_pair(sK2(X0,X1,cartesian_product2(cartesian_product2(X2,X3),X4)),sK3(X0,X1,cartesian_product2(cartesian_product2(X2,X3),X4))),singleton(sK2(X0,X1,cartesian_product2(cartesian_product2(X2,X3),X4)))) = sK1(X0,X1,cartesian_product2(cartesian_product2(X2,X3),X4)) ) ),
inference(superposition,[status(thm)],[c_58,c_2102]) ).
tcf(c_16632,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)),X5)
| ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_2102]) ).
tcf(c_16633,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)),X4)
| ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_2102]) ).
tcf(c_16634,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X3),X4) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK2(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_2102]) ).
tcf(c_16635,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X1,X2),X3)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK3(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_2102]) ).
tcf(c_16636,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(unordered_pair(X5,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK4(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X0)))),singleton(X5))) = X5 )
| ~ in(X0,cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X3),X4)) ),
inference(superposition,[status(thm)],[c_60,c_2102]) ).
tcf(c_16637,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(unordered_pair(X5,sK4(X2,X3,sK4(cartesian_product2(X2,X3),X4,sK5(X1,cartesian_product2(cartesian_product2(X2,X3),X4),X0)))),singleton(X5))) = X5 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(cartesian_product2(X2,X3),X4))) ),
inference(superposition,[status(thm)],[c_61,c_2102]) ).
tcf(c_16638,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(unordered_pair(X5,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X4,unordered_pair(unordered_pair(X0,X3),singleton(X0))))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_64,c_2102]) ).
tcf(c_16640,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(unordered_pair(X5,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X4,unordered_pair(unordered_pair(X3,X0),singleton(X0))))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_809,c_2102]) ).
tcf(c_16641,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(unordered_pair(X5,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X4,unordered_pair(singleton(X0),unordered_pair(X3,X0))))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_882,c_2102]) ).
tcf(c_16643,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(unordered_pair(X5,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X4,unordered_pair(singleton(X0),unordered_pair(X0,X3))))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_900,c_2102]) ).
tcf(c_16644,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(singleton(X4),X5) )
| ( sK2(singleton(X4),X5,cartesian_product2(cartesian_product2(X1,X2),X3)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(singleton(X4),X5,cartesian_product2(cartesian_product2(X1,X2),X3))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_2102]) ).
tcf(c_16645,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X3),X4) = singleton(X5) )
| ( sK1(cartesian_product2(cartesian_product2(X1,X2),X3),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK2(cartesian_product2(cartesian_product2(X1,X2),X3),X4,singleton(X5))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_2102]) ).
tcf(c_16646,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,singleton(X5)) )
| ( sK3(X4,singleton(X5),cartesian_product2(cartesian_product2(X1,X2),X3)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,singleton(X5),cartesian_product2(cartesian_product2(X1,X2),X3))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_2102]) ).
tcf(c_16647,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X1,X2),X3)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(cartesian_product2(X1,X2),X3),singleton(X5)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK3(X4,cartesian_product2(cartesian_product2(X1,X2),X3),singleton(X5))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_2102]) ).
tcf(c_16648,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X1,X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK3(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_2102]) ).
tcf(c_16649,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X1,X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK3(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_2102]) ).
tcf(c_16650,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X1,X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK3(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_2102]) ).
tcf(c_16651,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X1,X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK3(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_2102]) ).
tcf(c_16652,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK2(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_2102]) ).
tcf(c_16653,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK2(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_2102]) ).
tcf(c_16654,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK2(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_2102]) ).
tcf(c_16655,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK2(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_2102]) ).
tcf(c_16656,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_2102]) ).
tcf(c_16657,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_2102]) ).
tcf(c_16658,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_2102]) ).
tcf(c_16659,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_2102]) ).
tcf(c_16660,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_2102]) ).
tcf(c_16661,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_2102]) ).
tcf(c_16662,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_2102]) ).
tcf(c_16663,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_2102]) ).
tcf(c_16787,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),cartesian_product2(X1,singleton(X3)),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X3,X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2464]) ).
tcf(c_16788,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2464]) ).
tcf(c_16789,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2464]) ).
tcf(c_16790,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2464]) ).
tcf(c_16791,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2464]) ).
tcf(c_16792,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2464]) ).
tcf(c_16793,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X4,X1),unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X3),unordered_pair(sK4(X1,X2,X0),X3)),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2464]) ).
tcf(c_16794,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X4,X2),unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X3),unordered_pair(sK5(X1,X2,X0),X3)),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2464]) ).
tcf(c_16795,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X3,X1)),unordered_pair(singleton(X6),unordered_pair(unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X4)),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2464]) ).
tcf(c_16796,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X1,X3)),unordered_pair(singleton(X6),unordered_pair(unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X4)),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2464]) ).
tcf(c_16797,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X1,X3)),unordered_pair(singleton(X6),unordered_pair(unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X4)),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2464]) ).
tcf(c_16798,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X1,X3)),unordered_pair(singleton(X6),unordered_pair(unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X4)),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2464]) ).
tcf(c_16799,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X3,X1)),unordered_pair(singleton(X6),unordered_pair(unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X4)),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2464]) ).
tcf(c_16800,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X3,X1)),unordered_pair(singleton(X6),unordered_pair(unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X4)),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2464]) ).
tcf(c_16802,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK1(singleton(X4),X5,X3),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2464]) ).
tcf(c_16803,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,singleton(X5)),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2464]) ).
tcf(c_16804,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK1(X4,singleton(X5),X3),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2464]) ).
tcf(c_16805,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,singleton(X5)),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2464]) ).
tcf(c_16806,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2464]) ).
tcf(c_16807,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2464]) ).
tcf(c_16808,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2464]) ).
tcf(c_16809,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2464]) ).
tcf(c_16810,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2464]) ).
tcf(c_16811,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2464]) ).
tcf(c_16812,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2464]) ).
tcf(c_16813,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2464]) ).
tcf(c_16814,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2464]) ).
tcf(c_16815,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2464]) ).
tcf(c_16816,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2464]) ).
tcf(c_16817,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2464]) ).
tcf(c_16818,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2464]) ).
tcf(c_16819,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2464]) ).
tcf(c_16820,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2464]) ).
tcf(c_16821,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2464]) ).
tcf(c_17088,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X1),sK3(X3,X4,X1)),singleton(sK2(X3,X4,X1))) = sK1(X3,X4,X1) )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_16787]) ).
tcf(c_17089,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X1),X4)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_16787]) ).
tcf(c_17090,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X1),X3)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_16787]) ).
tcf(c_17091,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X1,X3,X4),X4)
| ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_16787]) ).
tcf(c_17092,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X1,X4),X4)
| ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_16787]) ).
tcf(c_17093,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(X1,singleton(X4)),unordered_pair(singleton(X3),unordered_pair(unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(X4,sK4(X1,X2,X0))),X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_16787]) ).
tcf(c_17094,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(X2,singleton(X4)),unordered_pair(singleton(X3),unordered_pair(unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(X4,sK5(X1,X2,X0))),X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_16787]) ).
tcf(c_17095,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X3,X1),singleton(X5)),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X2)))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_16787]) ).
tcf(c_17096,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X1,X3),singleton(X5)),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X0,X2)))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_16787]) ).
tcf(c_17097,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X1,X3),singleton(X5)),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X0)))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_16787]) ).
tcf(c_17098,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X1,X3),singleton(X5)),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X2,X0)))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_16787]) ).
tcf(c_17099,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X3,X1),singleton(X5)),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X0,X2)))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_16787]) ).
tcf(c_17100,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X3,X1),singleton(X5)),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X2,X0)))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_16787]) ).
tcf(c_17102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X1 )
| ( sK2(singleton(X3),X4,X1) = X3 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK1(singleton(X3),X4,X1)),unordered_pair(X2,sK1(singleton(X3),X4,X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_16787]) ).
tcf(c_17103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X3) = singleton(X4) )
| ( sK1(X1,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK2(X1,X3,singleton(X4))),unordered_pair(X2,sK2(X1,X3,singleton(X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_16787]) ).
tcf(c_17104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X1 )
| ( sK3(X3,singleton(X4),X1) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK1(X3,singleton(X4),X1)),unordered_pair(X2,sK1(X3,singleton(X4),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_16787]) ).
tcf(c_17105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X1) = singleton(X4) )
| ( sK1(X3,X1,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK3(X3,X1,singleton(X4))),unordered_pair(X2,sK3(X3,X1,singleton(X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_16787]) ).
tcf(c_17106,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_16787]) ).
tcf(c_17107,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_16787]) ).
tcf(c_17108,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_16787]) ).
tcf(c_17109,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X1,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_16787]) ).
tcf(c_17110,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_16787]) ).
tcf(c_17111,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_16787]) ).
tcf(c_17112,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_16787]) ).
tcf(c_17113,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X1,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_16787]) ).
tcf(c_17114,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_16787]) ).
tcf(c_17115,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_16787]) ).
tcf(c_17116,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_16787]) ).
tcf(c_17117,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_16787]) ).
tcf(c_17118,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_16787]) ).
tcf(c_17119,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_16787]) ).
tcf(c_17120,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_16787]) ).
tcf(c_17121,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_16787]) ).
tcf(c_17483,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),cartesian_product2(X1,singleton(X3)),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X3)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2465]) ).
tcf(c_17484,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2465]) ).
tcf(c_17485,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2465]) ).
tcf(c_17486,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2465]) ).
tcf(c_17487,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2465]) ).
tcf(c_17488,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2465]) ).
tcf(c_17489,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X4,X1),unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X3),unordered_pair(X3,sK4(X1,X2,X0))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2465]) ).
tcf(c_17490,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),cartesian_product2(X4,X2),unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X3),unordered_pair(X3,sK5(X1,X2,X0))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2465]) ).
tcf(c_17491,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X3,X1)),unordered_pair(singleton(X6),unordered_pair(unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2)))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2465]) ).
tcf(c_17492,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X1,X3)),unordered_pair(singleton(X6),unordered_pair(unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2)))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2465]) ).
tcf(c_17493,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X1,X3)),unordered_pair(singleton(X6),unordered_pair(unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0)))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2465]) ).
tcf(c_17494,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X1,X3)),unordered_pair(singleton(X6),unordered_pair(unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0)))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2465]) ).
tcf(c_17495,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X3,X1)),unordered_pair(singleton(X6),unordered_pair(unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2)))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2465]) ).
tcf(c_17496,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X5,cartesian_product2(X3,X1)),unordered_pair(singleton(X6),unordered_pair(unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0)))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2465]) ).
tcf(c_17498,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK1(singleton(X4),X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2465]) ).
tcf(c_17499,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,singleton(X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2465]) ).
tcf(c_17500,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,singleton(X5),X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2465]) ).
tcf(c_17501,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,singleton(X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2465]) ).
tcf(c_17502,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2465]) ).
tcf(c_17503,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2465]) ).
tcf(c_17504,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2465]) ).
tcf(c_17505,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2465]) ).
tcf(c_17506,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2465]) ).
tcf(c_17507,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2465]) ).
tcf(c_17508,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2465]) ).
tcf(c_17509,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2465]) ).
tcf(c_17510,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2465]) ).
tcf(c_17511,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2465]) ).
tcf(c_17512,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2465]) ).
tcf(c_17513,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2465]) ).
tcf(c_17514,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2465]) ).
tcf(c_17515,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2465]) ).
tcf(c_17516,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2465]) ).
tcf(c_17517,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2465]) ).
tcf(c_17725,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X1),sK3(X3,X4,X1)),singleton(sK2(X3,X4,X1))) = sK1(X3,X4,X1) )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_17483]) ).
tcf(c_17726,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X1),X4)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_17483]) ).
tcf(c_17727,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X1),X3)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_17483]) ).
tcf(c_17728,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X1,X3,X4),X4)
| ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_17483]) ).
tcf(c_17729,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X1,X4),X4)
| ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_17483]) ).
tcf(c_17730,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(X1,singleton(X4)),unordered_pair(singleton(X3),unordered_pair(unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(sK4(X1,X2,X0),X4)),X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_17483]) ).
tcf(c_17731,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),cartesian_product2(X2,singleton(X4)),unordered_pair(singleton(X3),unordered_pair(unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(sK5(X1,X2,X0),X4)),X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_17483]) ).
tcf(c_17732,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X3,X1),singleton(X5)),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_17483]) ).
tcf(c_17733,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X1,X3),singleton(X5)),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_17483]) ).
tcf(c_17734,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X1,X3),singleton(X5)),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_17483]) ).
tcf(c_17735,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X1,X3),singleton(X5)),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_17483]) ).
tcf(c_17736,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X3,X1),singleton(X5)),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_17483]) ).
tcf(c_17737,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(cartesian_product2(X3,X1),singleton(X5)),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_17483]) ).
tcf(c_17739,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X1 )
| ( sK2(singleton(X3),X4,X1) = X3 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK1(singleton(X3),X4,X1)),unordered_pair(sK1(singleton(X3),X4,X1),X2)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_17483]) ).
tcf(c_17740,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X3) = singleton(X4) )
| ( sK1(X1,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK2(X1,X3,singleton(X4))),unordered_pair(sK2(X1,X3,singleton(X4)),X2)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_17483]) ).
tcf(c_17741,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X1 )
| ( sK3(X3,singleton(X4),X1) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK1(X3,singleton(X4),X1)),unordered_pair(sK1(X3,singleton(X4),X1),X2)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_17483]) ).
tcf(c_17742,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X1) = singleton(X4) )
| ( sK1(X3,X1,singleton(X4)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK3(X3,X1,singleton(X4))),unordered_pair(sK3(X3,X1,singleton(X4)),X2)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_17483]) ).
tcf(c_17743,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_17483]) ).
tcf(c_17744,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_17483]) ).
tcf(c_17745,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_17483]) ).
tcf(c_17746,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X1,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_17483]) ).
tcf(c_17747,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_17483]) ).
tcf(c_17748,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_17483]) ).
tcf(c_17749,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_17483]) ).
tcf(c_17750,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X1,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_17483]) ).
tcf(c_17751,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_17483]) ).
tcf(c_17752,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_17483]) ).
tcf(c_17753,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_17483]) ).
tcf(c_17754,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_17483]) ).
tcf(c_17755,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_17483]) ).
tcf(c_17756,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_17483]) ).
tcf(c_17757,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_17483]) ).
tcf(c_17758,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_17483]) ).
tcf(c_17786,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(X3,X4)) = cartesian_product2(X0,X1) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK4(X3,X4,sK5(X2,cartesian_product2(X3,X4),sK1(X0,X1,cartesian_product2(X2,cartesian_product2(X3,X4)))))),singleton(X5))) = X5 )
| ( unordered_pair(unordered_pair(sK2(X0,X1,cartesian_product2(X2,cartesian_product2(X3,X4))),sK3(X0,X1,cartesian_product2(X2,cartesian_product2(X3,X4)))),singleton(sK2(X0,X1,cartesian_product2(X2,cartesian_product2(X3,X4))))) = sK1(X0,X1,cartesian_product2(X2,cartesian_product2(X3,X4))) ) ),
inference(superposition,[status(thm)],[c_58,c_2103]) ).
tcf(c_17787,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))),X5)
| ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_2103]) ).
tcf(c_17788,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))),X4)
| ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_2103]) ).
tcf(c_17789,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_2103]) ).
tcf(c_17790,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X1,X2))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK3(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_2103]) ).
tcf(c_17791,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(unordered_pair(X5,sK4(X2,X3,sK5(X1,cartesian_product2(X2,X3),sK4(cartesian_product2(X1,cartesian_product2(X2,X3)),X4,X0)))),singleton(X5))) = X5 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,cartesian_product2(X2,X3)),X4)) ),
inference(superposition,[status(thm)],[c_60,c_2103]) ).
tcf(c_17792,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK4(X3,X4,sK5(X2,cartesian_product2(X3,X4),sK5(X1,cartesian_product2(X2,cartesian_product2(X3,X4)),X0)))),singleton(X5))) = X5 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,cartesian_product2(X3,X4)))) ),
inference(superposition,[status(thm)],[c_61,c_2103]) ).
tcf(c_17793,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(unordered_pair(X5,sK4(X1,X2,sK5(X4,cartesian_product2(X1,X2),unordered_pair(unordered_pair(X3,X0),singleton(X3))))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_64,c_2103]) ).
tcf(c_17795,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(unordered_pair(X5,sK4(X1,X2,sK5(X4,cartesian_product2(X1,X2),unordered_pair(unordered_pair(X0,X3),singleton(X3))))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_809,c_2103]) ).
tcf(c_17796,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(unordered_pair(X5,sK4(X1,X2,sK5(X4,cartesian_product2(X1,X2),unordered_pair(singleton(X3),unordered_pair(X0,X3))))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_882,c_2103]) ).
tcf(c_17798,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(unordered_pair(X5,sK4(X1,X2,sK5(X4,cartesian_product2(X1,X2),unordered_pair(singleton(X3),unordered_pair(X3,X0))))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_900,c_2103]) ).
tcf(c_17799,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(singleton(X4),X5) )
| ( sK2(singleton(X4),X5,cartesian_product2(X3,cartesian_product2(X1,X2))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(singleton(X4),X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_2103]) ).
tcf(c_17800,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,singleton(X5))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_2103]) ).
tcf(c_17801,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,singleton(X5)) )
| ( sK3(X4,singleton(X5),cartesian_product2(X3,cartesian_product2(X1,X2))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,singleton(X5),cartesian_product2(X3,cartesian_product2(X1,X2)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_2103]) ).
tcf(c_17802,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X1,X2))) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),singleton(X5)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK3(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),singleton(X5))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_2103]) ).
tcf(c_17803,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X1,X2))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK3(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_2103]) ).
tcf(c_17804,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X1,X2))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK3(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_2103]) ).
tcf(c_17805,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X1,X2))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK3(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_2103]) ).
tcf(c_17806,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X1,X2))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK3(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_2103]) ).
tcf(c_17807,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_2103]) ).
tcf(c_17808,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_2103]) ).
tcf(c_17809,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_2103]) ).
tcf(c_17810,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_2103]) ).
tcf(c_17811,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_2103]) ).
tcf(c_17812,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_2103]) ).
tcf(c_17813,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_2103]) ).
tcf(c_17814,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_2103]) ).
tcf(c_17815,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_2103]) ).
tcf(c_17816,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_2103]) ).
tcf(c_17817,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_2103]) ).
tcf(c_17818,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_2103]) ).
tcf(c_18127,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,singleton(X3),unordered_pair(unordered_pair(X0,X3),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2104]) ).
tcf(c_18128,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2104]) ).
tcf(c_18129,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2104]) ).
tcf(c_18130,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2104]) ).
tcf(c_18131,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2104]) ).
tcf(c_18132,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2104]) ).
tcf(c_18133,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK4(X4,X1,unordered_pair(unordered_pair(X3,sK4(X1,X2,X0)),singleton(X3)))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2104]) ).
tcf(c_18134,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK4(X4,X2,unordered_pair(unordered_pair(X3,sK5(X1,X2,X0)),singleton(X3)))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2104]) ).
tcf(c_18135,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK4(X5,cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))),singleton(X4)))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2104]) ).
tcf(c_18136,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK4(X5,cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))),singleton(X4)))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2104]) ).
tcf(c_18137,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK4(X5,cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))),singleton(X4)))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2104]) ).
tcf(c_18138,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK4(X5,cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))),singleton(X4)))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2104]) ).
tcf(c_18139,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK4(X5,cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))),singleton(X4)))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2104]) ).
tcf(c_18140,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK4(X5,cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))),singleton(X4)))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2104]) ).
tcf(c_18142,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(singleton(X4),X5,X3)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2104]) ).
tcf(c_18143,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,singleton(X5))),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2104]) ).
tcf(c_18144,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,singleton(X5),X3)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2104]) ).
tcf(c_18145,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,singleton(X5))),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2104]) ).
tcf(c_18146,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2104]) ).
tcf(c_18147,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2104]) ).
tcf(c_18148,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2104]) ).
tcf(c_18149,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2104]) ).
tcf(c_18150,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2104]) ).
tcf(c_18151,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2104]) ).
tcf(c_18152,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2104]) ).
tcf(c_18153,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2104]) ).
tcf(c_18154,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2104]) ).
tcf(c_18155,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2104]) ).
tcf(c_18156,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2104]) ).
tcf(c_18157,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2104]) ).
tcf(c_18158,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2104]) ).
tcf(c_18159,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2104]) ).
tcf(c_18160,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2104]) ).
tcf(c_18161,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2104]) ).
tcf(c_18162,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),singleton(X2),unordered_pair(unordered_pair(X1,X2),singleton(X1)))),singleton(X0))) = X0,
inference(superposition,[status(thm)],[c_53,c_18127]) ).
tcf(c_18163,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X1),sK3(X3,X4,X1)),singleton(sK2(X3,X4,X1))) = sK1(X3,X4,X1) )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_18127]) ).
tcf(c_18164,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X1),X4)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_18127]) ).
tcf(c_18165,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X1),X3)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_18127]) ).
tcf(c_18166,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X1,X3,X4),X4)
| ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_18127]) ).
tcf(c_18167,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X1,X4),X4)
| ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_18127]) ).
tcf(c_18168,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X1,unordered_pair(unordered_pair(X3,sK4(X1,singleton(X4),unordered_pair(unordered_pair(sK4(X1,X2,X0),X4),singleton(sK4(X1,X2,X0))))),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_18127]) ).
tcf(c_18169,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X2,unordered_pair(unordered_pair(X3,sK4(X2,singleton(X4),unordered_pair(unordered_pair(sK5(X1,X2,X0),X4),singleton(sK5(X1,X2,X0))))),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_18127]) ).
tcf(c_18170,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,sK4(cartesian_product2(X3,X1),singleton(X5),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_18127]) ).
tcf(c_18171,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,sK4(cartesian_product2(X1,X3),singleton(X5),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5),singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_18127]) ).
tcf(c_18172,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,sK4(cartesian_product2(X1,X3),singleton(X5),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_18127]) ).
tcf(c_18173,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,sK4(cartesian_product2(X1,X3),singleton(X5),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5),singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_18127]) ).
tcf(c_18174,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,sK4(cartesian_product2(X3,X1),singleton(X5),unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5),singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_18127]) ).
tcf(c_18175,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,sK4(cartesian_product2(X3,X1),singleton(X5),unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5),singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_18127]) ).
tcf(c_18177,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X1 )
| ( sK2(singleton(X3),X4,X1) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(singleton(X3),X4,X1),X2),singleton(sK1(singleton(X3),X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_18127]) ).
tcf(c_18178,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X3) = singleton(X4) )
| ( sK1(X1,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK2(X1,X3,singleton(X4)),X2),singleton(sK2(X1,X3,singleton(X4)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_18127]) ).
tcf(c_18179,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X1 )
| ( sK3(X3,singleton(X4),X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,singleton(X4),X1),X2),singleton(sK1(X3,singleton(X4),X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_18127]) ).
tcf(c_18180,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X1) = singleton(X4) )
| ( sK1(X3,X1,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK3(X3,X1,singleton(X4)),X2),singleton(sK3(X3,X1,singleton(X4)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_18127]) ).
tcf(c_18181,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_18127]) ).
tcf(c_18182,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_18127]) ).
tcf(c_18183,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_18127]) ).
tcf(c_18184,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X1,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_18127]) ).
tcf(c_18185,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_18127]) ).
tcf(c_18186,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_18127]) ).
tcf(c_18187,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_18127]) ).
tcf(c_18188,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X1,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_18127]) ).
tcf(c_18189,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_18127]) ).
tcf(c_18190,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_18127]) ).
tcf(c_18191,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_18127]) ).
tcf(c_18192,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_18127]) ).
tcf(c_18193,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_18127]) ).
tcf(c_18194,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_18127]) ).
tcf(c_18195,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_18127]) ).
tcf(c_18196,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_18127]) ).
tcf(c_18608,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),singleton(X2),unordered_pair(unordered_pair(X1,X2),singleton(X1)))))) = X0,
inference(superposition,[status(thm)],[c_50,c_18162]) ).
tcf(c_18610,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),singleton(X2),unordered_pair(unordered_pair(X1,X2),singleton(X1))),X0),singleton(X0))) = X0,
inference(superposition,[status(thm)],[c_50,c_18162]) ).
tcf(c_18614,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),singleton(X2),unordered_pair(singleton(X1),unordered_pair(X1,X2)))),singleton(X0))) = X0,
inference(superposition,[status(thm)],[c_50,c_18162]) ).
tcf(c_18616,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),singleton(X2),unordered_pair(unordered_pair(X2,X1),singleton(X1)))),singleton(X0))) = X0,
inference(superposition,[status(thm)],[c_50,c_18162]) ).
tcf(c_18622,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),singleton(X2),unordered_pair(unordered_pair(X1,X2),singleton(X1))),X0))) = X0,
inference(superposition,[status(thm)],[c_50,c_18608]) ).
tcf(c_18626,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),singleton(X2),unordered_pair(singleton(X1),unordered_pair(X1,X2)))))) = X0,
inference(superposition,[status(thm)],[c_50,c_18608]) ).
tcf(c_18628,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),singleton(X2),unordered_pair(unordered_pair(X2,X1),singleton(X1)))))) = X0,
inference(superposition,[status(thm)],[c_50,c_18608]) ).
tcf(c_18639,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),singleton(X2),unordered_pair(singleton(X1),unordered_pair(X1,X2))),X0),singleton(X0))) = X0,
inference(superposition,[status(thm)],[c_50,c_18610]) ).
tcf(c_18641,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),singleton(X2),unordered_pair(unordered_pair(X2,X1),singleton(X1))),X0),singleton(X0))) = X0,
inference(superposition,[status(thm)],[c_50,c_18610]) ).
tcf(c_18643,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,singleton(X2))
| ~ in(unordered_pair(unordered_pair(sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,X1),singleton(X0))),X2),singleton(X2)),cartesian_product2(singleton(X2),singleton(X0))) ),
inference(superposition,[status(thm)],[c_18610,c_60]) ).
tcf(c_18651,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),singleton(X2),unordered_pair(singleton(X1),unordered_pair(X2,X1)))),singleton(X0))) = X0,
inference(superposition,[status(thm)],[c_50,c_18614]) ).
tcf(c_18669,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),singleton(X2),unordered_pair(singleton(X1),unordered_pair(X1,X2))),X0))) = X0,
inference(superposition,[status(thm)],[c_50,c_18622]) ).
tcf(c_18671,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),singleton(X2),unordered_pair(unordered_pair(X2,X1),singleton(X1))),X0))) = X0,
inference(superposition,[status(thm)],[c_50,c_18622]) ).
tcf(c_18679,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),singleton(X2),unordered_pair(singleton(X1),unordered_pair(X2,X1)))))) = X0,
inference(superposition,[status(thm)],[c_50,c_18626]) ).
tcf(c_18697,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),singleton(X2),unordered_pair(singleton(X1),unordered_pair(X2,X1))),X0),singleton(X0))) = X0,
inference(superposition,[status(thm)],[c_50,c_18639]) ).
tcf(c_18699,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,singleton(X2))
| ~ in(unordered_pair(unordered_pair(sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,X1))),X2),singleton(X2)),cartesian_product2(singleton(X2),singleton(X0))) ),
inference(superposition,[status(thm)],[c_18639,c_60]) ).
tcf(c_18710,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,singleton(X2))
| ~ in(unordered_pair(unordered_pair(sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X1,X0),singleton(X0))),X2),singleton(X2)),cartesian_product2(singleton(X2),singleton(X0))) ),
inference(superposition,[status(thm)],[c_18641,c_60]) ).
tcf(c_18724,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),singleton(X2),unordered_pair(singleton(X1),unordered_pair(X2,X1))),X0))) = X0,
inference(superposition,[status(thm)],[c_50,c_18669]) ).
tcf(c_18751,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,singleton(X2))
| ~ in(unordered_pair(unordered_pair(sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X1,X0))),X2),singleton(X2)),cartesian_product2(singleton(X2),singleton(X0))) ),
inference(superposition,[status(thm)],[c_18697,c_60]) ).
tcf(c_18803,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),singleton(X3),unordered_pair(unordered_pair(X2,sK4(singleton(X3),X1,unordered_pair(singleton(X3),unordered_pair(X3,X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2105]) ).
tcf(c_18804,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2105]) ).
tcf(c_18805,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2105]) ).
tcf(c_18806,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2105]) ).
tcf(c_18807,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2105]) ).
tcf(c_18808,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2105]) ).
tcf(c_18809,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(unordered_pair(X5,sK4(X1,X4,unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(sK4(X1,X2,X0),X3)))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2105]) ).
tcf(c_18810,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(unordered_pair(X5,sK4(X2,X4,unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(sK5(X1,X2,X0),X3)))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2105]) ).
tcf(c_18811,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X6,sK4(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X4)))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2105]) ).
tcf(c_18812,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X6,sK4(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X4)))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2105]) ).
tcf(c_18813,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X6,sK4(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X4)))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2105]) ).
tcf(c_18814,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X6,sK4(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X4)))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2105]) ).
tcf(c_18815,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X6,sK4(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X4)))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2105]) ).
tcf(c_18816,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X6,sK4(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X4)))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2105]) ).
tcf(c_18818,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(singleton(X4),X5,X3)),unordered_pair(sK1(singleton(X4),X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2105]) ).
tcf(c_18819,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,singleton(X5))),unordered_pair(sK2(X3,X4,singleton(X5)),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2105]) ).
tcf(c_18820,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,singleton(X5),X3)),unordered_pair(sK1(X4,singleton(X5),X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2105]) ).
tcf(c_18821,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,singleton(X5))),unordered_pair(sK3(X4,X3,singleton(X5)),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2105]) ).
tcf(c_18822,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2105]) ).
tcf(c_18823,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2105]) ).
tcf(c_18824,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2105]) ).
tcf(c_18825,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2105]) ).
tcf(c_18826,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2105]) ).
tcf(c_18827,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2105]) ).
tcf(c_18828,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2105]) ).
tcf(c_18829,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2105]) ).
tcf(c_18830,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2105]) ).
tcf(c_18831,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2105]) ).
tcf(c_18832,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2105]) ).
tcf(c_18833,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2105]) ).
tcf(c_18834,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2105]) ).
tcf(c_18835,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2105]) ).
tcf(c_18836,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2105]) ).
tcf(c_18837,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2105]) ).
tcf(c_18885,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X2),sK3(X3,X4,X2)),singleton(sK2(X3,X4,X2))) = sK1(X3,X4,X2) )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_18803]) ).
tcf(c_18886,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X2),X4)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_18803]) ).
tcf(c_18887,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X2),X3)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_18803]) ).
tcf(c_18888,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X2,X3,X4),X4)
| ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_18803]) ).
tcf(c_18889,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X2,X4),X4)
| ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_18803]) ).
tcf(c_18890,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(unordered_pair(X3,sK4(singleton(X4),X1,unordered_pair(singleton(X4),unordered_pair(X4,sK4(X1,X2,X0))))),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_18803]) ).
tcf(c_18891,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(unordered_pair(X3,sK4(singleton(X4),X2,unordered_pair(singleton(X4),unordered_pair(X4,sK5(X1,X2,X0))))),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_18803]) ).
tcf(c_18892,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(X4,sK4(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X2)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_18803]) ).
tcf(c_18893,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(X4,sK4(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X0,X2)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_18803]) ).
tcf(c_18894,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(X4,sK4(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X0)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_18803]) ).
tcf(c_18895,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(X4,sK4(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X2,X0)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_18803]) ).
tcf(c_18896,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(X4,sK4(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X0,X2)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_18803]) ).
tcf(c_18897,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(X4,sK4(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X2,X0)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_18803]) ).
tcf(c_18899,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X2 )
| ( sK2(singleton(X3),X4,X2) = X3 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(singleton(X3),X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_18803]) ).
tcf(c_18900,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK1(X2,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,singleton(X4)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_18803]) ).
tcf(c_18901,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X2 )
| ( sK3(X3,singleton(X4),X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,singleton(X4),X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_18803]) ).
tcf(c_18902,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X2) = singleton(X4) )
| ( sK1(X3,X2,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,singleton(X4)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_18803]) ).
tcf(c_18903,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_18803]) ).
tcf(c_18904,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_18803]) ).
tcf(c_18905,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_18803]) ).
tcf(c_18906,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X2,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_18803]) ).
tcf(c_18907,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_18803]) ).
tcf(c_18908,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_18803]) ).
tcf(c_18909,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_18803]) ).
tcf(c_18910,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X2,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_18803]) ).
tcf(c_18911,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_18803]) ).
tcf(c_18912,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_18803]) ).
tcf(c_18913,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_18803]) ).
tcf(c_18914,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_18803]) ).
tcf(c_18915,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_18803]) ).
tcf(c_18916,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_18803]) ).
tcf(c_18917,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_18803]) ).
tcf(c_18918,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_18803]) ).
tcf(c_19203,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = cartesian_product2(X0,X1) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK5(X2,X3,sK4(cartesian_product2(X2,X3),X4,sK1(X0,X1,cartesian_product2(cartesian_product2(X2,X3),X4))))),singleton(X5))) = X5 )
| ( unordered_pair(unordered_pair(sK2(X0,X1,cartesian_product2(cartesian_product2(X2,X3),X4)),sK3(X0,X1,cartesian_product2(cartesian_product2(X2,X3),X4))),singleton(sK2(X0,X1,cartesian_product2(cartesian_product2(X2,X3),X4)))) = sK1(X0,X1,cartesian_product2(cartesian_product2(X2,X3),X4)) ) ),
inference(superposition,[status(thm)],[c_58,c_2178]) ).
tcf(c_19204,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)),X5)
| ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_2178]) ).
tcf(c_19205,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)),X4)
| ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_2178]) ).
tcf(c_19206,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(cartesian_product2(X2,X1),X3),X4) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK2(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_2178]) ).
tcf(c_19207,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X2,X1),X3)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK3(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_2178]) ).
tcf(c_19208,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(unordered_pair(X5,sK5(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK4(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X0)))),singleton(X5))) = X5 )
| ~ in(X0,cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X3),X4)) ),
inference(superposition,[status(thm)],[c_60,c_2178]) ).
tcf(c_19209,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK5(X2,X3,sK4(cartesian_product2(X2,X3),X4,sK5(X1,cartesian_product2(cartesian_product2(X2,X3),X4),X0)))),singleton(X5))) = X5 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(cartesian_product2(X2,X3),X4))) ),
inference(superposition,[status(thm)],[c_61,c_2178]) ).
tcf(c_19210,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(unordered_pair(X5,sK5(X1,X2,sK4(cartesian_product2(X1,X2),X4,unordered_pair(unordered_pair(X0,X3),singleton(X0))))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_64,c_2178]) ).
tcf(c_19212,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(unordered_pair(X5,sK5(X1,X2,sK4(cartesian_product2(X1,X2),X4,unordered_pair(unordered_pair(X3,X0),singleton(X0))))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_809,c_2178]) ).
tcf(c_19213,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(unordered_pair(X5,sK5(X1,X2,sK4(cartesian_product2(X1,X2),X4,unordered_pair(singleton(X0),unordered_pair(X3,X0))))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_882,c_2178]) ).
tcf(c_19215,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(unordered_pair(X5,sK5(X1,X2,sK4(cartesian_product2(X1,X2),X4,unordered_pair(singleton(X0),unordered_pair(X0,X3))))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_900,c_2178]) ).
tcf(c_19216,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(singleton(X4),X5) )
| ( sK2(singleton(X4),X5,cartesian_product2(cartesian_product2(X2,X1),X3)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(singleton(X4),X5,cartesian_product2(cartesian_product2(X2,X1),X3))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_2178]) ).
tcf(c_19217,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X2,X1),X3),X4) = singleton(X5) )
| ( sK1(cartesian_product2(cartesian_product2(X2,X1),X3),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK2(cartesian_product2(cartesian_product2(X2,X1),X3),X4,singleton(X5))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_2178]) ).
tcf(c_19218,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,singleton(X5)) )
| ( sK3(X4,singleton(X5),cartesian_product2(cartesian_product2(X2,X1),X3)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,singleton(X5),cartesian_product2(cartesian_product2(X2,X1),X3))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_2178]) ).
tcf(c_19219,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X2,X1),X3)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(cartesian_product2(X2,X1),X3),singleton(X5)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK3(X4,cartesian_product2(cartesian_product2(X2,X1),X3),singleton(X5))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_2178]) ).
tcf(c_19220,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X2,X1),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK3(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_2178]) ).
tcf(c_19221,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X2,X1),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK3(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_2178]) ).
tcf(c_19222,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X2,X1),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK3(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_2178]) ).
tcf(c_19223,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X2,X1),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK3(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_2178]) ).
tcf(c_19224,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X2,X1),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK2(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_2178]) ).
tcf(c_19225,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X2,X1),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK2(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_2178]) ).
tcf(c_19226,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X2,X1),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK2(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_2178]) ).
tcf(c_19227,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X2,X1),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK2(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_2178]) ).
tcf(c_19228,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_2178]) ).
tcf(c_19229,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_2178]) ).
tcf(c_19230,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_2178]) ).
tcf(c_19231,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_2178]) ).
tcf(c_19232,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_2178]) ).
tcf(c_19233,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_2178]) ).
tcf(c_19234,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_2178]) ).
tcf(c_19235,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_2178]) ).
tcf(c_19578,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(X3,X4)) = cartesian_product2(X0,X1) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK5(X3,X4,sK5(X2,cartesian_product2(X3,X4),sK1(X0,X1,cartesian_product2(X2,cartesian_product2(X3,X4)))))),singleton(X5))) = X5 )
| ( unordered_pair(unordered_pair(sK2(X0,X1,cartesian_product2(X2,cartesian_product2(X3,X4))),sK3(X0,X1,cartesian_product2(X2,cartesian_product2(X3,X4)))),singleton(sK2(X0,X1,cartesian_product2(X2,cartesian_product2(X3,X4))))) = sK1(X0,X1,cartesian_product2(X2,cartesian_product2(X3,X4))) ) ),
inference(superposition,[status(thm)],[c_58,c_2179]) ).
tcf(c_19579,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))),X5)
| ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_2179]) ).
tcf(c_19580,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))),X4)
| ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_2179]) ).
tcf(c_19581,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_2179]) ).
tcf(c_19582,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X2,X1))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK3(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_2179]) ).
tcf(c_19583,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK5(X2,X3,sK5(X1,cartesian_product2(X2,X3),sK4(cartesian_product2(X1,cartesian_product2(X2,X3)),X4,X0)))),singleton(X5))) = X5 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,cartesian_product2(X2,X3)),X4)) ),
inference(superposition,[status(thm)],[c_60,c_2179]) ).
tcf(c_19584,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK5(X3,X4,sK5(X2,cartesian_product2(X3,X4),sK5(X1,cartesian_product2(X2,cartesian_product2(X3,X4)),X0)))),singleton(X5))) = X5 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,cartesian_product2(X3,X4)))) ),
inference(superposition,[status(thm)],[c_61,c_2179]) ).
tcf(c_19585,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(unordered_pair(X5,sK5(X1,X2,sK5(X4,cartesian_product2(X1,X2),unordered_pair(unordered_pair(X3,X0),singleton(X3))))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_64,c_2179]) ).
tcf(c_19587,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(unordered_pair(X5,sK5(X1,X2,sK5(X4,cartesian_product2(X1,X2),unordered_pair(unordered_pair(X0,X3),singleton(X3))))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_809,c_2179]) ).
tcf(c_19588,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(unordered_pair(X5,sK5(X1,X2,sK5(X4,cartesian_product2(X1,X2),unordered_pair(singleton(X3),unordered_pair(X0,X3))))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_882,c_2179]) ).
tcf(c_19590,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(unordered_pair(X5,sK5(X1,X2,sK5(X4,cartesian_product2(X1,X2),unordered_pair(singleton(X3),unordered_pair(X3,X0))))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_900,c_2179]) ).
tcf(c_19591,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(singleton(X4),X5) )
| ( sK2(singleton(X4),X5,cartesian_product2(X3,cartesian_product2(X2,X1))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(singleton(X4),X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_2179]) ).
tcf(c_19592,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,singleton(X5))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_2179]) ).
tcf(c_19593,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,singleton(X5)) )
| ( sK3(X4,singleton(X5),cartesian_product2(X3,cartesian_product2(X2,X1))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,singleton(X5),cartesian_product2(X3,cartesian_product2(X2,X1)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_2179]) ).
tcf(c_19594,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X2,X1))) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),singleton(X5)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK3(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),singleton(X5))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_2179]) ).
tcf(c_19595,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X2,X1))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK3(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_2179]) ).
tcf(c_19596,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X2,X1))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK3(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_2179]) ).
tcf(c_19597,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X2,X1))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK3(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_2179]) ).
tcf(c_19598,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X2,X1))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK3(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_2179]) ).
tcf(c_19599,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_2179]) ).
tcf(c_19600,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_2179]) ).
tcf(c_19601,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_2179]) ).
tcf(c_19602,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_2179]) ).
tcf(c_19603,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_2179]) ).
tcf(c_19604,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_2179]) ).
tcf(c_19605,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_2179]) ).
tcf(c_19606,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_2179]) ).
tcf(c_19607,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_2179]) ).
tcf(c_19608,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_2179]) ).
tcf(c_19609,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_2179]) ).
tcf(c_19610,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_2179]) ).
tcf(c_19855,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),singleton(X3),unordered_pair(unordered_pair(X2,sK5(X1,singleton(X3),unordered_pair(unordered_pair(X0,X3),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2180]) ).
tcf(c_19856,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2180]) ).
tcf(c_19857,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2180]) ).
tcf(c_19858,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2180]) ).
tcf(c_19859,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2180]) ).
tcf(c_19860,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2180]) ).
tcf(c_19861,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(unordered_pair(X5,sK5(X4,X1,unordered_pair(unordered_pair(X3,sK4(X1,X2,X0)),singleton(X3)))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2180]) ).
tcf(c_19862,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(unordered_pair(X5,sK5(X4,X2,unordered_pair(unordered_pair(X3,sK5(X1,X2,X0)),singleton(X3)))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2180]) ).
tcf(c_19863,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X6,sK5(X5,cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))),singleton(X4)))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2180]) ).
tcf(c_19864,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X6,sK5(X5,cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))),singleton(X4)))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2180]) ).
tcf(c_19865,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X6,sK5(X5,cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))),singleton(X4)))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2180]) ).
tcf(c_19866,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X6,sK5(X5,cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))),singleton(X4)))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2180]) ).
tcf(c_19867,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X6,sK5(X5,cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))),singleton(X4)))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2180]) ).
tcf(c_19868,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X6,sK5(X5,cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))),singleton(X4)))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2180]) ).
tcf(c_19870,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(singleton(X4),X5,X3)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2180]) ).
tcf(c_19871,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,singleton(X5))),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2180]) ).
tcf(c_19872,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,singleton(X5),X3)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2180]) ).
tcf(c_19873,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,singleton(X5))),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2180]) ).
tcf(c_19874,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2180]) ).
tcf(c_19875,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2180]) ).
tcf(c_19876,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2180]) ).
tcf(c_19877,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2180]) ).
tcf(c_19878,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2180]) ).
tcf(c_19879,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2180]) ).
tcf(c_19880,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2180]) ).
tcf(c_19881,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2180]) ).
tcf(c_19882,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2180]) ).
tcf(c_19883,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2180]) ).
tcf(c_19884,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2180]) ).
tcf(c_19885,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2180]) ).
tcf(c_19886,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2180]) ).
tcf(c_19887,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2180]) ).
tcf(c_19888,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2180]) ).
tcf(c_19889,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2180]) ).
tcf(c_19890,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(singleton(X2),singleton(X1),unordered_pair(unordered_pair(X2,X1),singleton(X2)))),singleton(X0))) = X0,
inference(superposition,[status(thm)],[c_53,c_19855]) ).
tcf(c_19891,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X2),sK3(X3,X4,X2)),singleton(sK2(X3,X4,X2))) = sK1(X3,X4,X2) )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_19855]) ).
tcf(c_19892,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X2),X4)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_19855]) ).
tcf(c_19893,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X2),X3)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_19855]) ).
tcf(c_19894,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X2,X3,X4),X4)
| ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(sK2(X2,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_19855]) ).
tcf(c_19895,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X2,X4),X4)
| ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(sK3(X3,X2,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_19855]) ).
tcf(c_19896,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(unordered_pair(X3,sK5(X1,singleton(X4),unordered_pair(unordered_pair(sK4(X1,X2,X0),X4),singleton(sK4(X1,X2,X0))))),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_19855]) ).
tcf(c_19897,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(unordered_pair(X3,sK5(X2,singleton(X4),unordered_pair(unordered_pair(sK5(X1,X2,X0),X4),singleton(sK5(X1,X2,X0))))),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_19855]) ).
tcf(c_19898,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(X4,sK5(cartesian_product2(X3,X1),singleton(X5),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_19855]) ).
tcf(c_19899,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(X4,sK5(cartesian_product2(X1,X3),singleton(X5),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5),singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_19855]) ).
tcf(c_19900,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(X4,sK5(cartesian_product2(X1,X3),singleton(X5),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_19855]) ).
tcf(c_19901,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(X4,sK5(cartesian_product2(X1,X3),singleton(X5),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5),singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_19855]) ).
tcf(c_19902,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(X4,sK5(cartesian_product2(X3,X1),singleton(X5),unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5),singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_19855]) ).
tcf(c_19903,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(X4,sK5(cartesian_product2(X3,X1),singleton(X5),unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5),singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_19855]) ).
tcf(c_19905,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X2 )
| ( sK2(singleton(X3),X4,X2) = X3 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(singleton(X3),X4,X2),X1),singleton(sK1(singleton(X3),X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_19855]) ).
tcf(c_19906,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK1(X2,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK2(X2,X3,singleton(X4)),X1),singleton(sK2(X2,X3,singleton(X4)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_19855]) ).
tcf(c_19907,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X2 )
| ( sK3(X3,singleton(X4),X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,singleton(X4),X2),X1),singleton(sK1(X3,singleton(X4),X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_19855]) ).
tcf(c_19908,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X2) = singleton(X4) )
| ( sK1(X3,X2,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK3(X3,X2,singleton(X4)),X1),singleton(sK3(X3,X2,singleton(X4)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_19855]) ).
tcf(c_19909,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(sK3(X3,X2,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_19855]) ).
tcf(c_19910,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(sK3(X3,X2,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_19855]) ).
tcf(c_19911,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(sK3(X3,X2,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_19855]) ).
tcf(c_19912,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X2,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(sK3(X3,X2,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_19855]) ).
tcf(c_19913,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(sK2(X2,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_19855]) ).
tcf(c_19914,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(sK2(X2,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_19855]) ).
tcf(c_19915,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(sK2(X2,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_19855]) ).
tcf(c_19916,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X2,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(sK2(X2,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_19855]) ).
tcf(c_19917,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_19855]) ).
tcf(c_19918,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_19855]) ).
tcf(c_19919,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_19855]) ).
tcf(c_19920,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_19855]) ).
tcf(c_19921,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_19855]) ).
tcf(c_19922,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_19855]) ).
tcf(c_19923,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_19855]) ).
tcf(c_19924,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_19855]) ).
tcf(c_20000,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),singleton(X1),unordered_pair(unordered_pair(X2,X1),singleton(X2)))))) = X0,
inference(superposition,[status(thm)],[c_50,c_19890]) ).
tcf(c_20002,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(singleton(X2),singleton(X1),unordered_pair(unordered_pair(X2,X1),singleton(X2))),X0),singleton(X0))) = X0,
inference(superposition,[status(thm)],[c_50,c_19890]) ).
tcf(c_20006,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(singleton(X2),singleton(X1),unordered_pair(singleton(X2),unordered_pair(X2,X1)))),singleton(X0))) = X0,
inference(superposition,[status(thm)],[c_50,c_19890]) ).
tcf(c_20008,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(singleton(X2),singleton(X1),unordered_pair(unordered_pair(X1,X2),singleton(X2)))),singleton(X0))) = X0,
inference(superposition,[status(thm)],[c_50,c_19890]) ).
tcf(c_20036,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),singleton(X1),unordered_pair(unordered_pair(X2,X1),singleton(X2))),X0))) = X0,
inference(superposition,[status(thm)],[c_50,c_20000]) ).
tcf(c_20040,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),singleton(X1),unordered_pair(singleton(X2),unordered_pair(X2,X1)))))) = X0,
inference(superposition,[status(thm)],[c_50,c_20000]) ).
tcf(c_20042,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),singleton(X1),unordered_pair(unordered_pair(X1,X2),singleton(X2)))))) = X0,
inference(superposition,[status(thm)],[c_50,c_20000]) ).
tcf(c_20076,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(singleton(X2),singleton(X1),unordered_pair(singleton(X2),unordered_pair(X2,X1))),X0),singleton(X0))) = X0,
inference(superposition,[status(thm)],[c_50,c_20002]) ).
tcf(c_20078,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(singleton(X2),singleton(X1),unordered_pair(unordered_pair(X1,X2),singleton(X2))),X0),singleton(X0))) = X0,
inference(superposition,[status(thm)],[c_50,c_20002]) ).
tcf(c_20080,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,singleton(X2))
| ~ in(unordered_pair(unordered_pair(sK5(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,X1),singleton(X0))),X2),singleton(X2)),cartesian_product2(singleton(X2),singleton(X1))) ),
inference(superposition,[status(thm)],[c_20002,c_60]) ).
tcf(c_20088,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(singleton(X2),singleton(X1),unordered_pair(singleton(X2),unordered_pair(X1,X2)))),singleton(X0))) = X0,
inference(superposition,[status(thm)],[c_50,c_20006]) ).
tcf(c_20130,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),singleton(X1),unordered_pair(singleton(X2),unordered_pair(X2,X1))),X0))) = X0,
inference(superposition,[status(thm)],[c_50,c_20036]) ).
tcf(c_20132,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),singleton(X1),unordered_pair(unordered_pair(X1,X2),singleton(X2))),X0))) = X0,
inference(superposition,[status(thm)],[c_50,c_20036]) ).
tcf(c_20140,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),singleton(X1),unordered_pair(singleton(X2),unordered_pair(X1,X2)))))) = X0,
inference(superposition,[status(thm)],[c_50,c_20040]) ).
tcf(c_20158,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(singleton(X2),singleton(X1),unordered_pair(singleton(X2),unordered_pair(X1,X2))),X0),singleton(X0))) = X0,
inference(superposition,[status(thm)],[c_50,c_20076]) ).
tcf(c_20160,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,singleton(X2))
| ~ in(unordered_pair(unordered_pair(sK5(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,X1))),X2),singleton(X2)),cartesian_product2(singleton(X2),singleton(X1))) ),
inference(superposition,[status(thm)],[c_20076,c_60]) ).
tcf(c_20193,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,singleton(X2))
| ~ in(unordered_pair(unordered_pair(sK5(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X1,X0),singleton(X0))),X2),singleton(X2)),cartesian_product2(singleton(X2),singleton(X1))) ),
inference(superposition,[status(thm)],[c_20078,c_60]) ).
tcf(c_20207,plain,
! [X0: $i,X1: $i,X2: $i] : sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),singleton(X1),unordered_pair(singleton(X2),unordered_pair(X1,X2))),X0))) = X0,
inference(superposition,[status(thm)],[c_50,c_20130]) ).
tcf(c_20234,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,singleton(X2))
| ~ in(unordered_pair(unordered_pair(sK5(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X1,X0))),X2),singleton(X2)),cartesian_product2(singleton(X2),singleton(X1))) ),
inference(superposition,[status(thm)],[c_20158,c_60]) ).
tcf(c_20286,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),singleton(X3),unordered_pair(unordered_pair(X2,sK4(singleton(X3),X1,unordered_pair(unordered_pair(X0,X3),singleton(X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2106]) ).
tcf(c_20287,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2106]) ).
tcf(c_20288,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2106]) ).
tcf(c_20289,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2106]) ).
tcf(c_20290,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2106]) ).
tcf(c_20291,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2106]) ).
tcf(c_20292,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(unordered_pair(X5,sK4(X1,X4,unordered_pair(unordered_pair(X3,sK4(X1,X2,X0)),singleton(sK4(X1,X2,X0))))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2106]) ).
tcf(c_20293,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(unordered_pair(X5,sK4(X2,X4,unordered_pair(unordered_pair(X3,sK5(X1,X2,X0)),singleton(sK5(X1,X2,X0))))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2106]) ).
tcf(c_20294,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X6,sK4(cartesian_product2(X3,X1),X5,unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2)))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2106]) ).
tcf(c_20295,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X6,sK4(cartesian_product2(X1,X3),X5,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))),singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2)))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2106]) ).
tcf(c_20296,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X6,sK4(cartesian_product2(X1,X3),X5,unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0)))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2106]) ).
tcf(c_20297,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X6,sK4(cartesian_product2(X1,X3),X5,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))),singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0)))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2106]) ).
tcf(c_20298,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X6,sK4(cartesian_product2(X3,X1),X5,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))),singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2)))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2106]) ).
tcf(c_20299,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X6,sK4(cartesian_product2(X3,X1),X5,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))),singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0)))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2106]) ).
tcf(c_20301,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(singleton(X4),X5,X3)),singleton(sK1(singleton(X4),X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2106]) ).
tcf(c_20302,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,singleton(X5))),singleton(sK2(X3,X4,singleton(X5)))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2106]) ).
tcf(c_20303,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,singleton(X5),X3)),singleton(sK1(X4,singleton(X5),X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2106]) ).
tcf(c_20304,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,singleton(X5))),singleton(sK3(X4,X3,singleton(X5)))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2106]) ).
tcf(c_20305,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2106]) ).
tcf(c_20306,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2106]) ).
tcf(c_20307,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2106]) ).
tcf(c_20308,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2106]) ).
tcf(c_20309,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2106]) ).
tcf(c_20310,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2106]) ).
tcf(c_20311,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2106]) ).
tcf(c_20312,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2106]) ).
tcf(c_20313,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2106]) ).
tcf(c_20314,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2106]) ).
tcf(c_20315,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2106]) ).
tcf(c_20316,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2106]) ).
tcf(c_20317,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2106]) ).
tcf(c_20318,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2106]) ).
tcf(c_20319,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2106]) ).
tcf(c_20320,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2106]) ).
tcf(c_20573,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X2),sK3(X3,X4,X2)),singleton(sK2(X3,X4,X2))) = sK1(X3,X4,X2) )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_20286]) ).
tcf(c_20574,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X2),X4)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_20286]) ).
tcf(c_20575,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X2),X3)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_20286]) ).
tcf(c_20576,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X2,X3,X4),X4)
| ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_20286]) ).
tcf(c_20577,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X2,X4),X4)
| ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_20286]) ).
tcf(c_20578,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(unordered_pair(X3,sK4(singleton(X4),X1,unordered_pair(unordered_pair(sK4(X1,X2,X0),X4),singleton(X4)))),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_20286]) ).
tcf(c_20579,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(unordered_pair(X3,sK4(singleton(X4),X2,unordered_pair(unordered_pair(sK5(X1,X2,X0),X4),singleton(X4)))),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_20286]) ).
tcf(c_20580,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(X4,sK4(singleton(X5),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5),singleton(X5)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_20286]) ).
tcf(c_20581,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(X4,sK4(singleton(X5),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5),singleton(X5)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_20286]) ).
tcf(c_20582,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(X4,sK4(singleton(X5),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5),singleton(X5)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_20286]) ).
tcf(c_20583,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(X4,sK4(singleton(X5),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5),singleton(X5)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_20286]) ).
tcf(c_20584,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(X4,sK4(singleton(X5),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5),singleton(X5)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_20286]) ).
tcf(c_20585,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(X4,sK4(singleton(X5),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5),singleton(X5)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_20286]) ).
tcf(c_20587,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X2 )
| ( sK2(singleton(X3),X4,X2) = X3 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(singleton(X3),X4,X2),X1),singleton(X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_20286]) ).
tcf(c_20588,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK1(X2,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK2(X2,X3,singleton(X4)),X1),singleton(X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_20286]) ).
tcf(c_20589,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X2 )
| ( sK3(X3,singleton(X4),X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,singleton(X4),X2),X1),singleton(X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_20286]) ).
tcf(c_20590,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X2) = singleton(X4) )
| ( sK1(X3,X2,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK3(X3,X2,singleton(X4)),X1),singleton(X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_20286]) ).
tcf(c_20591,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_20286]) ).
tcf(c_20592,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_20286]) ).
tcf(c_20593,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_20286]) ).
tcf(c_20594,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X2,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_20286]) ).
tcf(c_20595,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_20286]) ).
tcf(c_20596,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_20286]) ).
tcf(c_20597,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_20286]) ).
tcf(c_20598,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X2,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_20286]) ).
tcf(c_20599,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_20286]) ).
tcf(c_20600,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_20286]) ).
tcf(c_20601,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_20286]) ).
tcf(c_20602,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_20286]) ).
tcf(c_20603,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_20286]) ).
tcf(c_20604,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_20286]) ).
tcf(c_20605,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_20286]) ).
tcf(c_20606,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_20286]) ).
tcf(c_20765,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),singleton(X3),unordered_pair(unordered_pair(X2,sK4(singleton(X3),X1,unordered_pair(singleton(X3),unordered_pair(X0,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2107]) ).
tcf(c_20766,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2107]) ).
tcf(c_20767,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2107]) ).
tcf(c_20768,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2107]) ).
tcf(c_20769,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2107]) ).
tcf(c_20770,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2107]) ).
tcf(c_20771,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(unordered_pair(X5,sK4(X1,X4,unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(X3,sK4(X1,X2,X0))))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2107]) ).
tcf(c_20772,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(unordered_pair(X5,sK4(X2,X4,unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(X3,sK5(X1,X2,X0))))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2107]) ).
tcf(c_20773,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X6,sK4(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2)))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2107]) ).
tcf(c_20774,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X6,sK4(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2)))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2107]) ).
tcf(c_20775,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X6,sK4(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0)))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2107]) ).
tcf(c_20776,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X6,sK4(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0)))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2107]) ).
tcf(c_20777,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X6,sK4(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2)))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2107]) ).
tcf(c_20778,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X6,sK4(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0)))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2107]) ).
tcf(c_20780,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(singleton(X4),X5,X3)),unordered_pair(X0,sK1(singleton(X4),X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2107]) ).
tcf(c_20781,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,singleton(X5))),unordered_pair(X0,sK2(X3,X4,singleton(X5)))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2107]) ).
tcf(c_20782,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,singleton(X5),X3)),unordered_pair(X0,sK1(X4,singleton(X5),X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2107]) ).
tcf(c_20783,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,singleton(X5))),unordered_pair(X0,sK3(X4,X3,singleton(X5)))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2107]) ).
tcf(c_20784,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2107]) ).
tcf(c_20785,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2107]) ).
tcf(c_20786,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2107]) ).
tcf(c_20787,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2107]) ).
tcf(c_20788,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2107]) ).
tcf(c_20789,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2107]) ).
tcf(c_20790,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2107]) ).
tcf(c_20791,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2107]) ).
tcf(c_20792,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2107]) ).
tcf(c_20793,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2107]) ).
tcf(c_20794,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2107]) ).
tcf(c_20795,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2107]) ).
tcf(c_20796,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2107]) ).
tcf(c_20797,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2107]) ).
tcf(c_20798,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2107]) ).
tcf(c_20799,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2107]) ).
tcf(c_21014,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X2),sK3(X3,X4,X2)),singleton(sK2(X3,X4,X2))) = sK1(X3,X4,X2) )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_20765]) ).
tcf(c_21015,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X2),X4)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_20765]) ).
tcf(c_21016,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X2),X3)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_20765]) ).
tcf(c_21017,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X2,X3,X4),X4)
| ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_20765]) ).
tcf(c_21018,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X2,X4),X4)
| ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_20765]) ).
tcf(c_21019,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(unordered_pair(X3,sK4(singleton(X4),X1,unordered_pair(singleton(X4),unordered_pair(sK4(X1,X2,X0),X4)))),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_20765]) ).
tcf(c_21020,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(unordered_pair(X3,sK4(singleton(X4),X2,unordered_pair(singleton(X4),unordered_pair(sK5(X1,X2,X0),X4)))),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_20765]) ).
tcf(c_21021,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(X4,sK4(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_20765]) ).
tcf(c_21022,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(X4,sK4(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_20765]) ).
tcf(c_21023,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(X4,sK4(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_20765]) ).
tcf(c_21024,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(X4,sK4(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_20765]) ).
tcf(c_21025,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(X4,sK4(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_20765]) ).
tcf(c_21026,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(X4,sK4(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_20765]) ).
tcf(c_21028,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X2 )
| ( sK2(singleton(X3),X4,X2) = X3 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(singleton(X3),X4,X2),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_20765]) ).
tcf(c_21029,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK1(X2,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,singleton(X4)),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_20765]) ).
tcf(c_21030,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X2 )
| ( sK3(X3,singleton(X4),X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,singleton(X4),X2),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_20765]) ).
tcf(c_21031,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X2) = singleton(X4) )
| ( sK1(X3,X2,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,singleton(X4)),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_20765]) ).
tcf(c_21032,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_20765]) ).
tcf(c_21033,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_20765]) ).
tcf(c_21034,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_20765]) ).
tcf(c_21035,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X2,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_20765]) ).
tcf(c_21036,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_20765]) ).
tcf(c_21037,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_20765]) ).
tcf(c_21038,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_20765]) ).
tcf(c_21039,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X2,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_20765]) ).
tcf(c_21040,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_20765]) ).
tcf(c_21041,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_20765]) ).
tcf(c_21042,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_20765]) ).
tcf(c_21043,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_20765]) ).
tcf(c_21044,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_20765]) ).
tcf(c_21045,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_20765]) ).
tcf(c_21046,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_20765]) ).
tcf(c_21047,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_20765]) ).
tcf(c_21200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,singleton(X3),unordered_pair(singleton(X0),unordered_pair(X3,X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2108]) ).
tcf(c_21201,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2108]) ).
tcf(c_21202,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2108]) ).
tcf(c_21203,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2108]) ).
tcf(c_21204,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2108]) ).
tcf(c_21205,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2108]) ).
tcf(c_21206,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK4(X4,X1,unordered_pair(singleton(X3),unordered_pair(sK4(X1,X2,X0),X3)))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2108]) ).
tcf(c_21207,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK4(X4,X2,unordered_pair(singleton(X3),unordered_pair(sK5(X1,X2,X0),X3)))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2108]) ).
tcf(c_21208,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK4(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X4)))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2108]) ).
tcf(c_21209,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK4(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X4)))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2108]) ).
tcf(c_21210,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK4(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X4)))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2108]) ).
tcf(c_21211,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK4(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X4)))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2108]) ).
tcf(c_21212,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK4(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X4)))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2108]) ).
tcf(c_21213,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK4(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X4)))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2108]) ).
tcf(c_21215,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(singleton(X4),X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2108]) ).
tcf(c_21216,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,singleton(X5)),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2108]) ).
tcf(c_21217,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,singleton(X5),X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2108]) ).
tcf(c_21218,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,singleton(X5)),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2108]) ).
tcf(c_21219,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2108]) ).
tcf(c_21220,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2108]) ).
tcf(c_21221,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2108]) ).
tcf(c_21222,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2108]) ).
tcf(c_21223,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2108]) ).
tcf(c_21224,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2108]) ).
tcf(c_21225,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2108]) ).
tcf(c_21226,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2108]) ).
tcf(c_21227,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2108]) ).
tcf(c_21228,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2108]) ).
tcf(c_21229,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2108]) ).
tcf(c_21230,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2108]) ).
tcf(c_21231,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2108]) ).
tcf(c_21232,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2108]) ).
tcf(c_21233,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2108]) ).
tcf(c_21234,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2108]) ).
tcf(c_21306,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X1),sK3(X3,X4,X1)),singleton(sK2(X3,X4,X1))) = sK1(X3,X4,X1) )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_21200]) ).
tcf(c_21307,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X1),X4)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_21200]) ).
tcf(c_21308,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X1),X3)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_21200]) ).
tcf(c_21309,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X1,X3,X4),X4)
| ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_21200]) ).
tcf(c_21310,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X1,X4),X4)
| ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_21200]) ).
tcf(c_21311,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X1,unordered_pair(unordered_pair(X3,sK4(X1,singleton(X4),unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(X4,sK4(X1,X2,X0))))),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_21200]) ).
tcf(c_21312,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X2,unordered_pair(unordered_pair(X3,sK4(X2,singleton(X4),unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(X4,sK5(X1,X2,X0))))),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_21200]) ).
tcf(c_21313,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,sK4(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X2)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_21200]) ).
tcf(c_21314,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,sK4(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X0,X2)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_21200]) ).
tcf(c_21315,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,sK4(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X0)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_21200]) ).
tcf(c_21316,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,sK4(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X2,X0)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_21200]) ).
tcf(c_21317,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,sK4(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X0,X2)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_21200]) ).
tcf(c_21318,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,sK4(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X2,X0)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_21200]) ).
tcf(c_21320,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X1 )
| ( sK2(singleton(X3),X4,X1) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(singleton(X3),X4,X1)),unordered_pair(X2,sK1(singleton(X3),X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_21200]) ).
tcf(c_21321,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X3) = singleton(X4) )
| ( sK1(X1,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,singleton(X4))),unordered_pair(X2,sK2(X1,X3,singleton(X4)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_21200]) ).
tcf(c_21322,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X1 )
| ( sK3(X3,singleton(X4),X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,singleton(X4),X1)),unordered_pair(X2,sK1(X3,singleton(X4),X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_21200]) ).
tcf(c_21323,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X1) = singleton(X4) )
| ( sK1(X3,X1,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,singleton(X4))),unordered_pair(X2,sK3(X3,X1,singleton(X4)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_21200]) ).
tcf(c_21324,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_21200]) ).
tcf(c_21325,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_21200]) ).
tcf(c_21326,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_21200]) ).
tcf(c_21327,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X1,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_21200]) ).
tcf(c_21328,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_21200]) ).
tcf(c_21329,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_21200]) ).
tcf(c_21330,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_21200]) ).
tcf(c_21331,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X1,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_21200]) ).
tcf(c_21332,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_21200]) ).
tcf(c_21333,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_21200]) ).
tcf(c_21334,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_21200]) ).
tcf(c_21335,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_21200]) ).
tcf(c_21336,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_21200]) ).
tcf(c_21337,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_21200]) ).
tcf(c_21338,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_21200]) ).
tcf(c_21339,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_21200]) ).
tcf(c_21575,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,singleton(X3),unordered_pair(singleton(X0),unordered_pair(X0,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2109]) ).
tcf(c_21576,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2109]) ).
tcf(c_21577,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2109]) ).
tcf(c_21578,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2109]) ).
tcf(c_21579,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2109]) ).
tcf(c_21580,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2109]) ).
tcf(c_21581,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK4(X4,X1,unordered_pair(singleton(X3),unordered_pair(X3,sK4(X1,X2,X0))))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2109]) ).
tcf(c_21582,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK4(X4,X2,unordered_pair(singleton(X3),unordered_pair(X3,sK5(X1,X2,X0))))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2109]) ).
tcf(c_21583,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK4(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2)))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2109]) ).
tcf(c_21584,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK4(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2)))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2109]) ).
tcf(c_21585,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK4(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0)))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2109]) ).
tcf(c_21586,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK4(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0)))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2109]) ).
tcf(c_21587,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK4(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2)))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2109]) ).
tcf(c_21588,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK4(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0)))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2109]) ).
tcf(c_21590,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(singleton(X4),X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2109]) ).
tcf(c_21591,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,singleton(X5)))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2109]) ).
tcf(c_21592,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,singleton(X5),X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2109]) ).
tcf(c_21593,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,singleton(X5)))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2109]) ).
tcf(c_21594,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2109]) ).
tcf(c_21595,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2109]) ).
tcf(c_21596,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2109]) ).
tcf(c_21597,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2109]) ).
tcf(c_21598,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2109]) ).
tcf(c_21599,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2109]) ).
tcf(c_21600,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2109]) ).
tcf(c_21601,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2109]) ).
tcf(c_21602,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2109]) ).
tcf(c_21603,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2109]) ).
tcf(c_21604,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2109]) ).
tcf(c_21605,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2109]) ).
tcf(c_21606,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2109]) ).
tcf(c_21607,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2109]) ).
tcf(c_21608,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2109]) ).
tcf(c_21609,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2109]) ).
tcf(c_21833,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X1),sK3(X3,X4,X1)),singleton(sK2(X3,X4,X1))) = sK1(X3,X4,X1) )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_21575]) ).
tcf(c_21834,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X1),X4)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_21575]) ).
tcf(c_21835,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X1),X3)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_21575]) ).
tcf(c_21836,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X1,X3,X4),X4)
| ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_21575]) ).
tcf(c_21837,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X1,X4),X4)
| ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_21575]) ).
tcf(c_21838,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X1,unordered_pair(unordered_pair(X3,sK4(X1,singleton(X4),unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(sK4(X1,X2,X0),X4)))),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_21575]) ).
tcf(c_21839,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X2,unordered_pair(unordered_pair(X3,sK4(X2,singleton(X4),unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(sK5(X1,X2,X0),X4)))),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_21575]) ).
tcf(c_21840,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,sK4(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_21575]) ).
tcf(c_21841,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,sK4(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_21575]) ).
tcf(c_21842,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,sK4(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_21575]) ).
tcf(c_21843,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,sK4(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_21575]) ).
tcf(c_21844,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,sK4(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_21575]) ).
tcf(c_21845,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,sK4(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_21575]) ).
tcf(c_21847,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X1 )
| ( sK2(singleton(X3),X4,X1) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(singleton(X3),X4,X1)),unordered_pair(sK1(singleton(X3),X4,X1),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_21575]) ).
tcf(c_21848,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X3) = singleton(X4) )
| ( sK1(X1,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,singleton(X4))),unordered_pair(sK2(X1,X3,singleton(X4)),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_21575]) ).
tcf(c_21849,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X1 )
| ( sK3(X3,singleton(X4),X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,singleton(X4),X1)),unordered_pair(sK1(X3,singleton(X4),X1),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_21575]) ).
tcf(c_21850,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X1) = singleton(X4) )
| ( sK1(X3,X1,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,singleton(X4))),unordered_pair(sK3(X3,X1,singleton(X4)),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_21575]) ).
tcf(c_21851,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_21575]) ).
tcf(c_21852,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_21575]) ).
tcf(c_21853,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_21575]) ).
tcf(c_21854,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X1,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_21575]) ).
tcf(c_21855,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_21575]) ).
tcf(c_21856,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_21575]) ).
tcf(c_21857,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_21575]) ).
tcf(c_21858,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X1,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_21575]) ).
tcf(c_21859,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_21575]) ).
tcf(c_21860,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_21575]) ).
tcf(c_21861,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_21575]) ).
tcf(c_21862,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_21575]) ).
tcf(c_21863,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_21575]) ).
tcf(c_21864,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_21575]) ).
tcf(c_21865,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_21575]) ).
tcf(c_21866,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_21575]) ).
tcf(c_22006,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = cartesian_product2(X0,X1) )
| ( sK4(singleton(X5),X2,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X2,X3,sK4(cartesian_product2(X2,X3),X4,sK1(X0,X1,cartesian_product2(cartesian_product2(X2,X3),X4))))))) = X5 )
| ( unordered_pair(unordered_pair(sK2(X0,X1,cartesian_product2(cartesian_product2(X2,X3),X4)),sK3(X0,X1,cartesian_product2(cartesian_product2(X2,X3),X4))),singleton(sK2(X0,X1,cartesian_product2(cartesian_product2(X2,X3),X4)))) = sK1(X0,X1,cartesian_product2(cartesian_product2(X2,X3),X4)) ) ),
inference(superposition,[status(thm)],[c_58,c_2282]) ).
tcf(c_22007,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)),X5)
| ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_2282]) ).
tcf(c_22008,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)),X4)
| ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_2282]) ).
tcf(c_22009,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X3),X4) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK2(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_2282]) ).
tcf(c_22010,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X1,X2),X3)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK3(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_2282]) ).
tcf(c_22011,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK4(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X0)))))) = X5 )
| ~ in(X0,cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X3),X4)) ),
inference(superposition,[status(thm)],[c_60,c_2282]) ).
tcf(c_22012,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X2,X3,sK4(cartesian_product2(X2,X3),X4,sK5(X1,cartesian_product2(cartesian_product2(X2,X3),X4),X0)))))) = X5 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(cartesian_product2(X2,X3),X4))) ),
inference(superposition,[status(thm)],[c_61,c_2282]) ).
tcf(c_22013,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X4,unordered_pair(unordered_pair(X0,X3),singleton(X0))))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_64,c_2282]) ).
tcf(c_22015,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X4,unordered_pair(unordered_pair(X3,X0),singleton(X0))))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_809,c_2282]) ).
tcf(c_22016,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X4,unordered_pair(singleton(X0),unordered_pair(X3,X0))))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_882,c_2282]) ).
tcf(c_22018,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X4,unordered_pair(singleton(X0),unordered_pair(X0,X3))))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_900,c_2282]) ).
tcf(c_22019,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(singleton(X4),X5) )
| ( sK2(singleton(X4),X5,cartesian_product2(cartesian_product2(X1,X2),X3)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(singleton(X4),X5,cartesian_product2(cartesian_product2(X1,X2),X3))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_2282]) ).
tcf(c_22020,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X3),X4) = singleton(X5) )
| ( sK1(cartesian_product2(cartesian_product2(X1,X2),X3),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK2(cartesian_product2(cartesian_product2(X1,X2),X3),X4,singleton(X5))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_2282]) ).
tcf(c_22021,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,singleton(X5)) )
| ( sK3(X4,singleton(X5),cartesian_product2(cartesian_product2(X1,X2),X3)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,singleton(X5),cartesian_product2(cartesian_product2(X1,X2),X3))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_2282]) ).
tcf(c_22022,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X1,X2),X3)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(cartesian_product2(X1,X2),X3),singleton(X5)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK3(X4,cartesian_product2(cartesian_product2(X1,X2),X3),singleton(X5))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_2282]) ).
tcf(c_22023,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X1,X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK3(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_2282]) ).
tcf(c_22024,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X1,X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK3(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_2282]) ).
tcf(c_22025,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X1,X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK3(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_2282]) ).
tcf(c_22026,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X1,X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK3(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_2282]) ).
tcf(c_22027,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK2(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_2282]) ).
tcf(c_22028,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK2(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_2282]) ).
tcf(c_22029,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK2(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_2282]) ).
tcf(c_22030,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK2(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_2282]) ).
tcf(c_22031,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_2282]) ).
tcf(c_22032,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_2282]) ).
tcf(c_22033,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_2282]) ).
tcf(c_22034,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_2282]) ).
tcf(c_22035,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_2282]) ).
tcf(c_22036,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_2282]) ).
tcf(c_22037,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_2282]) ).
tcf(c_22038,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_2282]) ).
tcf(c_22298,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(X3,X4)) = cartesian_product2(X0,X1) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X3,X4,sK5(X2,cartesian_product2(X3,X4),sK1(X0,X1,cartesian_product2(X2,cartesian_product2(X3,X4)))))))) = X5 )
| ( unordered_pair(unordered_pair(sK2(X0,X1,cartesian_product2(X2,cartesian_product2(X3,X4))),sK3(X0,X1,cartesian_product2(X2,cartesian_product2(X3,X4)))),singleton(sK2(X0,X1,cartesian_product2(X2,cartesian_product2(X3,X4))))) = sK1(X0,X1,cartesian_product2(X2,cartesian_product2(X3,X4))) ) ),
inference(superposition,[status(thm)],[c_58,c_2283]) ).
tcf(c_22299,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))),X5)
| ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_2283]) ).
tcf(c_22300,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))),X4)
| ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_2283]) ).
tcf(c_22301,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_2283]) ).
tcf(c_22302,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X1,X2))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK3(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_2283]) ).
tcf(c_22303,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X2,X3,sK5(X1,cartesian_product2(X2,X3),sK4(cartesian_product2(X1,cartesian_product2(X2,X3)),X4,X0)))))) = X5 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,cartesian_product2(X2,X3)),X4)) ),
inference(superposition,[status(thm)],[c_60,c_2283]) ).
tcf(c_22304,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X3,X4,sK5(X2,cartesian_product2(X3,X4),sK5(X1,cartesian_product2(X2,cartesian_product2(X3,X4)),X0)))))) = X5 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,cartesian_product2(X3,X4)))) ),
inference(superposition,[status(thm)],[c_61,c_2283]) ).
tcf(c_22305,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X1,X2,sK5(X4,cartesian_product2(X1,X2),unordered_pair(unordered_pair(X3,X0),singleton(X3))))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_64,c_2283]) ).
tcf(c_22307,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X1,X2,sK5(X4,cartesian_product2(X1,X2),unordered_pair(unordered_pair(X0,X3),singleton(X3))))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_809,c_2283]) ).
tcf(c_22308,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X1,X2,sK5(X4,cartesian_product2(X1,X2),unordered_pair(singleton(X3),unordered_pair(X0,X3))))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_882,c_2283]) ).
tcf(c_22310,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X1,X2,sK5(X4,cartesian_product2(X1,X2),unordered_pair(singleton(X3),unordered_pair(X3,X0))))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_900,c_2283]) ).
tcf(c_22311,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(singleton(X4),X5) )
| ( sK2(singleton(X4),X5,cartesian_product2(X3,cartesian_product2(X1,X2))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(singleton(X4),X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_2283]) ).
tcf(c_22312,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,singleton(X5))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_2283]) ).
tcf(c_22313,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,singleton(X5)) )
| ( sK3(X4,singleton(X5),cartesian_product2(X3,cartesian_product2(X1,X2))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,singleton(X5),cartesian_product2(X3,cartesian_product2(X1,X2)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_2283]) ).
tcf(c_22314,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X1,X2))) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),singleton(X5)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK3(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),singleton(X5))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_2283]) ).
tcf(c_22315,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X1,X2))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK3(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_2283]) ).
tcf(c_22316,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X1,X2))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK3(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_2283]) ).
tcf(c_22317,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X1,X2))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK3(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_2283]) ).
tcf(c_22318,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X1,X2))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK3(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_2283]) ).
tcf(c_22319,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_2283]) ).
tcf(c_22320,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_2283]) ).
tcf(c_22321,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_2283]) ).
tcf(c_22322,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_2283]) ).
tcf(c_22323,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_2283]) ).
tcf(c_22324,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_2283]) ).
tcf(c_22325,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_2283]) ).
tcf(c_22326,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_2283]) ).
tcf(c_22327,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_2283]) ).
tcf(c_22328,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_2283]) ).
tcf(c_22329,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_2283]) ).
tcf(c_22330,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_2283]) ).
tcf(c_22587,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,singleton(X3),unordered_pair(unordered_pair(X0,X3),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2284]) ).
tcf(c_22588,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2284]) ).
tcf(c_22589,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2284]) ).
tcf(c_22590,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2284]) ).
tcf(c_22591,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2284]) ).
tcf(c_22592,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2284]) ).
tcf(c_22593,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X4,X1,unordered_pair(unordered_pair(X3,sK4(X1,X2,X0)),singleton(X3)))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2284]) ).
tcf(c_22594,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X4,X2,unordered_pair(unordered_pair(X3,sK5(X1,X2,X0)),singleton(X3)))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2284]) ).
tcf(c_22595,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK4(X5,cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))),singleton(X4)))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2284]) ).
tcf(c_22596,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK4(X5,cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))),singleton(X4)))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2284]) ).
tcf(c_22597,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK4(X5,cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))),singleton(X4)))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2284]) ).
tcf(c_22598,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK4(X5,cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))),singleton(X4)))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2284]) ).
tcf(c_22599,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK4(X5,cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))),singleton(X4)))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2284]) ).
tcf(c_22600,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK4(X5,cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))),singleton(X4)))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2284]) ).
tcf(c_22602,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(singleton(X4),X5,X3)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2284]) ).
tcf(c_22603,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,singleton(X5))),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2284]) ).
tcf(c_22604,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,singleton(X5),X3)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2284]) ).
tcf(c_22605,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,singleton(X5))),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2284]) ).
tcf(c_22606,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2284]) ).
tcf(c_22607,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2284]) ).
tcf(c_22608,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2284]) ).
tcf(c_22609,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2284]) ).
tcf(c_22610,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2284]) ).
tcf(c_22611,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2284]) ).
tcf(c_22612,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2284]) ).
tcf(c_22613,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2284]) ).
tcf(c_22614,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2284]) ).
tcf(c_22615,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2284]) ).
tcf(c_22616,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2284]) ).
tcf(c_22617,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2284]) ).
tcf(c_22618,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2284]) ).
tcf(c_22619,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2284]) ).
tcf(c_22620,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2284]) ).
tcf(c_22621,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2284]) ).
tcf(c_22623,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X1),sK3(X3,X4,X1)),singleton(sK2(X3,X4,X1))) = sK1(X3,X4,X1) )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_22587]) ).
tcf(c_22624,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X1),X4)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_22587]) ).
tcf(c_22625,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X1),X3)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_22587]) ).
tcf(c_22626,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X1,X3,X4),X4)
| ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_22587]) ).
tcf(c_22627,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X1,X4),X4)
| ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_22587]) ).
tcf(c_22628,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X1,unordered_pair(singleton(X3),unordered_pair(X3,sK4(X1,singleton(X4),unordered_pair(unordered_pair(sK4(X1,X2,X0),X4),singleton(sK4(X1,X2,X0))))))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_22587]) ).
tcf(c_22629,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X2,unordered_pair(singleton(X3),unordered_pair(X3,sK4(X2,singleton(X4),unordered_pair(unordered_pair(sK5(X1,X2,X0),X4),singleton(sK5(X1,X2,X0))))))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_22587]) ).
tcf(c_22630,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,sK4(cartesian_product2(X3,X1),singleton(X5),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_22587]) ).
tcf(c_22631,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,sK4(cartesian_product2(X1,X3),singleton(X5),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5),singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_22587]) ).
tcf(c_22632,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,sK4(cartesian_product2(X1,X3),singleton(X5),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_22587]) ).
tcf(c_22633,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,sK4(cartesian_product2(X1,X3),singleton(X5),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5),singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_22587]) ).
tcf(c_22634,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,sK4(cartesian_product2(X3,X1),singleton(X5),unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5),singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_22587]) ).
tcf(c_22635,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,sK4(cartesian_product2(X3,X1),singleton(X5),unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5),singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_22587]) ).
tcf(c_22637,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X1 )
| ( sK2(singleton(X3),X4,X1) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(singleton(X3),X4,X1),X2),singleton(sK1(singleton(X3),X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_22587]) ).
tcf(c_22638,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X3) = singleton(X4) )
| ( sK1(X1,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK2(X1,X3,singleton(X4)),X2),singleton(sK2(X1,X3,singleton(X4)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_22587]) ).
tcf(c_22639,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X1 )
| ( sK3(X3,singleton(X4),X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,singleton(X4),X1),X2),singleton(sK1(X3,singleton(X4),X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_22587]) ).
tcf(c_22640,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X1) = singleton(X4) )
| ( sK1(X3,X1,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK3(X3,X1,singleton(X4)),X2),singleton(sK3(X3,X1,singleton(X4)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_22587]) ).
tcf(c_22641,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_22587]) ).
tcf(c_22642,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_22587]) ).
tcf(c_22643,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_22587]) ).
tcf(c_22644,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X1,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_22587]) ).
tcf(c_22645,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_22587]) ).
tcf(c_22646,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_22587]) ).
tcf(c_22647,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_22587]) ).
tcf(c_22648,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X1,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_22587]) ).
tcf(c_22649,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_22587]) ).
tcf(c_22650,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_22587]) ).
tcf(c_22651,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_22587]) ).
tcf(c_22652,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_22587]) ).
tcf(c_22653,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_22587]) ).
tcf(c_22654,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_22587]) ).
tcf(c_22655,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_22587]) ).
tcf(c_22656,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_22587]) ).
tcf(c_22721,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(singleton(X3),X1,unordered_pair(singleton(X3),unordered_pair(X3,X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2181]) ).
tcf(c_22722,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2181]) ).
tcf(c_22723,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2181]) ).
tcf(c_22724,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2181]) ).
tcf(c_22725,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2181]) ).
tcf(c_22726,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2181]) ).
tcf(c_22727,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK5(X1,X4,unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(sK4(X1,X2,X0),X3)))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2181]) ).
tcf(c_22728,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK5(X2,X4,unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(sK5(X1,X2,X0),X3)))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2181]) ).
tcf(c_22729,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK5(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X4)))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2181]) ).
tcf(c_22730,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK5(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X4)))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2181]) ).
tcf(c_22731,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK5(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X4)))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2181]) ).
tcf(c_22732,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK5(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X4)))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2181]) ).
tcf(c_22733,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK5(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X4)))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2181]) ).
tcf(c_22734,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK5(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X4)))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2181]) ).
tcf(c_22736,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(singleton(X4),X5,X3)),unordered_pair(sK1(singleton(X4),X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2181]) ).
tcf(c_22737,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,singleton(X5))),unordered_pair(sK2(X3,X4,singleton(X5)),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2181]) ).
tcf(c_22738,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,singleton(X5),X3)),unordered_pair(sK1(X4,singleton(X5),X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2181]) ).
tcf(c_22739,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,singleton(X5))),unordered_pair(sK3(X4,X3,singleton(X5)),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2181]) ).
tcf(c_22740,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2181]) ).
tcf(c_22741,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2181]) ).
tcf(c_22742,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2181]) ).
tcf(c_22743,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2181]) ).
tcf(c_22744,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2181]) ).
tcf(c_22745,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2181]) ).
tcf(c_22746,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2181]) ).
tcf(c_22747,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2181]) ).
tcf(c_22748,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2181]) ).
tcf(c_22749,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2181]) ).
tcf(c_22750,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2181]) ).
tcf(c_22751,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2181]) ).
tcf(c_22752,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2181]) ).
tcf(c_22753,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2181]) ).
tcf(c_22754,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2181]) ).
tcf(c_22755,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2181]) ).
tcf(c_22825,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X1),sK3(X3,X4,X1)),singleton(sK2(X3,X4,X1))) = sK1(X3,X4,X1) )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_22721]) ).
tcf(c_22826,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X1),X4)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_22721]) ).
tcf(c_22827,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X1),X3)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_22721]) ).
tcf(c_22828,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X1,X3,X4),X4)
| ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK2(X1,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_22721]) ).
tcf(c_22829,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X1,X4),X4)
| ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK3(X3,X1,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_22721]) ).
tcf(c_22830,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X1,unordered_pair(unordered_pair(X3,sK5(singleton(X4),X1,unordered_pair(singleton(X4),unordered_pair(X4,sK4(X1,X2,X0))))),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_22721]) ).
tcf(c_22831,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X2,unordered_pair(unordered_pair(X3,sK5(singleton(X4),X2,unordered_pair(singleton(X4),unordered_pair(X4,sK5(X1,X2,X0))))),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_22721]) ).
tcf(c_22832,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,sK5(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X2)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_22721]) ).
tcf(c_22833,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,sK5(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X0,X2)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_22721]) ).
tcf(c_22834,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,sK5(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X0)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_22721]) ).
tcf(c_22835,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,sK5(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X2,X0)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_22721]) ).
tcf(c_22836,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,sK5(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X0,X2)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_22721]) ).
tcf(c_22837,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,sK5(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X2,X0)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_22721]) ).
tcf(c_22839,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X1 )
| ( sK2(singleton(X3),X4,X1) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(singleton(X3),X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_22721]) ).
tcf(c_22840,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X3) = singleton(X4) )
| ( sK1(X1,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK2(X1,X3,singleton(X4)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_22721]) ).
tcf(c_22841,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X1 )
| ( sK3(X3,singleton(X4),X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,singleton(X4),X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_22721]) ).
tcf(c_22842,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X1) = singleton(X4) )
| ( sK1(X3,X1,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK3(X3,X1,singleton(X4)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_22721]) ).
tcf(c_22843,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK3(X3,X1,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_22721]) ).
tcf(c_22844,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK3(X3,X1,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_22721]) ).
tcf(c_22845,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK3(X3,X1,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_22721]) ).
tcf(c_22846,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X1,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK3(X3,X1,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_22721]) ).
tcf(c_22847,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK2(X1,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_22721]) ).
tcf(c_22848,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK2(X1,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_22721]) ).
tcf(c_22849,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK2(X1,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_22721]) ).
tcf(c_22850,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X1,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK2(X1,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_22721]) ).
tcf(c_22851,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_22721]) ).
tcf(c_22852,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_22721]) ).
tcf(c_22853,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_22721]) ).
tcf(c_22854,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_22721]) ).
tcf(c_22855,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_22721]) ).
tcf(c_22856,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_22721]) ).
tcf(c_22857,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_22721]) ).
tcf(c_22858,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_22721]) ).
tcf(c_22960,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(singleton(X3),X1,unordered_pair(unordered_pair(X0,X3),singleton(X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2182]) ).
tcf(c_22961,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2182]) ).
tcf(c_22962,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2182]) ).
tcf(c_22963,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2182]) ).
tcf(c_22964,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2182]) ).
tcf(c_22965,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2182]) ).
tcf(c_22966,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK5(X1,X4,unordered_pair(unordered_pair(X3,sK4(X1,X2,X0)),singleton(sK4(X1,X2,X0))))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2182]) ).
tcf(c_22967,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK5(X2,X4,unordered_pair(unordered_pair(X3,sK5(X1,X2,X0)),singleton(sK5(X1,X2,X0))))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2182]) ).
tcf(c_22968,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK5(cartesian_product2(X3,X1),X5,unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2)))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2182]) ).
tcf(c_22969,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK5(cartesian_product2(X1,X3),X5,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))),singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2)))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2182]) ).
tcf(c_22970,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK5(cartesian_product2(X1,X3),X5,unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0)))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2182]) ).
tcf(c_22971,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK5(cartesian_product2(X1,X3),X5,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))),singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0)))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2182]) ).
tcf(c_22972,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK5(cartesian_product2(X3,X1),X5,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))),singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2)))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2182]) ).
tcf(c_22973,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK5(cartesian_product2(X3,X1),X5,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))),singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0)))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2182]) ).
tcf(c_22975,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(singleton(X4),X5,X3)),singleton(sK1(singleton(X4),X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2182]) ).
tcf(c_22976,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,singleton(X5))),singleton(sK2(X3,X4,singleton(X5)))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2182]) ).
tcf(c_22977,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,singleton(X5),X3)),singleton(sK1(X4,singleton(X5),X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2182]) ).
tcf(c_22978,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,singleton(X5))),singleton(sK3(X4,X3,singleton(X5)))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2182]) ).
tcf(c_22979,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2182]) ).
tcf(c_22980,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2182]) ).
tcf(c_22981,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2182]) ).
tcf(c_22982,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2182]) ).
tcf(c_22983,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2182]) ).
tcf(c_22984,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2182]) ).
tcf(c_22985,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2182]) ).
tcf(c_22986,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2182]) ).
tcf(c_22987,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2182]) ).
tcf(c_22988,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2182]) ).
tcf(c_22989,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2182]) ).
tcf(c_22990,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2182]) ).
tcf(c_22991,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2182]) ).
tcf(c_22992,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2182]) ).
tcf(c_22993,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2182]) ).
tcf(c_22994,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2182]) ).
tcf(c_23092,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X1),sK3(X3,X4,X1)),singleton(sK2(X3,X4,X1))) = sK1(X3,X4,X1) )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_22960]) ).
tcf(c_23093,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X1),X4)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_22960]) ).
tcf(c_23094,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X1),X3)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_22960]) ).
tcf(c_23095,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X1,X3,X4),X4)
| ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_22960]) ).
tcf(c_23096,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X1,X4),X4)
| ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_22960]) ).
tcf(c_23097,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X1,unordered_pair(unordered_pair(X3,sK5(singleton(X4),X1,unordered_pair(unordered_pair(sK4(X1,X2,X0),X4),singleton(X4)))),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_22960]) ).
tcf(c_23098,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X2,unordered_pair(unordered_pair(X3,sK5(singleton(X4),X2,unordered_pair(unordered_pair(sK5(X1,X2,X0),X4),singleton(X4)))),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_22960]) ).
tcf(c_23099,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,sK5(singleton(X5),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5),singleton(X5)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_22960]) ).
tcf(c_23100,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,sK5(singleton(X5),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5),singleton(X5)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_22960]) ).
tcf(c_23101,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,sK5(singleton(X5),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5),singleton(X5)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_22960]) ).
tcf(c_23102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,sK5(singleton(X5),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5),singleton(X5)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_22960]) ).
tcf(c_23103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,sK5(singleton(X5),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5),singleton(X5)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_22960]) ).
tcf(c_23104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,sK5(singleton(X5),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5),singleton(X5)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_22960]) ).
tcf(c_23106,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X1 )
| ( sK2(singleton(X3),X4,X1) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(singleton(X3),X4,X1),X2),singleton(X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_22960]) ).
tcf(c_23107,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X3) = singleton(X4) )
| ( sK1(X1,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK2(X1,X3,singleton(X4)),X2),singleton(X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_22960]) ).
tcf(c_23108,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X1 )
| ( sK3(X3,singleton(X4),X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,singleton(X4),X1),X2),singleton(X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_22960]) ).
tcf(c_23109,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X1) = singleton(X4) )
| ( sK1(X3,X1,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK3(X3,X1,singleton(X4)),X2),singleton(X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_22960]) ).
tcf(c_23110,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_22960]) ).
tcf(c_23111,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_22960]) ).
tcf(c_23112,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_22960]) ).
tcf(c_23113,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X1,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_22960]) ).
tcf(c_23114,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_22960]) ).
tcf(c_23115,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_22960]) ).
tcf(c_23116,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_22960]) ).
tcf(c_23117,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X1,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_22960]) ).
tcf(c_23118,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_22960]) ).
tcf(c_23119,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_22960]) ).
tcf(c_23120,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_22960]) ).
tcf(c_23121,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_22960]) ).
tcf(c_23122,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_22960]) ).
tcf(c_23123,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_22960]) ).
tcf(c_23124,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_22960]) ).
tcf(c_23125,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_22960]) ).
tcf(c_23253,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(singleton(X3),X1,unordered_pair(singleton(X3),unordered_pair(X0,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2183]) ).
tcf(c_23254,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2183]) ).
tcf(c_23255,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2183]) ).
tcf(c_23256,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2183]) ).
tcf(c_23257,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2183]) ).
tcf(c_23258,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2183]) ).
tcf(c_23259,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK5(X1,X4,unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(X3,sK4(X1,X2,X0))))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2183]) ).
tcf(c_23260,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK5(X2,X4,unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(X3,sK5(X1,X2,X0))))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2183]) ).
tcf(c_23261,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK5(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2)))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2183]) ).
tcf(c_23262,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK5(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2)))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2183]) ).
tcf(c_23263,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK5(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0)))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2183]) ).
tcf(c_23264,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK5(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0)))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2183]) ).
tcf(c_23265,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK5(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2)))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2183]) ).
tcf(c_23266,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK5(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0)))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2183]) ).
tcf(c_23268,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(singleton(X4),X5,X3)),unordered_pair(X0,sK1(singleton(X4),X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2183]) ).
tcf(c_23269,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,singleton(X5))),unordered_pair(X0,sK2(X3,X4,singleton(X5)))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2183]) ).
tcf(c_23270,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,singleton(X5),X3)),unordered_pair(X0,sK1(X4,singleton(X5),X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2183]) ).
tcf(c_23271,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,singleton(X5))),unordered_pair(X0,sK3(X4,X3,singleton(X5)))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2183]) ).
tcf(c_23272,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2183]) ).
tcf(c_23273,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2183]) ).
tcf(c_23274,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2183]) ).
tcf(c_23275,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2183]) ).
tcf(c_23276,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2183]) ).
tcf(c_23277,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2183]) ).
tcf(c_23278,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2183]) ).
tcf(c_23279,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2183]) ).
tcf(c_23280,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2183]) ).
tcf(c_23281,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2183]) ).
tcf(c_23282,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2183]) ).
tcf(c_23283,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2183]) ).
tcf(c_23284,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2183]) ).
tcf(c_23285,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2183]) ).
tcf(c_23286,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2183]) ).
tcf(c_23287,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2183]) ).
tcf(c_23342,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X1),sK3(X3,X4,X1)),singleton(sK2(X3,X4,X1))) = sK1(X3,X4,X1) )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_23253]) ).
tcf(c_23343,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X1),X4)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_23253]) ).
tcf(c_23344,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X1),X3)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_23253]) ).
tcf(c_23345,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X1,X3,X4),X4)
| ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK2(X1,X3,X4),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_23253]) ).
tcf(c_23346,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X1,X4),X4)
| ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK3(X3,X1,X4),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_23253]) ).
tcf(c_23347,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X1,unordered_pair(unordered_pair(X3,sK5(singleton(X4),X1,unordered_pair(singleton(X4),unordered_pair(sK4(X1,X2,X0),X4)))),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_23253]) ).
tcf(c_23348,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X2,unordered_pair(unordered_pair(X3,sK5(singleton(X4),X2,unordered_pair(singleton(X4),unordered_pair(sK5(X1,X2,X0),X4)))),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_23253]) ).
tcf(c_23349,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,sK5(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_23253]) ).
tcf(c_23350,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,sK5(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_23253]) ).
tcf(c_23351,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,sK5(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_23253]) ).
tcf(c_23352,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,sK5(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_23253]) ).
tcf(c_23353,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,sK5(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_23253]) ).
tcf(c_23354,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,sK5(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_23253]) ).
tcf(c_23356,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X1 )
| ( sK2(singleton(X3),X4,X1) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(singleton(X3),X4,X1),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_23253]) ).
tcf(c_23357,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X3) = singleton(X4) )
| ( sK1(X1,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK2(X1,X3,singleton(X4)),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_23253]) ).
tcf(c_23358,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X1 )
| ( sK3(X3,singleton(X4),X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,singleton(X4),X1),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_23253]) ).
tcf(c_23359,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X1) = singleton(X4) )
| ( sK1(X3,X1,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK3(X3,X1,singleton(X4)),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_23253]) ).
tcf(c_23360,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK3(X3,X1,X4),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_23253]) ).
tcf(c_23361,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK3(X3,X1,X4),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_23253]) ).
tcf(c_23362,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK3(X3,X1,X4),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_23253]) ).
tcf(c_23363,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X1,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK3(X3,X1,X4),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_23253]) ).
tcf(c_23364,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK2(X1,X3,X4),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_23253]) ).
tcf(c_23365,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK2(X1,X3,X4),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_23253]) ).
tcf(c_23366,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK2(X1,X3,X4),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_23253]) ).
tcf(c_23367,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X1,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK2(X1,X3,X4),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_23253]) ).
tcf(c_23368,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_23253]) ).
tcf(c_23369,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_23253]) ).
tcf(c_23370,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_23253]) ).
tcf(c_23371,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_23253]) ).
tcf(c_23372,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_23253]) ).
tcf(c_23373,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_23253]) ).
tcf(c_23374,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_23253]) ).
tcf(c_23375,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_23253]) ).
tcf(c_23739,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),singleton(X3),unordered_pair(unordered_pair(X2,sK5(X1,singleton(X3),unordered_pair(singleton(X0),unordered_pair(X3,X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2184]) ).
tcf(c_23740,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2184]) ).
tcf(c_23741,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2184]) ).
tcf(c_23742,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2184]) ).
tcf(c_23743,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2184]) ).
tcf(c_23744,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2184]) ).
tcf(c_23745,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(unordered_pair(X5,sK5(X4,X1,unordered_pair(singleton(X3),unordered_pair(sK4(X1,X2,X0),X3)))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2184]) ).
tcf(c_23746,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(unordered_pair(X5,sK5(X4,X2,unordered_pair(singleton(X3),unordered_pair(sK5(X1,X2,X0),X3)))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2184]) ).
tcf(c_23747,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X6,sK5(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X4)))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2184]) ).
tcf(c_23748,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X6,sK5(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X4)))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2184]) ).
tcf(c_23749,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X6,sK5(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X4)))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2184]) ).
tcf(c_23750,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X6,sK5(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X4)))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2184]) ).
tcf(c_23751,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X6,sK5(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X4)))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2184]) ).
tcf(c_23752,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X6,sK5(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X4)))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2184]) ).
tcf(c_23754,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(singleton(X4),X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2184]) ).
tcf(c_23755,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,singleton(X5)),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2184]) ).
tcf(c_23756,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,singleton(X5),X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2184]) ).
tcf(c_23757,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,singleton(X5)),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2184]) ).
tcf(c_23758,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2184]) ).
tcf(c_23759,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2184]) ).
tcf(c_23760,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2184]) ).
tcf(c_23761,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2184]) ).
tcf(c_23762,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2184]) ).
tcf(c_23763,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2184]) ).
tcf(c_23764,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2184]) ).
tcf(c_23765,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2184]) ).
tcf(c_23766,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2184]) ).
tcf(c_23767,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2184]) ).
tcf(c_23768,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2184]) ).
tcf(c_23769,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2184]) ).
tcf(c_23770,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2184]) ).
tcf(c_23771,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2184]) ).
tcf(c_23772,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2184]) ).
tcf(c_23773,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2184]) ).
tcf(c_23889,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X2),sK3(X3,X4,X2)),singleton(sK2(X3,X4,X2))) = sK1(X3,X4,X2) )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_23739]) ).
tcf(c_23890,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X2),X4)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_23739]) ).
tcf(c_23891,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X2),X3)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_23739]) ).
tcf(c_23892,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X2,X3,X4),X4)
| ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(X1,sK2(X2,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_23739]) ).
tcf(c_23893,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X2,X4),X4)
| ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(X1,sK3(X3,X2,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_23739]) ).
tcf(c_23894,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(unordered_pair(X3,sK5(X1,singleton(X4),unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(X4,sK4(X1,X2,X0))))),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_23739]) ).
tcf(c_23895,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(unordered_pair(X3,sK5(X2,singleton(X4),unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(X4,sK5(X1,X2,X0))))),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_23739]) ).
tcf(c_23896,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(X4,sK5(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X2)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_23739]) ).
tcf(c_23897,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(X4,sK5(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X0,X2)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_23739]) ).
tcf(c_23898,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(X4,sK5(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X0)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_23739]) ).
tcf(c_23899,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(X4,sK5(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X2,X0)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_23739]) ).
tcf(c_23900,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(X4,sK5(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X0,X2)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_23739]) ).
tcf(c_23901,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(X4,sK5(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X2,X0)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_23739]) ).
tcf(c_23903,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X2 )
| ( sK2(singleton(X3),X4,X2) = X3 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(singleton(X3),X4,X2)),unordered_pair(X1,sK1(singleton(X3),X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_23739]) ).
tcf(c_23904,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK1(X2,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,singleton(X4))),unordered_pair(X1,sK2(X2,X3,singleton(X4)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_23739]) ).
tcf(c_23905,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X2 )
| ( sK3(X3,singleton(X4),X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,singleton(X4),X2)),unordered_pair(X1,sK1(X3,singleton(X4),X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_23739]) ).
tcf(c_23906,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X2) = singleton(X4) )
| ( sK1(X3,X2,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,singleton(X4))),unordered_pair(X1,sK3(X3,X2,singleton(X4)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_23739]) ).
tcf(c_23907,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(X1,sK3(X3,X2,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_23739]) ).
tcf(c_23908,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(X1,sK3(X3,X2,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_23739]) ).
tcf(c_23909,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(X1,sK3(X3,X2,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_23739]) ).
tcf(c_23910,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X2,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(X1,sK3(X3,X2,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_23739]) ).
tcf(c_23911,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(X1,sK2(X2,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_23739]) ).
tcf(c_23912,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(X1,sK2(X2,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_23739]) ).
tcf(c_23913,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(X1,sK2(X2,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_23739]) ).
tcf(c_23914,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X2,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(X1,sK2(X2,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_23739]) ).
tcf(c_23915,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_23739]) ).
tcf(c_23916,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_23739]) ).
tcf(c_23917,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_23739]) ).
tcf(c_23918,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_23739]) ).
tcf(c_23919,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_23739]) ).
tcf(c_23920,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_23739]) ).
tcf(c_23921,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_23739]) ).
tcf(c_23922,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_23739]) ).
tcf(c_23980,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),singleton(X3),unordered_pair(unordered_pair(X2,sK5(X1,singleton(X3),unordered_pair(singleton(X0),unordered_pair(X0,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2185]) ).
tcf(c_23981,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2185]) ).
tcf(c_23982,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2185]) ).
tcf(c_23983,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2185]) ).
tcf(c_23984,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2185]) ).
tcf(c_23985,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2185]) ).
tcf(c_23986,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(unordered_pair(X5,sK5(X4,X1,unordered_pair(singleton(X3),unordered_pair(X3,sK4(X1,X2,X0))))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2185]) ).
tcf(c_23987,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(unordered_pair(X5,sK5(X4,X2,unordered_pair(singleton(X3),unordered_pair(X3,sK5(X1,X2,X0))))),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2185]) ).
tcf(c_23988,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X6,sK5(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2)))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2185]) ).
tcf(c_23989,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X6,sK5(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2)))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2185]) ).
tcf(c_23990,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X6,sK5(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0)))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2185]) ).
tcf(c_23991,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X6,sK5(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0)))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2185]) ).
tcf(c_23992,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X6,sK5(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2)))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2185]) ).
tcf(c_23993,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X6,sK5(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0)))))),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2185]) ).
tcf(c_23995,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(singleton(X4),X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2185]) ).
tcf(c_23996,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,singleton(X5)))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2185]) ).
tcf(c_23997,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,singleton(X5),X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2185]) ).
tcf(c_23998,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,singleton(X5)))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2185]) ).
tcf(c_23999,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2185]) ).
tcf(c_24000,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2185]) ).
tcf(c_24001,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2185]) ).
tcf(c_24002,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2185]) ).
tcf(c_24003,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2185]) ).
tcf(c_24004,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2185]) ).
tcf(c_24005,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2185]) ).
tcf(c_24006,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2185]) ).
tcf(c_24007,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2185]) ).
tcf(c_24008,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2185]) ).
tcf(c_24009,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2185]) ).
tcf(c_24010,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2185]) ).
tcf(c_24011,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2185]) ).
tcf(c_24012,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2185]) ).
tcf(c_24013,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2185]) ).
tcf(c_24014,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2185]) ).
tcf(c_24146,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X2),sK3(X3,X4,X2)),singleton(sK2(X3,X4,X2))) = sK1(X3,X4,X2) )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_23980]) ).
tcf(c_24147,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X2),X4)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_23980]) ).
tcf(c_24148,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X2),X3)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_23980]) ).
tcf(c_24149,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X2,X3,X4),X4)
| ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(sK2(X2,X3,X4),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_23980]) ).
tcf(c_24150,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X2,X4),X4)
| ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(sK3(X3,X2,X4),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_23980]) ).
tcf(c_24151,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(unordered_pair(X3,sK5(X1,singleton(X4),unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(sK4(X1,X2,X0),X4)))),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_23980]) ).
tcf(c_24152,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(unordered_pair(X3,sK5(X2,singleton(X4),unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(sK5(X1,X2,X0),X4)))),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_23980]) ).
tcf(c_24153,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(X4,sK5(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_23980]) ).
tcf(c_24154,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(X4,sK5(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_23980]) ).
tcf(c_24155,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(X4,sK5(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_23980]) ).
tcf(c_24156,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(X4,sK5(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_23980]) ).
tcf(c_24157,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(X4,sK5(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_23980]) ).
tcf(c_24158,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(X4,sK5(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5)))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_23980]) ).
tcf(c_24160,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X2 )
| ( sK2(singleton(X3),X4,X2) = X3 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(singleton(X3),X4,X2)),unordered_pair(sK1(singleton(X3),X4,X2),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_23980]) ).
tcf(c_24161,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK1(X2,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,singleton(X4))),unordered_pair(sK2(X2,X3,singleton(X4)),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_23980]) ).
tcf(c_24162,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X2 )
| ( sK3(X3,singleton(X4),X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,singleton(X4),X2)),unordered_pair(sK1(X3,singleton(X4),X2),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_23980]) ).
tcf(c_24163,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X2) = singleton(X4) )
| ( sK1(X3,X2,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,singleton(X4))),unordered_pair(sK3(X3,X2,singleton(X4)),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_23980]) ).
tcf(c_24164,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(sK3(X3,X2,X4),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_23980]) ).
tcf(c_24165,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(sK3(X3,X2,X4),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_23980]) ).
tcf(c_24166,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(sK3(X3,X2,X4),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_23980]) ).
tcf(c_24167,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X2,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(sK3(X3,X2,X4),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_23980]) ).
tcf(c_24168,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(sK2(X2,X3,X4),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_23980]) ).
tcf(c_24169,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(sK2(X2,X3,X4),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_23980]) ).
tcf(c_24170,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(sK2(X2,X3,X4),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_23980]) ).
tcf(c_24171,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X2,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(sK2(X2,X3,X4),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_23980]) ).
tcf(c_24172,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_23980]) ).
tcf(c_24173,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_23980]) ).
tcf(c_24174,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_23980]) ).
tcf(c_24175,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_23980]) ).
tcf(c_24176,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_23980]) ).
tcf(c_24177,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_23980]) ).
tcf(c_24178,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_23980]) ).
tcf(c_24179,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_23980]) ).
tcf(c_24337,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),singleton(X3),unordered_pair(singleton(X2),unordered_pair(X2,sK4(singleton(X3),X1,unordered_pair(singleton(X3),unordered_pair(X3,X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2285]) ).
tcf(c_24338,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2285]) ).
tcf(c_24339,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2285]) ).
tcf(c_24340,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2285]) ).
tcf(c_24341,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2285]) ).
tcf(c_24342,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2285]) ).
tcf(c_24343,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X1,X4,unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(sK4(X1,X2,X0),X3)))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2285]) ).
tcf(c_24344,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X2,X4,unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(sK5(X1,X2,X0),X3)))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2285]) ).
tcf(c_24345,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(singleton(X6),unordered_pair(X6,sK4(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X4)))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2285]) ).
tcf(c_24346,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(singleton(X6),unordered_pair(X6,sK4(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X4)))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2285]) ).
tcf(c_24347,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(singleton(X6),unordered_pair(X6,sK4(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X4)))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2285]) ).
tcf(c_24348,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(singleton(X6),unordered_pair(X6,sK4(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X4)))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2285]) ).
tcf(c_24349,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(singleton(X6),unordered_pair(X6,sK4(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X4)))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2285]) ).
tcf(c_24350,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(singleton(X6),unordered_pair(X6,sK4(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X4)))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2285]) ).
tcf(c_24352,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(singleton(X4),X5,X3)),unordered_pair(sK1(singleton(X4),X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2285]) ).
tcf(c_24353,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,singleton(X5))),unordered_pair(sK2(X3,X4,singleton(X5)),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2285]) ).
tcf(c_24354,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,singleton(X5),X3)),unordered_pair(sK1(X4,singleton(X5),X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2285]) ).
tcf(c_24355,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,singleton(X5))),unordered_pair(sK3(X4,X3,singleton(X5)),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2285]) ).
tcf(c_24356,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2285]) ).
tcf(c_24357,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2285]) ).
tcf(c_24358,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2285]) ).
tcf(c_24359,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2285]) ).
tcf(c_24360,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2285]) ).
tcf(c_24361,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2285]) ).
tcf(c_24362,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2285]) ).
tcf(c_24363,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2285]) ).
tcf(c_24364,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2285]) ).
tcf(c_24365,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2285]) ).
tcf(c_24366,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2285]) ).
tcf(c_24367,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2285]) ).
tcf(c_24368,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2285]) ).
tcf(c_24369,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2285]) ).
tcf(c_24370,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2285]) ).
tcf(c_24371,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2285]) ).
tcf(c_24507,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X2),sK3(X3,X4,X2)),singleton(sK2(X3,X4,X2))) = sK1(X3,X4,X2) )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_24337]) ).
tcf(c_24508,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X2),X4)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_24337]) ).
tcf(c_24509,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X2),X3)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_24337]) ).
tcf(c_24510,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X2,X3,X4),X4)
| ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_24337]) ).
tcf(c_24511,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X2,X4),X4)
| ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_24337]) ).
tcf(c_24512,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(singleton(X3),unordered_pair(X3,sK4(singleton(X4),X1,unordered_pair(singleton(X4),unordered_pair(X4,sK4(X1,X2,X0))))))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_24337]) ).
tcf(c_24513,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(singleton(X3),unordered_pair(X3,sK4(singleton(X4),X2,unordered_pair(singleton(X4),unordered_pair(X4,sK5(X1,X2,X0))))))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_24337]) ).
tcf(c_24514,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(X4,sK4(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X2)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_24337]) ).
tcf(c_24515,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(X4,sK4(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X0,X2)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_24337]) ).
tcf(c_24516,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(X4,sK4(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X0)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_24337]) ).
tcf(c_24517,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(X4,sK4(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X2,X0)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_24337]) ).
tcf(c_24518,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(X4,sK4(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X0,X2)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_24337]) ).
tcf(c_24519,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(X4,sK4(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X2,X0)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_24337]) ).
tcf(c_24521,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X2 )
| ( sK2(singleton(X3),X4,X2) = X3 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(singleton(X3),X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_24337]) ).
tcf(c_24522,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK1(X2,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,singleton(X4)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_24337]) ).
tcf(c_24523,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X2 )
| ( sK3(X3,singleton(X4),X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,singleton(X4),X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_24337]) ).
tcf(c_24524,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X2) = singleton(X4) )
| ( sK1(X3,X2,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,singleton(X4)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_24337]) ).
tcf(c_24525,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_24337]) ).
tcf(c_24526,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_24337]) ).
tcf(c_24527,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_24337]) ).
tcf(c_24528,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X2,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_24337]) ).
tcf(c_24529,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_24337]) ).
tcf(c_24530,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_24337]) ).
tcf(c_24531,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_24337]) ).
tcf(c_24532,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X2,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_24337]) ).
tcf(c_24533,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_24337]) ).
tcf(c_24534,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_24337]) ).
tcf(c_24535,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_24337]) ).
tcf(c_24536,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_24337]) ).
tcf(c_24537,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_24337]) ).
tcf(c_24538,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_24337]) ).
tcf(c_24539,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_24337]) ).
tcf(c_24540,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_24337]) ).
tcf(c_24873,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = cartesian_product2(X0,X1) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X2,X3,sK4(cartesian_product2(X2,X3),X4,sK1(X0,X1,cartesian_product2(cartesian_product2(X2,X3),X4))))))) = X5 )
| ( unordered_pair(unordered_pair(sK2(X0,X1,cartesian_product2(cartesian_product2(X2,X3),X4)),sK3(X0,X1,cartesian_product2(cartesian_product2(X2,X3),X4))),singleton(sK2(X0,X1,cartesian_product2(cartesian_product2(X2,X3),X4)))) = sK1(X0,X1,cartesian_product2(cartesian_product2(X2,X3),X4)) ) ),
inference(superposition,[status(thm)],[c_58,c_2340]) ).
tcf(c_24874,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)),X5)
| ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_2340]) ).
tcf(c_24875,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)),X4)
| ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_2340]) ).
tcf(c_24876,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(cartesian_product2(X2,X1),X3),X4) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK2(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_2340]) ).
tcf(c_24877,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X2,X1),X3)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK3(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_2340]) ).
tcf(c_24878,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK4(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X0)))))) = X5 )
| ~ in(X0,cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X3),X4)) ),
inference(superposition,[status(thm)],[c_60,c_2340]) ).
tcf(c_24879,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X2,X3,sK4(cartesian_product2(X2,X3),X4,sK5(X1,cartesian_product2(cartesian_product2(X2,X3),X4),X0)))))) = X5 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(cartesian_product2(X2,X3),X4))) ),
inference(superposition,[status(thm)],[c_61,c_2340]) ).
tcf(c_24880,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X1,X2,sK4(cartesian_product2(X1,X2),X4,unordered_pair(unordered_pair(X0,X3),singleton(X0))))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_64,c_2340]) ).
tcf(c_24882,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X1,X2,sK4(cartesian_product2(X1,X2),X4,unordered_pair(unordered_pair(X3,X0),singleton(X0))))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_809,c_2340]) ).
tcf(c_24883,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X1,X2,sK4(cartesian_product2(X1,X2),X4,unordered_pair(singleton(X0),unordered_pair(X3,X0))))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_882,c_2340]) ).
tcf(c_24885,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X1,X2,sK4(cartesian_product2(X1,X2),X4,unordered_pair(singleton(X0),unordered_pair(X0,X3))))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_900,c_2340]) ).
tcf(c_24886,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(singleton(X4),X5) )
| ( sK2(singleton(X4),X5,cartesian_product2(cartesian_product2(X2,X1),X3)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(singleton(X4),X5,cartesian_product2(cartesian_product2(X2,X1),X3))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_2340]) ).
tcf(c_24887,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X2,X1),X3),X4) = singleton(X5) )
| ( sK1(cartesian_product2(cartesian_product2(X2,X1),X3),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK2(cartesian_product2(cartesian_product2(X2,X1),X3),X4,singleton(X5))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_2340]) ).
tcf(c_24888,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,singleton(X5)) )
| ( sK3(X4,singleton(X5),cartesian_product2(cartesian_product2(X2,X1),X3)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,singleton(X5),cartesian_product2(cartesian_product2(X2,X1),X3))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_2340]) ).
tcf(c_24889,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X2,X1),X3)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(cartesian_product2(X2,X1),X3),singleton(X5)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK3(X4,cartesian_product2(cartesian_product2(X2,X1),X3),singleton(X5))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_2340]) ).
tcf(c_24890,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X2,X1),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK3(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_2340]) ).
tcf(c_24891,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X2,X1),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK3(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_2340]) ).
tcf(c_24892,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X2,X1),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK3(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_2340]) ).
tcf(c_24893,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X2,X1),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK3(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_2340]) ).
tcf(c_24894,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X2,X1),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK2(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_2340]) ).
tcf(c_24895,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X2,X1),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK2(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_2340]) ).
tcf(c_24896,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X2,X1),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK2(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_2340]) ).
tcf(c_24897,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X2,X1),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK2(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_2340]) ).
tcf(c_24898,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_2340]) ).
tcf(c_24899,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_2340]) ).
tcf(c_24900,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_2340]) ).
tcf(c_24901,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_2340]) ).
tcf(c_24902,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_2340]) ).
tcf(c_24903,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_2340]) ).
tcf(c_24904,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_2340]) ).
tcf(c_24905,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_2340]) ).
tcf(c_25150,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(X3,X4)) = cartesian_product2(X0,X1) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X3,X4,sK5(X2,cartesian_product2(X3,X4),sK1(X0,X1,cartesian_product2(X2,cartesian_product2(X3,X4)))))))) = X5 )
| ( unordered_pair(unordered_pair(sK2(X0,X1,cartesian_product2(X2,cartesian_product2(X3,X4))),sK3(X0,X1,cartesian_product2(X2,cartesian_product2(X3,X4)))),singleton(sK2(X0,X1,cartesian_product2(X2,cartesian_product2(X3,X4))))) = sK1(X0,X1,cartesian_product2(X2,cartesian_product2(X3,X4))) ) ),
inference(superposition,[status(thm)],[c_58,c_2341]) ).
tcf(c_25151,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))),X5)
| ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_2341]) ).
tcf(c_25152,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))),X4)
| ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_2341]) ).
tcf(c_25153,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_2341]) ).
tcf(c_25154,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X2,X1))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK3(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_2341]) ).
tcf(c_25155,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X2,X3,sK5(X1,cartesian_product2(X2,X3),sK4(cartesian_product2(X1,cartesian_product2(X2,X3)),X4,X0)))))) = X5 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,cartesian_product2(X2,X3)),X4)) ),
inference(superposition,[status(thm)],[c_60,c_2341]) ).
tcf(c_25156,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X3,X4,sK5(X2,cartesian_product2(X3,X4),sK5(X1,cartesian_product2(X2,cartesian_product2(X3,X4)),X0)))))) = X5 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,cartesian_product2(X3,X4)))) ),
inference(superposition,[status(thm)],[c_61,c_2341]) ).
tcf(c_25157,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X1,X2,sK5(X4,cartesian_product2(X1,X2),unordered_pair(unordered_pair(X3,X0),singleton(X3))))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_64,c_2341]) ).
tcf(c_25159,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X1,X2,sK5(X4,cartesian_product2(X1,X2),unordered_pair(unordered_pair(X0,X3),singleton(X3))))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_809,c_2341]) ).
tcf(c_25160,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X1,X2,sK5(X4,cartesian_product2(X1,X2),unordered_pair(singleton(X3),unordered_pair(X0,X3))))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_882,c_2341]) ).
tcf(c_25162,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X1,X2,sK5(X4,cartesian_product2(X1,X2),unordered_pair(singleton(X3),unordered_pair(X3,X0))))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_900,c_2341]) ).
tcf(c_25163,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(singleton(X4),X5) )
| ( sK2(singleton(X4),X5,cartesian_product2(X3,cartesian_product2(X2,X1))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(singleton(X4),X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_2341]) ).
tcf(c_25164,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,singleton(X5))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_2341]) ).
tcf(c_25165,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,singleton(X5)) )
| ( sK3(X4,singleton(X5),cartesian_product2(X3,cartesian_product2(X2,X1))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,singleton(X5),cartesian_product2(X3,cartesian_product2(X2,X1)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_2341]) ).
tcf(c_25166,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X2,X1))) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),singleton(X5)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK3(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),singleton(X5))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_2341]) ).
tcf(c_25167,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X2,X1))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK3(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_2341]) ).
tcf(c_25168,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X2,X1))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK3(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_2341]) ).
tcf(c_25169,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X2,X1))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK3(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_2341]) ).
tcf(c_25170,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X2,X1))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK3(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_2341]) ).
tcf(c_25171,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_2341]) ).
tcf(c_25172,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_2341]) ).
tcf(c_25173,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_2341]) ).
tcf(c_25174,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_2341]) ).
tcf(c_25175,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_2341]) ).
tcf(c_25176,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_2341]) ).
tcf(c_25177,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_2341]) ).
tcf(c_25178,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_2341]) ).
tcf(c_25179,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_2341]) ).
tcf(c_25180,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_2341]) ).
tcf(c_25181,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_2341]) ).
tcf(c_25182,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_2341]) ).
tcf(c_25328,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),singleton(X3),unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,singleton(X3),unordered_pair(unordered_pair(X0,X3),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2342]) ).
tcf(c_25329,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2342]) ).
tcf(c_25330,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2342]) ).
tcf(c_25331,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2342]) ).
tcf(c_25332,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2342]) ).
tcf(c_25333,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2342]) ).
tcf(c_25334,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X4,X1,unordered_pair(unordered_pair(X3,sK4(X1,X2,X0)),singleton(X3)))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2342]) ).
tcf(c_25335,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X4,X2,unordered_pair(unordered_pair(X3,sK5(X1,X2,X0)),singleton(X3)))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2342]) ).
tcf(c_25336,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(singleton(X6),unordered_pair(X6,sK5(X5,cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))),singleton(X4)))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2342]) ).
tcf(c_25337,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(singleton(X6),unordered_pair(X6,sK5(X5,cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))),singleton(X4)))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2342]) ).
tcf(c_25338,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(singleton(X6),unordered_pair(X6,sK5(X5,cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))),singleton(X4)))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2342]) ).
tcf(c_25339,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(singleton(X6),unordered_pair(X6,sK5(X5,cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))),singleton(X4)))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2342]) ).
tcf(c_25340,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(singleton(X6),unordered_pair(X6,sK5(X5,cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))),singleton(X4)))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2342]) ).
tcf(c_25341,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(singleton(X6),unordered_pair(X6,sK5(X5,cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))),singleton(X4)))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2342]) ).
tcf(c_25343,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(singleton(X4),X5,X3)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2342]) ).
tcf(c_25344,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,singleton(X5))),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2342]) ).
tcf(c_25345,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,singleton(X5),X3)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2342]) ).
tcf(c_25346,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,singleton(X5))),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2342]) ).
tcf(c_25347,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2342]) ).
tcf(c_25348,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2342]) ).
tcf(c_25349,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2342]) ).
tcf(c_25350,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2342]) ).
tcf(c_25351,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2342]) ).
tcf(c_25352,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2342]) ).
tcf(c_25353,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2342]) ).
tcf(c_25354,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2342]) ).
tcf(c_25355,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2342]) ).
tcf(c_25356,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2342]) ).
tcf(c_25357,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2342]) ).
tcf(c_25358,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2342]) ).
tcf(c_25359,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2342]) ).
tcf(c_25360,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2342]) ).
tcf(c_25361,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2342]) ).
tcf(c_25362,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2342]) ).
tcf(c_25500,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X2),sK3(X3,X4,X2)),singleton(sK2(X3,X4,X2))) = sK1(X3,X4,X2) )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_25328]) ).
tcf(c_25501,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X2),X4)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_25328]) ).
tcf(c_25502,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X2),X3)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_25328]) ).
tcf(c_25503,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X2,X3,X4),X4)
| ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(sK2(X2,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_25328]) ).
tcf(c_25504,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X2,X4),X4)
| ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(sK3(X3,X2,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_25328]) ).
tcf(c_25505,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(singleton(X3),unordered_pair(X3,sK5(X1,singleton(X4),unordered_pair(unordered_pair(sK4(X1,X2,X0),X4),singleton(sK4(X1,X2,X0))))))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_25328]) ).
tcf(c_25506,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(singleton(X3),unordered_pair(X3,sK5(X2,singleton(X4),unordered_pair(unordered_pair(sK5(X1,X2,X0),X4),singleton(sK5(X1,X2,X0))))))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_25328]) ).
tcf(c_25507,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(X4,sK5(cartesian_product2(X3,X1),singleton(X5),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_25328]) ).
tcf(c_25508,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(X4,sK5(cartesian_product2(X1,X3),singleton(X5),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5),singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_25328]) ).
tcf(c_25509,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(X4,sK5(cartesian_product2(X1,X3),singleton(X5),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_25328]) ).
tcf(c_25510,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(X4,sK5(cartesian_product2(X1,X3),singleton(X5),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5),singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_25328]) ).
tcf(c_25511,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(X4,sK5(cartesian_product2(X3,X1),singleton(X5),unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5),singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_25328]) ).
tcf(c_25512,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(X4,sK5(cartesian_product2(X3,X1),singleton(X5),unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5),singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_25328]) ).
tcf(c_25514,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X2 )
| ( sK2(singleton(X3),X4,X2) = X3 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(singleton(X3),X4,X2),X1),singleton(sK1(singleton(X3),X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_25328]) ).
tcf(c_25515,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK1(X2,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK2(X2,X3,singleton(X4)),X1),singleton(sK2(X2,X3,singleton(X4)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_25328]) ).
tcf(c_25516,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X2 )
| ( sK3(X3,singleton(X4),X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,singleton(X4),X2),X1),singleton(sK1(X3,singleton(X4),X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_25328]) ).
tcf(c_25517,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X2) = singleton(X4) )
| ( sK1(X3,X2,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK3(X3,X2,singleton(X4)),X1),singleton(sK3(X3,X2,singleton(X4)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_25328]) ).
tcf(c_25518,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(sK3(X3,X2,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_25328]) ).
tcf(c_25519,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(sK3(X3,X2,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_25328]) ).
tcf(c_25520,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(sK3(X3,X2,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_25328]) ).
tcf(c_25521,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X2,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(sK3(X3,X2,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_25328]) ).
tcf(c_25522,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(sK2(X2,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_25328]) ).
tcf(c_25523,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(sK2(X2,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_25328]) ).
tcf(c_25524,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(sK2(X2,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_25328]) ).
tcf(c_25525,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X2,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(sK2(X2,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_25328]) ).
tcf(c_25526,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_25328]) ).
tcf(c_25527,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_25328]) ).
tcf(c_25528,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_25328]) ).
tcf(c_25529,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_25328]) ).
tcf(c_25530,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_25328]) ).
tcf(c_25531,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_25328]) ).
tcf(c_25532,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_25328]) ).
tcf(c_25533,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_25328]) ).
tcf(c_25743,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),singleton(X3),unordered_pair(singleton(X2),unordered_pair(X2,sK4(singleton(X3),X1,unordered_pair(unordered_pair(X0,X3),singleton(X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2286]) ).
tcf(c_25744,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2286]) ).
tcf(c_25745,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2286]) ).
tcf(c_25746,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2286]) ).
tcf(c_25747,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2286]) ).
tcf(c_25748,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2286]) ).
tcf(c_25749,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X1,X4,unordered_pair(unordered_pair(X3,sK4(X1,X2,X0)),singleton(sK4(X1,X2,X0))))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2286]) ).
tcf(c_25750,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X2,X4,unordered_pair(unordered_pair(X3,sK5(X1,X2,X0)),singleton(sK5(X1,X2,X0))))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2286]) ).
tcf(c_25751,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(singleton(X6),unordered_pair(X6,sK4(cartesian_product2(X3,X1),X5,unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2)))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2286]) ).
tcf(c_25752,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(singleton(X6),unordered_pair(X6,sK4(cartesian_product2(X1,X3),X5,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))),singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2)))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2286]) ).
tcf(c_25753,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(singleton(X6),unordered_pair(X6,sK4(cartesian_product2(X1,X3),X5,unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0)))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2286]) ).
tcf(c_25754,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(singleton(X6),unordered_pair(X6,sK4(cartesian_product2(X1,X3),X5,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))),singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0)))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2286]) ).
tcf(c_25755,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(singleton(X6),unordered_pair(X6,sK4(cartesian_product2(X3,X1),X5,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))),singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2)))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2286]) ).
tcf(c_25756,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(singleton(X6),unordered_pair(X6,sK4(cartesian_product2(X3,X1),X5,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))),singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0)))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2286]) ).
tcf(c_25758,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(singleton(X4),X5,X3)),singleton(sK1(singleton(X4),X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2286]) ).
tcf(c_25759,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,singleton(X5))),singleton(sK2(X3,X4,singleton(X5)))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2286]) ).
tcf(c_25760,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,singleton(X5),X3)),singleton(sK1(X4,singleton(X5),X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2286]) ).
tcf(c_25761,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,singleton(X5))),singleton(sK3(X4,X3,singleton(X5)))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2286]) ).
tcf(c_25762,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2286]) ).
tcf(c_25763,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2286]) ).
tcf(c_25764,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2286]) ).
tcf(c_25765,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2286]) ).
tcf(c_25766,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2286]) ).
tcf(c_25767,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2286]) ).
tcf(c_25768,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2286]) ).
tcf(c_25769,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2286]) ).
tcf(c_25770,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2286]) ).
tcf(c_25771,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2286]) ).
tcf(c_25772,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2286]) ).
tcf(c_25773,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2286]) ).
tcf(c_25774,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2286]) ).
tcf(c_25775,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2286]) ).
tcf(c_25776,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2286]) ).
tcf(c_25777,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2286]) ).
tcf(c_25892,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X2),sK3(X3,X4,X2)),singleton(sK2(X3,X4,X2))) = sK1(X3,X4,X2) )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_25743]) ).
tcf(c_25893,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X2),X4)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_25743]) ).
tcf(c_25894,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X2),X3)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_25743]) ).
tcf(c_25895,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X2,X3,X4),X4)
| ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_25743]) ).
tcf(c_25896,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X2,X4),X4)
| ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_25743]) ).
tcf(c_25897,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(singleton(X3),unordered_pair(X3,sK4(singleton(X4),X1,unordered_pair(unordered_pair(sK4(X1,X2,X0),X4),singleton(X4)))))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_25743]) ).
tcf(c_25898,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(singleton(X3),unordered_pair(X3,sK4(singleton(X4),X2,unordered_pair(unordered_pair(sK5(X1,X2,X0),X4),singleton(X4)))))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_25743]) ).
tcf(c_25899,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(X4,sK4(singleton(X5),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5),singleton(X5)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_25743]) ).
tcf(c_25900,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(X4,sK4(singleton(X5),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5),singleton(X5)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_25743]) ).
tcf(c_25901,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(X4,sK4(singleton(X5),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5),singleton(X5)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_25743]) ).
tcf(c_25902,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(X4,sK4(singleton(X5),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5),singleton(X5)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_25743]) ).
tcf(c_25903,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(X4,sK4(singleton(X5),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5),singleton(X5)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_25743]) ).
tcf(c_25904,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(X4,sK4(singleton(X5),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5),singleton(X5)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_25743]) ).
tcf(c_25906,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X2 )
| ( sK2(singleton(X3),X4,X2) = X3 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(singleton(X3),X4,X2),X1),singleton(X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_25743]) ).
tcf(c_25907,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK1(X2,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK2(X2,X3,singleton(X4)),X1),singleton(X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_25743]) ).
tcf(c_25908,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X2 )
| ( sK3(X3,singleton(X4),X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,singleton(X4),X2),X1),singleton(X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_25743]) ).
tcf(c_25909,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X2) = singleton(X4) )
| ( sK1(X3,X2,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK3(X3,X2,singleton(X4)),X1),singleton(X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_25743]) ).
tcf(c_25910,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_25743]) ).
tcf(c_25911,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_25743]) ).
tcf(c_25912,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_25743]) ).
tcf(c_25913,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X2,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_25743]) ).
tcf(c_25914,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_25743]) ).
tcf(c_25915,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_25743]) ).
tcf(c_25916,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_25743]) ).
tcf(c_25917,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X2,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_25743]) ).
tcf(c_25918,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_25743]) ).
tcf(c_25919,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_25743]) ).
tcf(c_25920,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_25743]) ).
tcf(c_25921,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_25743]) ).
tcf(c_25922,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_25743]) ).
tcf(c_25923,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_25743]) ).
tcf(c_25924,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_25743]) ).
tcf(c_25925,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_25743]) ).
tcf(c_26012,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),singleton(X3),unordered_pair(singleton(X2),unordered_pair(X2,sK4(singleton(X3),X1,unordered_pair(singleton(X3),unordered_pair(X0,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2287]) ).
tcf(c_26013,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2287]) ).
tcf(c_26014,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2287]) ).
tcf(c_26015,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2287]) ).
tcf(c_26016,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2287]) ).
tcf(c_26017,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2287]) ).
tcf(c_26018,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X1,X4,unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(X3,sK4(X1,X2,X0))))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2287]) ).
tcf(c_26019,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X2,X4,unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(X3,sK5(X1,X2,X0))))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2287]) ).
tcf(c_26020,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(singleton(X6),unordered_pair(X6,sK4(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2)))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2287]) ).
tcf(c_26021,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(singleton(X6),unordered_pair(X6,sK4(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2)))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2287]) ).
tcf(c_26022,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(singleton(X6),unordered_pair(X6,sK4(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0)))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2287]) ).
tcf(c_26023,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(singleton(X6),unordered_pair(X6,sK4(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0)))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2287]) ).
tcf(c_26024,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(singleton(X6),unordered_pair(X6,sK4(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2)))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2287]) ).
tcf(c_26025,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(singleton(X6),unordered_pair(X6,sK4(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0)))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2287]) ).
tcf(c_26027,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(singleton(X4),X5,X3)),unordered_pair(X0,sK1(singleton(X4),X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2287]) ).
tcf(c_26028,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,singleton(X5))),unordered_pair(X0,sK2(X3,X4,singleton(X5)))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2287]) ).
tcf(c_26029,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,singleton(X5),X3)),unordered_pair(X0,sK1(X4,singleton(X5),X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2287]) ).
tcf(c_26030,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,singleton(X5))),unordered_pair(X0,sK3(X4,X3,singleton(X5)))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2287]) ).
tcf(c_26031,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2287]) ).
tcf(c_26032,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2287]) ).
tcf(c_26033,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2287]) ).
tcf(c_26034,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2287]) ).
tcf(c_26035,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2287]) ).
tcf(c_26036,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2287]) ).
tcf(c_26037,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2287]) ).
tcf(c_26038,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2287]) ).
tcf(c_26039,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2287]) ).
tcf(c_26040,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2287]) ).
tcf(c_26041,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2287]) ).
tcf(c_26042,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2287]) ).
tcf(c_26043,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2287]) ).
tcf(c_26044,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2287]) ).
tcf(c_26045,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2287]) ).
tcf(c_26046,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2287]) ).
tcf(c_26180,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X2),sK3(X3,X4,X2)),singleton(sK2(X3,X4,X2))) = sK1(X3,X4,X2) )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_26012]) ).
tcf(c_26181,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X2),X4)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_26012]) ).
tcf(c_26182,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X2),X3)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_26012]) ).
tcf(c_26183,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X2,X3,X4),X4)
| ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_26012]) ).
tcf(c_26184,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X2,X4),X4)
| ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_26012]) ).
tcf(c_26185,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(singleton(X3),unordered_pair(X3,sK4(singleton(X4),X1,unordered_pair(singleton(X4),unordered_pair(sK4(X1,X2,X0),X4)))))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_26012]) ).
tcf(c_26186,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(singleton(X3),unordered_pair(X3,sK4(singleton(X4),X2,unordered_pair(singleton(X4),unordered_pair(sK5(X1,X2,X0),X4)))))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_26012]) ).
tcf(c_26187,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(X4,sK4(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_26012]) ).
tcf(c_26188,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(X4,sK4(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_26012]) ).
tcf(c_26189,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(X4,sK4(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_26012]) ).
tcf(c_26190,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(X4,sK4(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_26012]) ).
tcf(c_26191,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(X4,sK4(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_26012]) ).
tcf(c_26192,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(X4,sK4(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_26012]) ).
tcf(c_26194,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X2 )
| ( sK2(singleton(X3),X4,X2) = X3 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(singleton(X3),X4,X2),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_26012]) ).
tcf(c_26195,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK1(X2,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,singleton(X4)),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_26012]) ).
tcf(c_26196,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X2 )
| ( sK3(X3,singleton(X4),X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,singleton(X4),X2),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_26012]) ).
tcf(c_26197,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X2) = singleton(X4) )
| ( sK1(X3,X2,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,singleton(X4)),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_26012]) ).
tcf(c_26198,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_26012]) ).
tcf(c_26199,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_26012]) ).
tcf(c_26200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_26012]) ).
tcf(c_26201,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X2,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_26012]) ).
tcf(c_26202,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_26012]) ).
tcf(c_26203,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_26012]) ).
tcf(c_26204,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_26012]) ).
tcf(c_26205,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X2,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_26012]) ).
tcf(c_26206,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_26012]) ).
tcf(c_26207,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_26012]) ).
tcf(c_26208,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_26012]) ).
tcf(c_26209,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_26012]) ).
tcf(c_26210,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_26012]) ).
tcf(c_26211,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_26012]) ).
tcf(c_26212,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_26012]) ).
tcf(c_26213,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_26012]) ).
tcf(c_26385,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,singleton(X3),unordered_pair(singleton(X0),unordered_pair(X3,X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2288]) ).
tcf(c_26386,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2288]) ).
tcf(c_26387,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2288]) ).
tcf(c_26388,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2288]) ).
tcf(c_26389,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2288]) ).
tcf(c_26390,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2288]) ).
tcf(c_26391,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X4,X1,unordered_pair(singleton(X3),unordered_pair(sK4(X1,X2,X0),X3)))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2288]) ).
tcf(c_26392,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X4,X2,unordered_pair(singleton(X3),unordered_pair(sK5(X1,X2,X0),X3)))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2288]) ).
tcf(c_26393,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK4(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X4)))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2288]) ).
tcf(c_26394,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK4(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X4)))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2288]) ).
tcf(c_26395,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK4(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X4)))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2288]) ).
tcf(c_26396,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK4(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X4)))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2288]) ).
tcf(c_26397,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK4(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X4)))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2288]) ).
tcf(c_26398,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK4(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X4)))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2288]) ).
tcf(c_26400,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(singleton(X4),X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2288]) ).
tcf(c_26401,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,singleton(X5)),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2288]) ).
tcf(c_26402,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,singleton(X5),X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2288]) ).
tcf(c_26403,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,singleton(X5)),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2288]) ).
tcf(c_26404,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2288]) ).
tcf(c_26405,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2288]) ).
tcf(c_26406,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2288]) ).
tcf(c_26407,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2288]) ).
tcf(c_26408,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2288]) ).
tcf(c_26409,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2288]) ).
tcf(c_26410,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2288]) ).
tcf(c_26411,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2288]) ).
tcf(c_26412,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2288]) ).
tcf(c_26413,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2288]) ).
tcf(c_26414,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2288]) ).
tcf(c_26415,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2288]) ).
tcf(c_26416,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2288]) ).
tcf(c_26417,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2288]) ).
tcf(c_26418,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2288]) ).
tcf(c_26419,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2288]) ).
tcf(c_26560,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X1),sK3(X3,X4,X1)),singleton(sK2(X3,X4,X1))) = sK1(X3,X4,X1) )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_26385]) ).
tcf(c_26561,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X1),X4)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_26385]) ).
tcf(c_26562,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X1),X3)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_26385]) ).
tcf(c_26563,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X1,X3,X4),X4)
| ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_26385]) ).
tcf(c_26564,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X1,X4),X4)
| ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_26385]) ).
tcf(c_26565,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X1,unordered_pair(singleton(X3),unordered_pair(X3,sK4(X1,singleton(X4),unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(X4,sK4(X1,X2,X0))))))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_26385]) ).
tcf(c_26566,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X2,unordered_pair(singleton(X3),unordered_pair(X3,sK4(X2,singleton(X4),unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(X4,sK5(X1,X2,X0))))))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_26385]) ).
tcf(c_26567,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,sK4(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X2)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_26385]) ).
tcf(c_26568,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,sK4(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X0,X2)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_26385]) ).
tcf(c_26569,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,sK4(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X0)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_26385]) ).
tcf(c_26570,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,sK4(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X2,X0)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_26385]) ).
tcf(c_26571,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,sK4(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X0,X2)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_26385]) ).
tcf(c_26572,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,sK4(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X2,X0)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_26385]) ).
tcf(c_26574,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X1 )
| ( sK2(singleton(X3),X4,X1) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(singleton(X3),X4,X1)),unordered_pair(X2,sK1(singleton(X3),X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_26385]) ).
tcf(c_26575,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X3) = singleton(X4) )
| ( sK1(X1,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,singleton(X4))),unordered_pair(X2,sK2(X1,X3,singleton(X4)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_26385]) ).
tcf(c_26576,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X1 )
| ( sK3(X3,singleton(X4),X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,singleton(X4),X1)),unordered_pair(X2,sK1(X3,singleton(X4),X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_26385]) ).
tcf(c_26577,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X1) = singleton(X4) )
| ( sK1(X3,X1,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,singleton(X4))),unordered_pair(X2,sK3(X3,X1,singleton(X4)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_26385]) ).
tcf(c_26578,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_26385]) ).
tcf(c_26579,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_26385]) ).
tcf(c_26580,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_26385]) ).
tcf(c_26581,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X1,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_26385]) ).
tcf(c_26582,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_26385]) ).
tcf(c_26583,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_26385]) ).
tcf(c_26584,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_26385]) ).
tcf(c_26585,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X1,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_26385]) ).
tcf(c_26586,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_26385]) ).
tcf(c_26587,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_26385]) ).
tcf(c_26588,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_26385]) ).
tcf(c_26589,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_26385]) ).
tcf(c_26590,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_26385]) ).
tcf(c_26591,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_26385]) ).
tcf(c_26592,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_26385]) ).
tcf(c_26593,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_26385]) ).
tcf(c_26883,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,singleton(X3),unordered_pair(singleton(X0),unordered_pair(X0,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2289]) ).
tcf(c_26884,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2289]) ).
tcf(c_26885,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2289]) ).
tcf(c_26886,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2289]) ).
tcf(c_26887,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2289]) ).
tcf(c_26888,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2289]) ).
tcf(c_26889,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X4,X1,unordered_pair(singleton(X3),unordered_pair(X3,sK4(X1,X2,X0))))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2289]) ).
tcf(c_26890,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X4,X2,unordered_pair(singleton(X3),unordered_pair(X3,sK5(X1,X2,X0))))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2289]) ).
tcf(c_26891,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK4(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2)))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2289]) ).
tcf(c_26892,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK4(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2)))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2289]) ).
tcf(c_26893,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK4(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0)))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2289]) ).
tcf(c_26894,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK4(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0)))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2289]) ).
tcf(c_26895,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK4(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2)))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2289]) ).
tcf(c_26896,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK4(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0)))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2289]) ).
tcf(c_26898,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(singleton(X4),X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2289]) ).
tcf(c_26899,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,singleton(X5)))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2289]) ).
tcf(c_26900,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,singleton(X5),X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2289]) ).
tcf(c_26901,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,singleton(X5)))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2289]) ).
tcf(c_26902,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2289]) ).
tcf(c_26903,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2289]) ).
tcf(c_26904,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2289]) ).
tcf(c_26905,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2289]) ).
tcf(c_26906,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2289]) ).
tcf(c_26907,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2289]) ).
tcf(c_26908,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2289]) ).
tcf(c_26909,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2289]) ).
tcf(c_26910,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2289]) ).
tcf(c_26911,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2289]) ).
tcf(c_26912,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2289]) ).
tcf(c_26913,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2289]) ).
tcf(c_26914,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2289]) ).
tcf(c_26915,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2289]) ).
tcf(c_26916,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2289]) ).
tcf(c_26917,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2289]) ).
tcf(c_27073,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X1),sK3(X3,X4,X1)),singleton(sK2(X3,X4,X1))) = sK1(X3,X4,X1) )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_26883]) ).
tcf(c_27074,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X1),X4)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_26883]) ).
tcf(c_27075,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X1),X3)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_26883]) ).
tcf(c_27076,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X1,X3,X4),X4)
| ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_26883]) ).
tcf(c_27077,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X1,X4),X4)
| ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_26883]) ).
tcf(c_27078,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X1,unordered_pair(singleton(X3),unordered_pair(X3,sK4(X1,singleton(X4),unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(sK4(X1,X2,X0),X4)))))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_26883]) ).
tcf(c_27079,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X2,unordered_pair(singleton(X3),unordered_pair(X3,sK4(X2,singleton(X4),unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(sK5(X1,X2,X0),X4)))))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_26883]) ).
tcf(c_27080,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,sK4(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_26883]) ).
tcf(c_27081,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,sK4(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_26883]) ).
tcf(c_27082,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,sK4(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_26883]) ).
tcf(c_27083,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,sK4(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_26883]) ).
tcf(c_27084,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,sK4(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_26883]) ).
tcf(c_27085,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,sK4(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_26883]) ).
tcf(c_27087,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X1 )
| ( sK2(singleton(X3),X4,X1) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(singleton(X3),X4,X1)),unordered_pair(sK1(singleton(X3),X4,X1),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_26883]) ).
tcf(c_27088,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X3) = singleton(X4) )
| ( sK1(X1,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,singleton(X4))),unordered_pair(sK2(X1,X3,singleton(X4)),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_26883]) ).
tcf(c_27089,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X1 )
| ( sK3(X3,singleton(X4),X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,singleton(X4),X1)),unordered_pair(sK1(X3,singleton(X4),X1),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_26883]) ).
tcf(c_27090,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X1) = singleton(X4) )
| ( sK1(X3,X1,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,singleton(X4))),unordered_pair(sK3(X3,X1,singleton(X4)),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_26883]) ).
tcf(c_27091,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_26883]) ).
tcf(c_27092,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_26883]) ).
tcf(c_27093,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_26883]) ).
tcf(c_27094,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X1,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_26883]) ).
tcf(c_27095,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_26883]) ).
tcf(c_27096,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_26883]) ).
tcf(c_27097,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_26883]) ).
tcf(c_27098,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X1,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_26883]) ).
tcf(c_27099,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_26883]) ).
tcf(c_27100,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_26883]) ).
tcf(c_27101,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_26883]) ).
tcf(c_27102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_26883]) ).
tcf(c_27103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_26883]) ).
tcf(c_27104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_26883]) ).
tcf(c_27105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_26883]) ).
tcf(c_27106,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_26883]) ).
tcf(c_27245,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(singleton(X3),X1,unordered_pair(singleton(X3),unordered_pair(X3,X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2343]) ).
tcf(c_27246,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2343]) ).
tcf(c_27247,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2343]) ).
tcf(c_27248,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2343]) ).
tcf(c_27249,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2343]) ).
tcf(c_27250,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2343]) ).
tcf(c_27251,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X1,X4,unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(sK4(X1,X2,X0),X3)))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2343]) ).
tcf(c_27252,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X2,X4,unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(sK5(X1,X2,X0),X3)))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2343]) ).
tcf(c_27253,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK5(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X4)))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2343]) ).
tcf(c_27254,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK5(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X4)))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2343]) ).
tcf(c_27255,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK5(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X4)))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2343]) ).
tcf(c_27256,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK5(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X4)))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2343]) ).
tcf(c_27257,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK5(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X4)))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2343]) ).
tcf(c_27258,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK5(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X4)))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2343]) ).
tcf(c_27260,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(singleton(X4),X5,X3)),unordered_pair(sK1(singleton(X4),X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2343]) ).
tcf(c_27261,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,singleton(X5))),unordered_pair(sK2(X3,X4,singleton(X5)),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2343]) ).
tcf(c_27262,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,singleton(X5),X3)),unordered_pair(sK1(X4,singleton(X5),X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2343]) ).
tcf(c_27263,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,singleton(X5))),unordered_pair(sK3(X4,X3,singleton(X5)),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2343]) ).
tcf(c_27264,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2343]) ).
tcf(c_27265,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2343]) ).
tcf(c_27266,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2343]) ).
tcf(c_27267,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2343]) ).
tcf(c_27268,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2343]) ).
tcf(c_27269,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2343]) ).
tcf(c_27270,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2343]) ).
tcf(c_27271,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2343]) ).
tcf(c_27272,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2343]) ).
tcf(c_27273,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2343]) ).
tcf(c_27274,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2343]) ).
tcf(c_27275,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2343]) ).
tcf(c_27276,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2343]) ).
tcf(c_27277,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2343]) ).
tcf(c_27278,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2343]) ).
tcf(c_27279,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2343]) ).
tcf(c_27384,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X1),sK3(X3,X4,X1)),singleton(sK2(X3,X4,X1))) = sK1(X3,X4,X1) )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_27245]) ).
tcf(c_27385,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X1),X4)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_27245]) ).
tcf(c_27386,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X1),X3)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_27245]) ).
tcf(c_27387,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X1,X3,X4),X4)
| ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK2(X1,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_27245]) ).
tcf(c_27388,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X1,X4),X4)
| ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK3(X3,X1,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_27245]) ).
tcf(c_27389,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X1,unordered_pair(singleton(X3),unordered_pair(X3,sK5(singleton(X4),X1,unordered_pair(singleton(X4),unordered_pair(X4,sK4(X1,X2,X0))))))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_27245]) ).
tcf(c_27390,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X2,unordered_pair(singleton(X3),unordered_pair(X3,sK5(singleton(X4),X2,unordered_pair(singleton(X4),unordered_pair(X4,sK5(X1,X2,X0))))))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_27245]) ).
tcf(c_27391,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,sK5(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X2)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_27245]) ).
tcf(c_27392,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,sK5(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X0,X2)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_27245]) ).
tcf(c_27393,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,sK5(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X0)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_27245]) ).
tcf(c_27394,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,sK5(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X2,X0)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_27245]) ).
tcf(c_27395,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,sK5(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X0,X2)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_27245]) ).
tcf(c_27396,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,sK5(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X2,X0)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_27245]) ).
tcf(c_27398,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X1 )
| ( sK2(singleton(X3),X4,X1) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(singleton(X3),X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_27245]) ).
tcf(c_27399,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X3) = singleton(X4) )
| ( sK1(X1,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK2(X1,X3,singleton(X4)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_27245]) ).
tcf(c_27400,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X1 )
| ( sK3(X3,singleton(X4),X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,singleton(X4),X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_27245]) ).
tcf(c_27401,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X1) = singleton(X4) )
| ( sK1(X3,X1,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK3(X3,X1,singleton(X4)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_27245]) ).
tcf(c_27402,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK3(X3,X1,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_27245]) ).
tcf(c_27403,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK3(X3,X1,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_27245]) ).
tcf(c_27404,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK3(X3,X1,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_27245]) ).
tcf(c_27405,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X1,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK3(X3,X1,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_27245]) ).
tcf(c_27406,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK2(X1,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_27245]) ).
tcf(c_27407,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK2(X1,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_27245]) ).
tcf(c_27408,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK2(X1,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_27245]) ).
tcf(c_27409,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X1,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK2(X1,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_27245]) ).
tcf(c_27410,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_27245]) ).
tcf(c_27411,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_27245]) ).
tcf(c_27412,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_27245]) ).
tcf(c_27413,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_27245]) ).
tcf(c_27414,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_27245]) ).
tcf(c_27415,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_27245]) ).
tcf(c_27416,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_27245]) ).
tcf(c_27417,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_27245]) ).
tcf(c_27575,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(singleton(X3),X1,unordered_pair(unordered_pair(X0,X3),singleton(X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2344]) ).
tcf(c_27576,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2344]) ).
tcf(c_27577,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2344]) ).
tcf(c_27578,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2344]) ).
tcf(c_27579,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2344]) ).
tcf(c_27580,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2344]) ).
tcf(c_27581,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X1,X4,unordered_pair(unordered_pair(X3,sK4(X1,X2,X0)),singleton(sK4(X1,X2,X0))))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2344]) ).
tcf(c_27582,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X2,X4,unordered_pair(unordered_pair(X3,sK5(X1,X2,X0)),singleton(sK5(X1,X2,X0))))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2344]) ).
tcf(c_27583,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK5(cartesian_product2(X3,X1),X5,unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2)))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2344]) ).
tcf(c_27584,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK5(cartesian_product2(X1,X3),X5,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))),singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2)))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2344]) ).
tcf(c_27585,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK5(cartesian_product2(X1,X3),X5,unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0)))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2344]) ).
tcf(c_27586,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK5(cartesian_product2(X1,X3),X5,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))),singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0)))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2344]) ).
tcf(c_27587,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK5(cartesian_product2(X3,X1),X5,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))),singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2)))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2344]) ).
tcf(c_27588,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK5(cartesian_product2(X3,X1),X5,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))),singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0)))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2344]) ).
tcf(c_27590,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(singleton(X4),X5,X3)),singleton(sK1(singleton(X4),X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2344]) ).
tcf(c_27591,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,singleton(X5))),singleton(sK2(X3,X4,singleton(X5)))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2344]) ).
tcf(c_27592,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,singleton(X5),X3)),singleton(sK1(X4,singleton(X5),X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2344]) ).
tcf(c_27593,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,singleton(X5))),singleton(sK3(X4,X3,singleton(X5)))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2344]) ).
tcf(c_27594,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2344]) ).
tcf(c_27595,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2344]) ).
tcf(c_27596,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2344]) ).
tcf(c_27597,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2344]) ).
tcf(c_27598,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2344]) ).
tcf(c_27599,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2344]) ).
tcf(c_27600,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2344]) ).
tcf(c_27601,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2344]) ).
tcf(c_27602,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2344]) ).
tcf(c_27603,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2344]) ).
tcf(c_27604,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2344]) ).
tcf(c_27605,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2344]) ).
tcf(c_27606,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2344]) ).
tcf(c_27607,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2344]) ).
tcf(c_27608,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2344]) ).
tcf(c_27609,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2344]) ).
tcf(c_27770,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X1),sK3(X3,X4,X1)),singleton(sK2(X3,X4,X1))) = sK1(X3,X4,X1) )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_27575]) ).
tcf(c_27771,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X1),X4)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_27575]) ).
tcf(c_27772,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X1),X3)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_27575]) ).
tcf(c_27773,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X1,X3,X4),X4)
| ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_27575]) ).
tcf(c_27774,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X1,X4),X4)
| ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_27575]) ).
tcf(c_27775,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X1,unordered_pair(singleton(X3),unordered_pair(X3,sK5(singleton(X4),X1,unordered_pair(unordered_pair(sK4(X1,X2,X0),X4),singleton(X4)))))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_27575]) ).
tcf(c_27776,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X2,unordered_pair(singleton(X3),unordered_pair(X3,sK5(singleton(X4),X2,unordered_pair(unordered_pair(sK5(X1,X2,X0),X4),singleton(X4)))))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_27575]) ).
tcf(c_27777,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,sK5(singleton(X5),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5),singleton(X5)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_27575]) ).
tcf(c_27778,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,sK5(singleton(X5),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5),singleton(X5)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_27575]) ).
tcf(c_27779,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,sK5(singleton(X5),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5),singleton(X5)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_27575]) ).
tcf(c_27780,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,sK5(singleton(X5),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5),singleton(X5)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_27575]) ).
tcf(c_27781,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,sK5(singleton(X5),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5),singleton(X5)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_27575]) ).
tcf(c_27782,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,sK5(singleton(X5),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5),singleton(X5)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_27575]) ).
tcf(c_27784,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X1 )
| ( sK2(singleton(X3),X4,X1) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(singleton(X3),X4,X1),X2),singleton(X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_27575]) ).
tcf(c_27785,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X3) = singleton(X4) )
| ( sK1(X1,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK2(X1,X3,singleton(X4)),X2),singleton(X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_27575]) ).
tcf(c_27786,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X1 )
| ( sK3(X3,singleton(X4),X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,singleton(X4),X1),X2),singleton(X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_27575]) ).
tcf(c_27787,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X1) = singleton(X4) )
| ( sK1(X3,X1,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK3(X3,X1,singleton(X4)),X2),singleton(X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_27575]) ).
tcf(c_27788,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_27575]) ).
tcf(c_27789,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_27575]) ).
tcf(c_27790,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_27575]) ).
tcf(c_27791,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X1,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_27575]) ).
tcf(c_27792,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_27575]) ).
tcf(c_27793,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_27575]) ).
tcf(c_27794,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_27575]) ).
tcf(c_27795,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X1,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_27575]) ).
tcf(c_27796,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_27575]) ).
tcf(c_27797,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_27575]) ).
tcf(c_27798,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_27575]) ).
tcf(c_27799,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_27575]) ).
tcf(c_27800,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_27575]) ).
tcf(c_27801,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_27575]) ).
tcf(c_27802,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_27575]) ).
tcf(c_27803,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_27575]) ).
tcf(c_27946,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = cartesian_product2(X0,X1) )
| ( sK4(singleton(X5),X2,unordered_pair(unordered_pair(sK4(X2,X3,sK4(cartesian_product2(X2,X3),X4,sK1(X0,X1,cartesian_product2(cartesian_product2(X2,X3),X4)))),X5),singleton(X5))) = X5 )
| ( unordered_pair(unordered_pair(sK2(X0,X1,cartesian_product2(cartesian_product2(X2,X3),X4)),sK3(X0,X1,cartesian_product2(cartesian_product2(X2,X3),X4))),singleton(sK2(X0,X1,cartesian_product2(cartesian_product2(X2,X3),X4)))) = sK1(X0,X1,cartesian_product2(cartesian_product2(X2,X3),X4)) ) ),
inference(superposition,[status(thm)],[c_58,c_2672]) ).
tcf(c_27947,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)),X5)
| ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_2672]) ).
tcf(c_27948,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)),X4)
| ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_2672]) ).
tcf(c_27949,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X3),X4) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK2(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_2672]) ).
tcf(c_27950,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X1,X2),X3)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK3(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_2672]) ).
tcf(c_27951,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK4(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X0))),X5),singleton(X5))) = X5 )
| ~ in(X0,cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X3),X4)) ),
inference(superposition,[status(thm)],[c_60,c_2672]) ).
tcf(c_27952,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(unordered_pair(sK4(X2,X3,sK4(cartesian_product2(X2,X3),X4,sK5(X1,cartesian_product2(cartesian_product2(X2,X3),X4),X0))),X5),singleton(X5))) = X5 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(cartesian_product2(X2,X3),X4))) ),
inference(superposition,[status(thm)],[c_61,c_2672]) ).
tcf(c_27953,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X4,unordered_pair(unordered_pair(X0,X3),singleton(X0)))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_64,c_2672]) ).
tcf(c_27955,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X4,unordered_pair(unordered_pair(X3,X0),singleton(X0)))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_809,c_2672]) ).
tcf(c_27956,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X4,unordered_pair(singleton(X0),unordered_pair(X3,X0)))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_882,c_2672]) ).
tcf(c_27958,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X4,unordered_pair(singleton(X0),unordered_pair(X0,X3)))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_900,c_2672]) ).
tcf(c_27959,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(singleton(X4),X5) )
| ( sK2(singleton(X4),X5,cartesian_product2(cartesian_product2(X1,X2),X3)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(singleton(X4),X5,cartesian_product2(cartesian_product2(X1,X2),X3)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_2672]) ).
tcf(c_27960,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X3),X4) = singleton(X5) )
| ( sK1(cartesian_product2(cartesian_product2(X1,X2),X3),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK2(cartesian_product2(cartesian_product2(X1,X2),X3),X4,singleton(X5)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_2672]) ).
tcf(c_27961,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,singleton(X5)) )
| ( sK3(X4,singleton(X5),cartesian_product2(cartesian_product2(X1,X2),X3)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,singleton(X5),cartesian_product2(cartesian_product2(X1,X2),X3)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_2672]) ).
tcf(c_27962,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X1,X2),X3)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(cartesian_product2(X1,X2),X3),singleton(X5)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK3(X4,cartesian_product2(cartesian_product2(X1,X2),X3),singleton(X5)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_2672]) ).
tcf(c_27963,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X1,X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK3(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_2672]) ).
tcf(c_27964,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X1,X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK3(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_2672]) ).
tcf(c_27965,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X1,X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK3(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_2672]) ).
tcf(c_27966,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X1,X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK3(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_2672]) ).
tcf(c_27967,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK2(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_2672]) ).
tcf(c_27968,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK2(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_2672]) ).
tcf(c_27969,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK2(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_2672]) ).
tcf(c_27970,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK2(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_2672]) ).
tcf(c_27971,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_2672]) ).
tcf(c_27972,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_2672]) ).
tcf(c_27973,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_2672]) ).
tcf(c_27974,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_2672]) ).
tcf(c_27975,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_2672]) ).
tcf(c_27976,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_2672]) ).
tcf(c_27977,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_2672]) ).
tcf(c_27978,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_2672]) ).
tcf(c_28121,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(X3,X4)) = cartesian_product2(X0,X1) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK4(X3,X4,sK5(X2,cartesian_product2(X3,X4),sK1(X0,X1,cartesian_product2(X2,cartesian_product2(X3,X4))))),X5),singleton(X5))) = X5 )
| ( unordered_pair(unordered_pair(sK2(X0,X1,cartesian_product2(X2,cartesian_product2(X3,X4))),sK3(X0,X1,cartesian_product2(X2,cartesian_product2(X3,X4)))),singleton(sK2(X0,X1,cartesian_product2(X2,cartesian_product2(X3,X4))))) = sK1(X0,X1,cartesian_product2(X2,cartesian_product2(X3,X4))) ) ),
inference(superposition,[status(thm)],[c_58,c_2673]) ).
tcf(c_28122,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))),X5)
| ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_2673]) ).
tcf(c_28123,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))),X4)
| ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_2673]) ).
tcf(c_28124,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_2673]) ).
tcf(c_28125,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X1,X2))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK3(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_2673]) ).
tcf(c_28126,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(unordered_pair(sK4(X2,X3,sK5(X1,cartesian_product2(X2,X3),sK4(cartesian_product2(X1,cartesian_product2(X2,X3)),X4,X0))),X5),singleton(X5))) = X5 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,cartesian_product2(X2,X3)),X4)) ),
inference(superposition,[status(thm)],[c_60,c_2673]) ).
tcf(c_28127,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK4(X3,X4,sK5(X2,cartesian_product2(X3,X4),sK5(X1,cartesian_product2(X2,cartesian_product2(X3,X4)),X0))),X5),singleton(X5))) = X5 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,cartesian_product2(X3,X4)))) ),
inference(superposition,[status(thm)],[c_61,c_2673]) ).
tcf(c_28128,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK5(X4,cartesian_product2(X1,X2),unordered_pair(unordered_pair(X3,X0),singleton(X3)))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_64,c_2673]) ).
tcf(c_28130,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK5(X4,cartesian_product2(X1,X2),unordered_pair(unordered_pair(X0,X3),singleton(X3)))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_809,c_2673]) ).
tcf(c_28131,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK5(X4,cartesian_product2(X1,X2),unordered_pair(singleton(X3),unordered_pair(X0,X3)))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_882,c_2673]) ).
tcf(c_28133,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK5(X4,cartesian_product2(X1,X2),unordered_pair(singleton(X3),unordered_pair(X3,X0)))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_900,c_2673]) ).
tcf(c_28134,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(singleton(X4),X5) )
| ( sK2(singleton(X4),X5,cartesian_product2(X3,cartesian_product2(X1,X2))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(singleton(X4),X5,cartesian_product2(X3,cartesian_product2(X1,X2))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_2673]) ).
tcf(c_28135,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,singleton(X5)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_2673]) ).
tcf(c_28136,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,singleton(X5)) )
| ( sK3(X4,singleton(X5),cartesian_product2(X3,cartesian_product2(X1,X2))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,singleton(X5),cartesian_product2(X3,cartesian_product2(X1,X2))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_2673]) ).
tcf(c_28137,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X1,X2))) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),singleton(X5)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK3(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),singleton(X5)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_2673]) ).
tcf(c_28138,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X1,X2))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK3(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_2673]) ).
tcf(c_28139,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X1,X2))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK3(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_2673]) ).
tcf(c_28140,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X1,X2))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK3(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_2673]) ).
tcf(c_28141,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X1,X2))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK3(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_2673]) ).
tcf(c_28142,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_2673]) ).
tcf(c_28143,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_2673]) ).
tcf(c_28144,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_2673]) ).
tcf(c_28145,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_2673]) ).
tcf(c_28146,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_2673]) ).
tcf(c_28147,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_2673]) ).
tcf(c_28148,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_2673]) ).
tcf(c_28149,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_2673]) ).
tcf(c_28150,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_2673]) ).
tcf(c_28151,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_2673]) ).
tcf(c_28152,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_2673]) ).
tcf(c_28153,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_2673]) ).
tcf(c_28296,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X3),unordered_pair(unordered_pair(X0,X3),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2674]) ).
tcf(c_28297,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2674]) ).
tcf(c_28298,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2674]) ).
tcf(c_28299,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2674]) ).
tcf(c_28300,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2674]) ).
tcf(c_28301,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2674]) ).
tcf(c_28302,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK4(X4,X1,unordered_pair(unordered_pair(X3,sK4(X1,X2,X0)),singleton(X3))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2674]) ).
tcf(c_28303,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK4(X4,X2,unordered_pair(unordered_pair(X3,sK5(X1,X2,X0)),singleton(X3))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2674]) ).
tcf(c_28304,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK4(X5,cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))),singleton(X4))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2674]) ).
tcf(c_28305,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK4(X5,cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))),singleton(X4))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2674]) ).
tcf(c_28306,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK4(X5,cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))),singleton(X4))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2674]) ).
tcf(c_28307,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK4(X5,cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))),singleton(X4))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2674]) ).
tcf(c_28308,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK4(X5,cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))),singleton(X4))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2674]) ).
tcf(c_28309,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK4(X5,cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))),singleton(X4))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2674]) ).
tcf(c_28311,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(singleton(X4),X5,X3)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2674]) ).
tcf(c_28312,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,singleton(X5))),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2674]) ).
tcf(c_28313,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,singleton(X5),X3)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2674]) ).
tcf(c_28314,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,singleton(X5))),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2674]) ).
tcf(c_28315,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2674]) ).
tcf(c_28316,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2674]) ).
tcf(c_28317,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2674]) ).
tcf(c_28318,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2674]) ).
tcf(c_28319,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2674]) ).
tcf(c_28320,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2674]) ).
tcf(c_28321,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2674]) ).
tcf(c_28322,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2674]) ).
tcf(c_28323,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2674]) ).
tcf(c_28324,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2674]) ).
tcf(c_28325,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2674]) ).
tcf(c_28326,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2674]) ).
tcf(c_28327,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2674]) ).
tcf(c_28328,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2674]) ).
tcf(c_28329,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2674]) ).
tcf(c_28330,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2674]) ).
tcf(c_28567,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X1),sK3(X3,X4,X1)),singleton(sK2(X3,X4,X1))) = sK1(X3,X4,X1) )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_28296]) ).
tcf(c_28568,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X1),X4)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_28296]) ).
tcf(c_28569,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X1),X3)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_28296]) ).
tcf(c_28570,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X1,X3,X4),X4)
| ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_28296]) ).
tcf(c_28571,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X1,X4),X4)
| ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_28296]) ).
tcf(c_28572,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X4),unordered_pair(unordered_pair(sK4(X1,X2,X0),X4),singleton(sK4(X1,X2,X0)))),X3),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_28296]) ).
tcf(c_28573,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X2,unordered_pair(unordered_pair(sK4(X2,singleton(X4),unordered_pair(unordered_pair(sK5(X1,X2,X0),X4),singleton(sK5(X1,X2,X0)))),X3),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_28296]) ).
tcf(c_28574,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(sK4(cartesian_product2(X3,X1),singleton(X5),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_28296]) ).
tcf(c_28575,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(sK4(cartesian_product2(X1,X3),singleton(X5),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5),singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_28296]) ).
tcf(c_28576,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(sK4(cartesian_product2(X1,X3),singleton(X5),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_28296]) ).
tcf(c_28577,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(sK4(cartesian_product2(X1,X3),singleton(X5),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5),singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_28296]) ).
tcf(c_28578,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(sK4(cartesian_product2(X3,X1),singleton(X5),unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5),singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_28296]) ).
tcf(c_28579,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(sK4(cartesian_product2(X3,X1),singleton(X5),unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5),singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_28296]) ).
tcf(c_28581,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X1 )
| ( sK2(singleton(X3),X4,X1) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(singleton(X3),X4,X1),X2),singleton(sK1(singleton(X3),X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_28296]) ).
tcf(c_28582,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X3) = singleton(X4) )
| ( sK1(X1,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK2(X1,X3,singleton(X4)),X2),singleton(sK2(X1,X3,singleton(X4))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_28296]) ).
tcf(c_28583,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X1 )
| ( sK3(X3,singleton(X4),X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,singleton(X4),X1),X2),singleton(sK1(X3,singleton(X4),X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_28296]) ).
tcf(c_28584,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X1) = singleton(X4) )
| ( sK1(X3,X1,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK3(X3,X1,singleton(X4)),X2),singleton(sK3(X3,X1,singleton(X4))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_28296]) ).
tcf(c_28585,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_28296]) ).
tcf(c_28586,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_28296]) ).
tcf(c_28587,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_28296]) ).
tcf(c_28588,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X1,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_28296]) ).
tcf(c_28589,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_28296]) ).
tcf(c_28590,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_28296]) ).
tcf(c_28591,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_28296]) ).
tcf(c_28592,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X1,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_28296]) ).
tcf(c_28593,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_28296]) ).
tcf(c_28594,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_28296]) ).
tcf(c_28595,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_28296]) ).
tcf(c_28596,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_28296]) ).
tcf(c_28597,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_28296]) ).
tcf(c_28598,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_28296]) ).
tcf(c_28599,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_28296]) ).
tcf(c_28600,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_28296]) ).
tcf(c_28822,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(singleton(X3),X1,unordered_pair(singleton(X3),unordered_pair(X0,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2345]) ).
tcf(c_28823,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2345]) ).
tcf(c_28824,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2345]) ).
tcf(c_28825,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2345]) ).
tcf(c_28826,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2345]) ).
tcf(c_28827,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2345]) ).
tcf(c_28828,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X1,X4,unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(X3,sK4(X1,X2,X0))))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2345]) ).
tcf(c_28829,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X2,X4,unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(X3,sK5(X1,X2,X0))))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2345]) ).
tcf(c_28830,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK5(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2)))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2345]) ).
tcf(c_28831,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK5(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2)))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2345]) ).
tcf(c_28832,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK5(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0)))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2345]) ).
tcf(c_28833,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK5(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0)))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2345]) ).
tcf(c_28834,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK5(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2)))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2345]) ).
tcf(c_28835,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK5(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0)))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2345]) ).
tcf(c_28837,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(singleton(X4),X5,X3)),unordered_pair(X0,sK1(singleton(X4),X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2345]) ).
tcf(c_28838,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,singleton(X5))),unordered_pair(X0,sK2(X3,X4,singleton(X5)))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2345]) ).
tcf(c_28839,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,singleton(X5),X3)),unordered_pair(X0,sK1(X4,singleton(X5),X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2345]) ).
tcf(c_28840,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,singleton(X5))),unordered_pair(X0,sK3(X4,X3,singleton(X5)))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2345]) ).
tcf(c_28841,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2345]) ).
tcf(c_28842,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2345]) ).
tcf(c_28843,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2345]) ).
tcf(c_28844,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2345]) ).
tcf(c_28845,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2345]) ).
tcf(c_28846,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2345]) ).
tcf(c_28847,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2345]) ).
tcf(c_28848,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2345]) ).
tcf(c_28849,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2345]) ).
tcf(c_28850,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2345]) ).
tcf(c_28851,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2345]) ).
tcf(c_28852,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2345]) ).
tcf(c_28853,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2345]) ).
tcf(c_28854,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2345]) ).
tcf(c_28855,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2345]) ).
tcf(c_28856,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2345]) ).
tcf(c_29004,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X1),sK3(X3,X4,X1)),singleton(sK2(X3,X4,X1))) = sK1(X3,X4,X1) )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_28822]) ).
tcf(c_29005,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X1),X4)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_28822]) ).
tcf(c_29006,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X1),X3)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_28822]) ).
tcf(c_29007,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X1,X3,X4),X4)
| ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK2(X1,X3,X4),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_28822]) ).
tcf(c_29008,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X1,X4),X4)
| ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK3(X3,X1,X4),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_28822]) ).
tcf(c_29009,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X1,unordered_pair(singleton(X3),unordered_pair(X3,sK5(singleton(X4),X1,unordered_pair(singleton(X4),unordered_pair(sK4(X1,X2,X0),X4)))))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_28822]) ).
tcf(c_29010,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X2,unordered_pair(singleton(X3),unordered_pair(X3,sK5(singleton(X4),X2,unordered_pair(singleton(X4),unordered_pair(sK5(X1,X2,X0),X4)))))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_28822]) ).
tcf(c_29011,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,sK5(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_28822]) ).
tcf(c_29012,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,sK5(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_28822]) ).
tcf(c_29013,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,sK5(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_28822]) ).
tcf(c_29014,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,sK5(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_28822]) ).
tcf(c_29015,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,sK5(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_28822]) ).
tcf(c_29016,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,sK5(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_28822]) ).
tcf(c_29018,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X1 )
| ( sK2(singleton(X3),X4,X1) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(singleton(X3),X4,X1),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_28822]) ).
tcf(c_29019,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X3) = singleton(X4) )
| ( sK1(X1,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK2(X1,X3,singleton(X4)),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_28822]) ).
tcf(c_29020,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X1 )
| ( sK3(X3,singleton(X4),X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,singleton(X4),X1),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_28822]) ).
tcf(c_29021,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X1) = singleton(X4) )
| ( sK1(X3,X1,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK3(X3,X1,singleton(X4)),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_28822]) ).
tcf(c_29022,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK3(X3,X1,X4),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_28822]) ).
tcf(c_29023,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK3(X3,X1,X4),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_28822]) ).
tcf(c_29024,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK3(X3,X1,X4),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_28822]) ).
tcf(c_29025,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X1,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK3(X3,X1,X4),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_28822]) ).
tcf(c_29026,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK2(X1,X3,X4),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_28822]) ).
tcf(c_29027,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK2(X1,X3,X4),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_28822]) ).
tcf(c_29028,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK2(X1,X3,X4),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_28822]) ).
tcf(c_29029,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X1,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK2(X1,X3,X4),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_28822]) ).
tcf(c_29030,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_28822]) ).
tcf(c_29031,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_28822]) ).
tcf(c_29032,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_28822]) ).
tcf(c_29033,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_28822]) ).
tcf(c_29034,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_28822]) ).
tcf(c_29035,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_28822]) ).
tcf(c_29036,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_28822]) ).
tcf(c_29037,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_28822]) ).
tcf(c_29355,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),singleton(X3),unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,singleton(X3),unordered_pair(singleton(X0),unordered_pair(X3,X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2346]) ).
tcf(c_29356,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2346]) ).
tcf(c_29357,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2346]) ).
tcf(c_29358,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2346]) ).
tcf(c_29359,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2346]) ).
tcf(c_29360,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2346]) ).
tcf(c_29361,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X4,X1,unordered_pair(singleton(X3),unordered_pair(sK4(X1,X2,X0),X3)))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2346]) ).
tcf(c_29362,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X4,X2,unordered_pair(singleton(X3),unordered_pair(sK5(X1,X2,X0),X3)))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2346]) ).
tcf(c_29363,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(singleton(X6),unordered_pair(X6,sK5(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X4)))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2346]) ).
tcf(c_29364,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(singleton(X6),unordered_pair(X6,sK5(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X4)))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2346]) ).
tcf(c_29365,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(singleton(X6),unordered_pair(X6,sK5(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X4)))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2346]) ).
tcf(c_29366,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(singleton(X6),unordered_pair(X6,sK5(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X4)))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2346]) ).
tcf(c_29367,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(singleton(X6),unordered_pair(X6,sK5(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X4)))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2346]) ).
tcf(c_29368,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(singleton(X6),unordered_pair(X6,sK5(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X4)))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2346]) ).
tcf(c_29370,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(singleton(X4),X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2346]) ).
tcf(c_29371,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,singleton(X5)),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2346]) ).
tcf(c_29372,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,singleton(X5),X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2346]) ).
tcf(c_29373,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,singleton(X5)),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2346]) ).
tcf(c_29374,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2346]) ).
tcf(c_29375,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2346]) ).
tcf(c_29376,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2346]) ).
tcf(c_29377,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2346]) ).
tcf(c_29378,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2346]) ).
tcf(c_29379,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2346]) ).
tcf(c_29380,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2346]) ).
tcf(c_29381,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2346]) ).
tcf(c_29382,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2346]) ).
tcf(c_29383,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2346]) ).
tcf(c_29384,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2346]) ).
tcf(c_29385,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2346]) ).
tcf(c_29386,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2346]) ).
tcf(c_29387,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2346]) ).
tcf(c_29388,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2346]) ).
tcf(c_29389,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2346]) ).
tcf(c_29505,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X2),sK3(X3,X4,X2)),singleton(sK2(X3,X4,X2))) = sK1(X3,X4,X2) )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_29355]) ).
tcf(c_29506,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X2),X4)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_29355]) ).
tcf(c_29507,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X2),X3)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_29355]) ).
tcf(c_29508,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X2,X3,X4),X4)
| ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(X1,sK2(X2,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_29355]) ).
tcf(c_29509,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X2,X4),X4)
| ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(X1,sK3(X3,X2,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_29355]) ).
tcf(c_29510,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(singleton(X3),unordered_pair(X3,sK5(X1,singleton(X4),unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(X4,sK4(X1,X2,X0))))))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_29355]) ).
tcf(c_29511,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(singleton(X3),unordered_pair(X3,sK5(X2,singleton(X4),unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(X4,sK5(X1,X2,X0))))))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_29355]) ).
tcf(c_29512,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(X4,sK5(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X2)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_29355]) ).
tcf(c_29513,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(X4,sK5(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X0,X2)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_29355]) ).
tcf(c_29514,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(X4,sK5(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X0)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_29355]) ).
tcf(c_29515,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(X4,sK5(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X2,X0)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_29355]) ).
tcf(c_29516,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(X4,sK5(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X0,X2)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_29355]) ).
tcf(c_29517,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(X4,sK5(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X2,X0)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_29355]) ).
tcf(c_29519,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X2 )
| ( sK2(singleton(X3),X4,X2) = X3 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(singleton(X3),X4,X2)),unordered_pair(X1,sK1(singleton(X3),X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_29355]) ).
tcf(c_29520,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK1(X2,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,singleton(X4))),unordered_pair(X1,sK2(X2,X3,singleton(X4)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_29355]) ).
tcf(c_29521,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X2 )
| ( sK3(X3,singleton(X4),X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,singleton(X4),X2)),unordered_pair(X1,sK1(X3,singleton(X4),X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_29355]) ).
tcf(c_29522,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X2) = singleton(X4) )
| ( sK1(X3,X2,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,singleton(X4))),unordered_pair(X1,sK3(X3,X2,singleton(X4)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_29355]) ).
tcf(c_29523,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(X1,sK3(X3,X2,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_29355]) ).
tcf(c_29524,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(X1,sK3(X3,X2,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_29355]) ).
tcf(c_29525,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(X1,sK3(X3,X2,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_29355]) ).
tcf(c_29526,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X2,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(X1,sK3(X3,X2,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_29355]) ).
tcf(c_29527,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(X1,sK2(X2,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_29355]) ).
tcf(c_29528,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(X1,sK2(X2,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_29355]) ).
tcf(c_29529,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(X1,sK2(X2,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_29355]) ).
tcf(c_29530,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X2,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(X1,sK2(X2,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_29355]) ).
tcf(c_29531,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_29355]) ).
tcf(c_29532,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_29355]) ).
tcf(c_29533,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_29355]) ).
tcf(c_29534,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_29355]) ).
tcf(c_29535,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_29355]) ).
tcf(c_29536,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_29355]) ).
tcf(c_29537,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_29355]) ).
tcf(c_29538,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_29355]) ).
tcf(c_29608,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),singleton(X3),unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,singleton(X3),unordered_pair(singleton(X0),unordered_pair(X0,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2347]) ).
tcf(c_29609,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2347]) ).
tcf(c_29610,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2347]) ).
tcf(c_29611,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2347]) ).
tcf(c_29612,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2347]) ).
tcf(c_29613,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2347]) ).
tcf(c_29614,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X4,X1,unordered_pair(singleton(X3),unordered_pair(X3,sK4(X1,X2,X0))))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2347]) ).
tcf(c_29615,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X4,X2,unordered_pair(singleton(X3),unordered_pair(X3,sK5(X1,X2,X0))))))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2347]) ).
tcf(c_29616,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(singleton(X6),unordered_pair(X6,sK5(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2)))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2347]) ).
tcf(c_29617,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(singleton(X6),unordered_pair(X6,sK5(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2)))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2347]) ).
tcf(c_29618,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(singleton(X6),unordered_pair(X6,sK5(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0)))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2347]) ).
tcf(c_29619,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(singleton(X6),unordered_pair(X6,sK5(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0)))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2347]) ).
tcf(c_29620,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(singleton(X6),unordered_pair(X6,sK5(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2)))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2347]) ).
tcf(c_29621,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(singleton(X6),unordered_pair(X6,sK5(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0)))))))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2347]) ).
tcf(c_29623,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(singleton(X4),X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2347]) ).
tcf(c_29624,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,singleton(X5)))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2347]) ).
tcf(c_29625,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,singleton(X5),X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2347]) ).
tcf(c_29626,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,singleton(X5)))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2347]) ).
tcf(c_29627,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2347]) ).
tcf(c_29628,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2347]) ).
tcf(c_29629,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2347]) ).
tcf(c_29630,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2347]) ).
tcf(c_29631,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2347]) ).
tcf(c_29632,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2347]) ).
tcf(c_29633,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2347]) ).
tcf(c_29634,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2347]) ).
tcf(c_29635,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2347]) ).
tcf(c_29636,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2347]) ).
tcf(c_29637,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2347]) ).
tcf(c_29638,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2347]) ).
tcf(c_29639,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2347]) ).
tcf(c_29640,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2347]) ).
tcf(c_29641,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2347]) ).
tcf(c_29642,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2347]) ).
tcf(c_29875,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X2),sK3(X3,X4,X2)),singleton(sK2(X3,X4,X2))) = sK1(X3,X4,X2) )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_29608]) ).
tcf(c_29876,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X2),X4)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_29608]) ).
tcf(c_29877,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X2),X3)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_29608]) ).
tcf(c_29878,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X2,X3,X4),X4)
| ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(sK2(X2,X3,X4),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_29608]) ).
tcf(c_29879,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X2,X4),X4)
| ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(sK3(X3,X2,X4),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_29608]) ).
tcf(c_29880,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(singleton(X3),unordered_pair(X3,sK5(X1,singleton(X4),unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(sK4(X1,X2,X0),X4)))))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_29608]) ).
tcf(c_29881,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(singleton(X3),unordered_pair(X3,sK5(X2,singleton(X4),unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(sK5(X1,X2,X0),X4)))))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_29608]) ).
tcf(c_29882,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(X4,sK5(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_29608]) ).
tcf(c_29883,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(X4,sK5(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_29608]) ).
tcf(c_29884,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(X4,sK5(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_29608]) ).
tcf(c_29885,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(X4,sK5(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_29608]) ).
tcf(c_29886,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(X4,sK5(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_29608]) ).
tcf(c_29887,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(X4,sK5(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5)))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_29608]) ).
tcf(c_29889,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X2 )
| ( sK2(singleton(X3),X4,X2) = X3 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(singleton(X3),X4,X2)),unordered_pair(sK1(singleton(X3),X4,X2),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_29608]) ).
tcf(c_29890,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK1(X2,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,singleton(X4))),unordered_pair(sK2(X2,X3,singleton(X4)),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_29608]) ).
tcf(c_29891,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X2 )
| ( sK3(X3,singleton(X4),X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,singleton(X4),X2)),unordered_pair(sK1(X3,singleton(X4),X2),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_29608]) ).
tcf(c_29892,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X2) = singleton(X4) )
| ( sK1(X3,X2,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,singleton(X4))),unordered_pair(sK3(X3,X2,singleton(X4)),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_29608]) ).
tcf(c_29893,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(sK3(X3,X2,X4),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_29608]) ).
tcf(c_29894,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(sK3(X3,X2,X4),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_29608]) ).
tcf(c_29895,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(sK3(X3,X2,X4),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_29608]) ).
tcf(c_29896,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X2,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(sK3(X3,X2,X4),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_29608]) ).
tcf(c_29897,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(sK2(X2,X3,X4),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_29608]) ).
tcf(c_29898,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(sK2(X2,X3,X4),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_29608]) ).
tcf(c_29899,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(sK2(X2,X3,X4),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_29608]) ).
tcf(c_29900,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X2,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(sK2(X2,X3,X4),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_29608]) ).
tcf(c_29901,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_29608]) ).
tcf(c_29902,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_29608]) ).
tcf(c_29903,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_29608]) ).
tcf(c_29904,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_29608]) ).
tcf(c_29905,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_29608]) ).
tcf(c_29906,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_29608]) ).
tcf(c_29907,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_29608]) ).
tcf(c_29908,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_29608]) ).
tcf(c_30093,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),singleton(X3),unordered_pair(unordered_pair(sK4(singleton(X3),X1,unordered_pair(singleton(X3),unordered_pair(X3,X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2675]) ).
tcf(c_30094,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2675]) ).
tcf(c_30095,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2675]) ).
tcf(c_30096,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2675]) ).
tcf(c_30097,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2675]) ).
tcf(c_30098,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2675]) ).
tcf(c_30099,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(unordered_pair(sK4(X1,X4,unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(sK4(X1,X2,X0),X3))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2675]) ).
tcf(c_30100,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(unordered_pair(sK4(X2,X4,unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(sK5(X1,X2,X0),X3))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2675]) ).
tcf(c_30101,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(unordered_pair(sK4(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X4))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2675]) ).
tcf(c_30102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(unordered_pair(sK4(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X4))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2675]) ).
tcf(c_30103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(unordered_pair(sK4(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X4))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2675]) ).
tcf(c_30104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(unordered_pair(sK4(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X4))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2675]) ).
tcf(c_30105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(unordered_pair(sK4(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X4))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2675]) ).
tcf(c_30106,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(unordered_pair(sK4(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X4))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2675]) ).
tcf(c_30108,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(singleton(X4),X5,X3)),unordered_pair(sK1(singleton(X4),X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2675]) ).
tcf(c_30109,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,singleton(X5))),unordered_pair(sK2(X3,X4,singleton(X5)),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2675]) ).
tcf(c_30110,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,singleton(X5),X3)),unordered_pair(sK1(X4,singleton(X5),X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2675]) ).
tcf(c_30111,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,singleton(X5))),unordered_pair(sK3(X4,X3,singleton(X5)),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2675]) ).
tcf(c_30112,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2675]) ).
tcf(c_30113,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2675]) ).
tcf(c_30114,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2675]) ).
tcf(c_30115,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2675]) ).
tcf(c_30116,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2675]) ).
tcf(c_30117,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2675]) ).
tcf(c_30118,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2675]) ).
tcf(c_30119,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2675]) ).
tcf(c_30120,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2675]) ).
tcf(c_30121,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2675]) ).
tcf(c_30122,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2675]) ).
tcf(c_30123,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2675]) ).
tcf(c_30124,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2675]) ).
tcf(c_30125,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2675]) ).
tcf(c_30126,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2675]) ).
tcf(c_30127,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2675]) ).
tcf(c_30321,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X2),sK3(X3,X4,X2)),singleton(sK2(X3,X4,X2))) = sK1(X3,X4,X2) )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_30093]) ).
tcf(c_30322,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X2),X4)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_30093]) ).
tcf(c_30323,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X2),X3)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_30093]) ).
tcf(c_30324,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X2,X3,X4),X4)
| ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_30093]) ).
tcf(c_30325,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X2,X4),X4)
| ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_30093]) ).
tcf(c_30326,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(unordered_pair(sK4(singleton(X4),X1,unordered_pair(singleton(X4),unordered_pair(X4,sK4(X1,X2,X0)))),X3),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_30093]) ).
tcf(c_30327,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(unordered_pair(sK4(singleton(X4),X2,unordered_pair(singleton(X4),unordered_pair(X4,sK5(X1,X2,X0)))),X3),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_30093]) ).
tcf(c_30328,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(sK4(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X2))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_30093]) ).
tcf(c_30329,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(sK4(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X0,X2))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_30093]) ).
tcf(c_30330,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(sK4(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X0))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_30093]) ).
tcf(c_30331,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(sK4(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X2,X0))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_30093]) ).
tcf(c_30332,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(sK4(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X0,X2))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_30093]) ).
tcf(c_30333,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(sK4(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X2,X0))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_30093]) ).
tcf(c_30335,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X2 )
| ( sK2(singleton(X3),X4,X2) = X3 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(singleton(X3),X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_30093]) ).
tcf(c_30336,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK1(X2,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,singleton(X4))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_30093]) ).
tcf(c_30337,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X2 )
| ( sK3(X3,singleton(X4),X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,singleton(X4),X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_30093]) ).
tcf(c_30338,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X2) = singleton(X4) )
| ( sK1(X3,X2,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,singleton(X4))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_30093]) ).
tcf(c_30339,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_30093]) ).
tcf(c_30340,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_30093]) ).
tcf(c_30341,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_30093]) ).
tcf(c_30342,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X2,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_30093]) ).
tcf(c_30343,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_30093]) ).
tcf(c_30344,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_30093]) ).
tcf(c_30345,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_30093]) ).
tcf(c_30346,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X2,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_30093]) ).
tcf(c_30347,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_30093]) ).
tcf(c_30348,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_30093]) ).
tcf(c_30349,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_30093]) ).
tcf(c_30350,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_30093]) ).
tcf(c_30351,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_30093]) ).
tcf(c_30352,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_30093]) ).
tcf(c_30353,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_30093]) ).
tcf(c_30354,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_30093]) ).
tcf(c_30471,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),singleton(X3),unordered_pair(unordered_pair(sK4(singleton(X3),X1,unordered_pair(unordered_pair(X0,X3),singleton(X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2676]) ).
tcf(c_30472,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2676]) ).
tcf(c_30473,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2676]) ).
tcf(c_30474,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2676]) ).
tcf(c_30475,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2676]) ).
tcf(c_30476,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2676]) ).
tcf(c_30477,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(unordered_pair(sK4(X1,X4,unordered_pair(unordered_pair(X3,sK4(X1,X2,X0)),singleton(sK4(X1,X2,X0)))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2676]) ).
tcf(c_30478,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(unordered_pair(sK4(X2,X4,unordered_pair(unordered_pair(X3,sK5(X1,X2,X0)),singleton(sK5(X1,X2,X0)))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2676]) ).
tcf(c_30479,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(unordered_pair(sK4(cartesian_product2(X3,X1),X5,unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2676]) ).
tcf(c_30480,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(unordered_pair(sK4(cartesian_product2(X1,X3),X5,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))),singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2676]) ).
tcf(c_30481,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(unordered_pair(sK4(cartesian_product2(X1,X3),X5,unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2676]) ).
tcf(c_30482,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(unordered_pair(sK4(cartesian_product2(X1,X3),X5,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))),singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2676]) ).
tcf(c_30483,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(unordered_pair(sK4(cartesian_product2(X3,X1),X5,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))),singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2676]) ).
tcf(c_30484,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(unordered_pair(sK4(cartesian_product2(X3,X1),X5,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))),singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2676]) ).
tcf(c_30486,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(singleton(X4),X5,X3)),singleton(sK1(singleton(X4),X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2676]) ).
tcf(c_30487,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,singleton(X5))),singleton(sK2(X3,X4,singleton(X5))))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2676]) ).
tcf(c_30488,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,singleton(X5),X3)),singleton(sK1(X4,singleton(X5),X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2676]) ).
tcf(c_30489,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,singleton(X5))),singleton(sK3(X4,X3,singleton(X5))))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2676]) ).
tcf(c_30490,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2676]) ).
tcf(c_30491,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2676]) ).
tcf(c_30492,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2676]) ).
tcf(c_30493,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2676]) ).
tcf(c_30494,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2676]) ).
tcf(c_30495,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2676]) ).
tcf(c_30496,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2676]) ).
tcf(c_30497,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2676]) ).
tcf(c_30498,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2676]) ).
tcf(c_30499,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2676]) ).
tcf(c_30500,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2676]) ).
tcf(c_30501,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2676]) ).
tcf(c_30502,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2676]) ).
tcf(c_30503,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2676]) ).
tcf(c_30504,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2676]) ).
tcf(c_30505,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2676]) ).
tcf(c_31292,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X2),sK3(X3,X4,X2)),singleton(sK2(X3,X4,X2))) = sK1(X3,X4,X2) )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_30471]) ).
tcf(c_31293,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X2),X4)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_30471]) ).
tcf(c_31294,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X2),X3)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_30471]) ).
tcf(c_31295,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X2,X3,X4),X4)
| ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_30471]) ).
tcf(c_31296,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X2,X4),X4)
| ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_30471]) ).
tcf(c_31297,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(unordered_pair(sK4(singleton(X4),X1,unordered_pair(unordered_pair(sK4(X1,X2,X0),X4),singleton(X4))),X3),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_30471]) ).
tcf(c_31298,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(unordered_pair(sK4(singleton(X4),X2,unordered_pair(unordered_pair(sK5(X1,X2,X0),X4),singleton(X4))),X3),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_30471]) ).
tcf(c_31299,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(sK4(singleton(X5),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5),singleton(X5))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_30471]) ).
tcf(c_31300,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(sK4(singleton(X5),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5),singleton(X5))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_30471]) ).
tcf(c_31301,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(sK4(singleton(X5),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5),singleton(X5))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_30471]) ).
tcf(c_31302,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(sK4(singleton(X5),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5),singleton(X5))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_30471]) ).
tcf(c_31303,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(sK4(singleton(X5),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5),singleton(X5))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_30471]) ).
tcf(c_31304,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(sK4(singleton(X5),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5),singleton(X5))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_30471]) ).
tcf(c_31306,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X2 )
| ( sK2(singleton(X3),X4,X2) = X3 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(singleton(X3),X4,X2),X1),singleton(X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_30471]) ).
tcf(c_31307,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK1(X2,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK2(X2,X3,singleton(X4)),X1),singleton(X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_30471]) ).
tcf(c_31308,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X2 )
| ( sK3(X3,singleton(X4),X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,singleton(X4),X2),X1),singleton(X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_30471]) ).
tcf(c_31309,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X2) = singleton(X4) )
| ( sK1(X3,X2,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK3(X3,X2,singleton(X4)),X1),singleton(X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_30471]) ).
tcf(c_31310,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_30471]) ).
tcf(c_31311,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_30471]) ).
tcf(c_31312,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_30471]) ).
tcf(c_31313,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X2,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_30471]) ).
tcf(c_31314,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_30471]) ).
tcf(c_31315,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_30471]) ).
tcf(c_31316,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_30471]) ).
tcf(c_31317,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X2,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_30471]) ).
tcf(c_31318,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_30471]) ).
tcf(c_31319,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_30471]) ).
tcf(c_31320,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_30471]) ).
tcf(c_31321,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_30471]) ).
tcf(c_31322,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_30471]) ).
tcf(c_31323,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_30471]) ).
tcf(c_31324,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_30471]) ).
tcf(c_31325,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_30471]) ).
tcf(c_31618,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),singleton(X3),unordered_pair(unordered_pair(sK4(singleton(X3),X1,unordered_pair(singleton(X3),unordered_pair(X0,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2677]) ).
tcf(c_31619,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2677]) ).
tcf(c_31620,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2677]) ).
tcf(c_31621,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2677]) ).
tcf(c_31622,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2677]) ).
tcf(c_31623,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2677]) ).
tcf(c_31624,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(unordered_pair(sK4(X1,X4,unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(X3,sK4(X1,X2,X0)))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2677]) ).
tcf(c_31625,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(unordered_pair(sK4(X2,X4,unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(X3,sK5(X1,X2,X0)))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2677]) ).
tcf(c_31626,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(unordered_pair(sK4(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2677]) ).
tcf(c_31627,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(unordered_pair(sK4(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2677]) ).
tcf(c_31628,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(unordered_pair(sK4(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2677]) ).
tcf(c_31629,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(unordered_pair(sK4(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2677]) ).
tcf(c_31630,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(unordered_pair(sK4(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2677]) ).
tcf(c_31631,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(unordered_pair(sK4(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2677]) ).
tcf(c_31633,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(singleton(X4),X5,X3)),unordered_pair(X0,sK1(singleton(X4),X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2677]) ).
tcf(c_31634,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,singleton(X5))),unordered_pair(X0,sK2(X3,X4,singleton(X5))))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2677]) ).
tcf(c_31635,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,singleton(X5),X3)),unordered_pair(X0,sK1(X4,singleton(X5),X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2677]) ).
tcf(c_31636,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,singleton(X5))),unordered_pair(X0,sK3(X4,X3,singleton(X5))))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2677]) ).
tcf(c_31637,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2677]) ).
tcf(c_31638,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2677]) ).
tcf(c_31639,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2677]) ).
tcf(c_31640,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2677]) ).
tcf(c_31641,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2677]) ).
tcf(c_31642,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2677]) ).
tcf(c_31643,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2677]) ).
tcf(c_31644,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2677]) ).
tcf(c_31645,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2677]) ).
tcf(c_31646,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2677]) ).
tcf(c_31647,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2677]) ).
tcf(c_31648,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2677]) ).
tcf(c_31649,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2677]) ).
tcf(c_31650,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2677]) ).
tcf(c_31651,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2677]) ).
tcf(c_31652,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2677]) ).
tcf(c_31971,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X2),sK3(X3,X4,X2)),singleton(sK2(X3,X4,X2))) = sK1(X3,X4,X2) )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_31618]) ).
tcf(c_31972,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X2),X4)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_31618]) ).
tcf(c_31973,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X2),X3)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_31618]) ).
tcf(c_31974,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X2,X3,X4),X4)
| ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_31618]) ).
tcf(c_31975,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X2,X4),X4)
| ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_31618]) ).
tcf(c_31976,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(unordered_pair(sK4(singleton(X4),X1,unordered_pair(singleton(X4),unordered_pair(sK4(X1,X2,X0),X4))),X3),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_31618]) ).
tcf(c_31977,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(unordered_pair(sK4(singleton(X4),X2,unordered_pair(singleton(X4),unordered_pair(sK5(X1,X2,X0),X4))),X3),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_31618]) ).
tcf(c_31978,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(sK4(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_31618]) ).
tcf(c_31979,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(sK4(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_31618]) ).
tcf(c_31980,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(sK4(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_31618]) ).
tcf(c_31981,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(sK4(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_31618]) ).
tcf(c_31982,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(sK4(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_31618]) ).
tcf(c_31983,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(sK4(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_31618]) ).
tcf(c_31985,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X2 )
| ( sK2(singleton(X3),X4,X2) = X3 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(singleton(X3),X4,X2),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_31618]) ).
tcf(c_31986,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK1(X2,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,singleton(X4)),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_31618]) ).
tcf(c_31987,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X2 )
| ( sK3(X3,singleton(X4),X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,singleton(X4),X2),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_31618]) ).
tcf(c_31988,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X2) = singleton(X4) )
| ( sK1(X3,X2,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,singleton(X4)),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_31618]) ).
tcf(c_31989,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_31618]) ).
tcf(c_31990,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_31618]) ).
tcf(c_31991,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_31618]) ).
tcf(c_31992,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X2,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_31618]) ).
tcf(c_31993,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_31618]) ).
tcf(c_31994,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_31618]) ).
tcf(c_31995,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_31618]) ).
tcf(c_31996,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X2,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_31618]) ).
tcf(c_31997,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_31618]) ).
tcf(c_31998,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_31618]) ).
tcf(c_31999,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_31618]) ).
tcf(c_32000,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_31618]) ).
tcf(c_32001,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_31618]) ).
tcf(c_32002,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_31618]) ).
tcf(c_32003,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_31618]) ).
tcf(c_32004,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_31618]) ).
tcf(c_32332,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = cartesian_product2(X0,X1) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK5(X2,X3,sK4(cartesian_product2(X2,X3),X4,sK1(X0,X1,cartesian_product2(cartesian_product2(X2,X3),X4)))),X5),singleton(X5))) = X5 )
| ( unordered_pair(unordered_pair(sK2(X0,X1,cartesian_product2(cartesian_product2(X2,X3),X4)),sK3(X0,X1,cartesian_product2(cartesian_product2(X2,X3),X4))),singleton(sK2(X0,X1,cartesian_product2(cartesian_product2(X2,X3),X4)))) = sK1(X0,X1,cartesian_product2(cartesian_product2(X2,X3),X4)) ) ),
inference(superposition,[status(thm)],[c_58,c_2729]) ).
tcf(c_32333,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)),X5)
| ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_2729]) ).
tcf(c_32334,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)),X4)
| ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_2729]) ).
tcf(c_32335,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(cartesian_product2(X2,X1),X3),X4) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK2(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_2729]) ).
tcf(c_32336,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X2,X1),X3)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK3(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_2729]) ).
tcf(c_32337,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(unordered_pair(sK5(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK4(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X0))),X5),singleton(X5))) = X5 )
| ~ in(X0,cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X3),X4)) ),
inference(superposition,[status(thm)],[c_60,c_2729]) ).
tcf(c_32338,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK5(X2,X3,sK4(cartesian_product2(X2,X3),X4,sK5(X1,cartesian_product2(cartesian_product2(X2,X3),X4),X0))),X5),singleton(X5))) = X5 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(cartesian_product2(X2,X3),X4))) ),
inference(superposition,[status(thm)],[c_61,c_2729]) ).
tcf(c_32339,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(unordered_pair(sK5(X1,X2,sK4(cartesian_product2(X1,X2),X4,unordered_pair(unordered_pair(X0,X3),singleton(X0)))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_64,c_2729]) ).
tcf(c_32341,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(unordered_pair(sK5(X1,X2,sK4(cartesian_product2(X1,X2),X4,unordered_pair(unordered_pair(X3,X0),singleton(X0)))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_809,c_2729]) ).
tcf(c_32342,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(unordered_pair(sK5(X1,X2,sK4(cartesian_product2(X1,X2),X4,unordered_pair(singleton(X0),unordered_pair(X3,X0)))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_882,c_2729]) ).
tcf(c_32344,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(unordered_pair(sK5(X1,X2,sK4(cartesian_product2(X1,X2),X4,unordered_pair(singleton(X0),unordered_pair(X0,X3)))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_900,c_2729]) ).
tcf(c_32345,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(singleton(X4),X5) )
| ( sK2(singleton(X4),X5,cartesian_product2(cartesian_product2(X2,X1),X3)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(singleton(X4),X5,cartesian_product2(cartesian_product2(X2,X1),X3)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_2729]) ).
tcf(c_32346,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X2,X1),X3),X4) = singleton(X5) )
| ( sK1(cartesian_product2(cartesian_product2(X2,X1),X3),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK2(cartesian_product2(cartesian_product2(X2,X1),X3),X4,singleton(X5)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_2729]) ).
tcf(c_32347,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,singleton(X5)) )
| ( sK3(X4,singleton(X5),cartesian_product2(cartesian_product2(X2,X1),X3)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,singleton(X5),cartesian_product2(cartesian_product2(X2,X1),X3)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_2729]) ).
tcf(c_32348,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X2,X1),X3)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(cartesian_product2(X2,X1),X3),singleton(X5)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK3(X4,cartesian_product2(cartesian_product2(X2,X1),X3),singleton(X5)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_2729]) ).
tcf(c_32349,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X2,X1),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK3(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_2729]) ).
tcf(c_32350,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X2,X1),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK3(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_2729]) ).
tcf(c_32351,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X2,X1),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK3(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_2729]) ).
tcf(c_32352,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X2,X1),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK3(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_2729]) ).
tcf(c_32353,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X2,X1),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK2(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_2729]) ).
tcf(c_32354,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X2,X1),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK2(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_2729]) ).
tcf(c_32355,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X2,X1),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK2(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_2729]) ).
tcf(c_32356,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X2,X1),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK2(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_2729]) ).
tcf(c_32357,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_2729]) ).
tcf(c_32358,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_2729]) ).
tcf(c_32359,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_2729]) ).
tcf(c_32360,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_2729]) ).
tcf(c_32361,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_2729]) ).
tcf(c_32362,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_2729]) ).
tcf(c_32363,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_2729]) ).
tcf(c_32364,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_2729]) ).
tcf(c_32537,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(X3,X4)) = cartesian_product2(X0,X1) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK5(X3,X4,sK5(X2,cartesian_product2(X3,X4),sK1(X0,X1,cartesian_product2(X2,cartesian_product2(X3,X4))))),X5),singleton(X5))) = X5 )
| ( unordered_pair(unordered_pair(sK2(X0,X1,cartesian_product2(X2,cartesian_product2(X3,X4))),sK3(X0,X1,cartesian_product2(X2,cartesian_product2(X3,X4)))),singleton(sK2(X0,X1,cartesian_product2(X2,cartesian_product2(X3,X4))))) = sK1(X0,X1,cartesian_product2(X2,cartesian_product2(X3,X4))) ) ),
inference(superposition,[status(thm)],[c_58,c_2730]) ).
tcf(c_32538,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))),X5)
| ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_2730]) ).
tcf(c_32539,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))),X4)
| ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_2730]) ).
tcf(c_32540,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_2730]) ).
tcf(c_32541,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X2,X1))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK3(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_2730]) ).
tcf(c_32542,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK5(X2,X3,sK5(X1,cartesian_product2(X2,X3),sK4(cartesian_product2(X1,cartesian_product2(X2,X3)),X4,X0))),X5),singleton(X5))) = X5 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,cartesian_product2(X2,X3)),X4)) ),
inference(superposition,[status(thm)],[c_60,c_2730]) ).
tcf(c_32543,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK5(X3,X4,sK5(X2,cartesian_product2(X3,X4),sK5(X1,cartesian_product2(X2,cartesian_product2(X3,X4)),X0))),X5),singleton(X5))) = X5 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,cartesian_product2(X3,X4)))) ),
inference(superposition,[status(thm)],[c_61,c_2730]) ).
tcf(c_32544,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(unordered_pair(sK5(X1,X2,sK5(X4,cartesian_product2(X1,X2),unordered_pair(unordered_pair(X3,X0),singleton(X3)))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_64,c_2730]) ).
tcf(c_32546,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(unordered_pair(sK5(X1,X2,sK5(X4,cartesian_product2(X1,X2),unordered_pair(unordered_pair(X0,X3),singleton(X3)))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_809,c_2730]) ).
tcf(c_32547,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(unordered_pair(sK5(X1,X2,sK5(X4,cartesian_product2(X1,X2),unordered_pair(singleton(X3),unordered_pair(X0,X3)))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_882,c_2730]) ).
tcf(c_32549,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(unordered_pair(sK5(X1,X2,sK5(X4,cartesian_product2(X1,X2),unordered_pair(singleton(X3),unordered_pair(X3,X0)))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_900,c_2730]) ).
tcf(c_32550,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(singleton(X4),X5) )
| ( sK2(singleton(X4),X5,cartesian_product2(X3,cartesian_product2(X2,X1))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(singleton(X4),X5,cartesian_product2(X3,cartesian_product2(X2,X1))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_2730]) ).
tcf(c_32551,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,singleton(X5)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_2730]) ).
tcf(c_32552,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,singleton(X5)) )
| ( sK3(X4,singleton(X5),cartesian_product2(X3,cartesian_product2(X2,X1))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,singleton(X5),cartesian_product2(X3,cartesian_product2(X2,X1))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_2730]) ).
tcf(c_32553,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X2,X1))) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),singleton(X5)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK3(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),singleton(X5)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_2730]) ).
tcf(c_32554,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X2,X1))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK3(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_2730]) ).
tcf(c_32555,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X2,X1))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK3(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_2730]) ).
tcf(c_32556,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X2,X1))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK3(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_2730]) ).
tcf(c_32557,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X2,X1))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK3(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_2730]) ).
tcf(c_32558,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_2730]) ).
tcf(c_32559,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_2730]) ).
tcf(c_32560,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_2730]) ).
tcf(c_32561,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_2730]) ).
tcf(c_32562,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_2730]) ).
tcf(c_32563,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_2730]) ).
tcf(c_32564,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_2730]) ).
tcf(c_32565,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_2730]) ).
tcf(c_32566,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_2730]) ).
tcf(c_32567,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_2730]) ).
tcf(c_32568,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_2730]) ).
tcf(c_32569,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_2730]) ).
tcf(c_32955,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),singleton(X3),unordered_pair(unordered_pair(sK5(X1,singleton(X3),unordered_pair(unordered_pair(X0,X3),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2731]) ).
tcf(c_32956,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2731]) ).
tcf(c_32957,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2731]) ).
tcf(c_32958,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2731]) ).
tcf(c_32959,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2731]) ).
tcf(c_32960,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2731]) ).
tcf(c_32961,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(unordered_pair(sK5(X4,X1,unordered_pair(unordered_pair(X3,sK4(X1,X2,X0)),singleton(X3))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2731]) ).
tcf(c_32962,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(unordered_pair(sK5(X4,X2,unordered_pair(unordered_pair(X3,sK5(X1,X2,X0)),singleton(X3))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2731]) ).
tcf(c_32963,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(unordered_pair(sK5(X5,cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))),singleton(X4))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2731]) ).
tcf(c_32964,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(unordered_pair(sK5(X5,cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))),singleton(X4))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2731]) ).
tcf(c_32965,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(unordered_pair(sK5(X5,cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))),singleton(X4))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2731]) ).
tcf(c_32966,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(unordered_pair(sK5(X5,cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))),singleton(X4))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2731]) ).
tcf(c_32967,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(unordered_pair(sK5(X5,cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))),singleton(X4))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2731]) ).
tcf(c_32968,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(unordered_pair(sK5(X5,cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))),singleton(X4))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2731]) ).
tcf(c_32970,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(singleton(X4),X5,X3)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2731]) ).
tcf(c_32971,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,singleton(X5))),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2731]) ).
tcf(c_32972,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,singleton(X5),X3)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2731]) ).
tcf(c_32973,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,singleton(X5))),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2731]) ).
tcf(c_32974,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2731]) ).
tcf(c_32975,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2731]) ).
tcf(c_32976,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2731]) ).
tcf(c_32977,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2731]) ).
tcf(c_32978,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2731]) ).
tcf(c_32979,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2731]) ).
tcf(c_32980,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2731]) ).
tcf(c_32981,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2731]) ).
tcf(c_32982,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2731]) ).
tcf(c_32983,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2731]) ).
tcf(c_32984,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2731]) ).
tcf(c_32985,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2731]) ).
tcf(c_32986,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2731]) ).
tcf(c_32987,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2731]) ).
tcf(c_32988,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2731]) ).
tcf(c_32989,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2731]) ).
tcf(c_33078,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X2),sK3(X3,X4,X2)),singleton(sK2(X3,X4,X2))) = sK1(X3,X4,X2) )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_32955]) ).
tcf(c_33079,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X2),X4)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_32955]) ).
tcf(c_33080,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X2),X3)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_32955]) ).
tcf(c_33081,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X2,X3,X4),X4)
| ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(sK2(X2,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_32955]) ).
tcf(c_33082,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X2,X4),X4)
| ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(sK3(X3,X2,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_32955]) ).
tcf(c_33083,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(unordered_pair(sK5(X1,singleton(X4),unordered_pair(unordered_pair(sK4(X1,X2,X0),X4),singleton(sK4(X1,X2,X0)))),X3),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_32955]) ).
tcf(c_33084,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(unordered_pair(sK5(X2,singleton(X4),unordered_pair(unordered_pair(sK5(X1,X2,X0),X4),singleton(sK5(X1,X2,X0)))),X3),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_32955]) ).
tcf(c_33085,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(sK5(cartesian_product2(X3,X1),singleton(X5),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_32955]) ).
tcf(c_33086,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(sK5(cartesian_product2(X1,X3),singleton(X5),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5),singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_32955]) ).
tcf(c_33087,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(sK5(cartesian_product2(X1,X3),singleton(X5),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_32955]) ).
tcf(c_33088,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(sK5(cartesian_product2(X1,X3),singleton(X5),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5),singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_32955]) ).
tcf(c_33089,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(sK5(cartesian_product2(X3,X1),singleton(X5),unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5),singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_32955]) ).
tcf(c_33090,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(sK5(cartesian_product2(X3,X1),singleton(X5),unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5),singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_32955]) ).
tcf(c_33092,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X2 )
| ( sK2(singleton(X3),X4,X2) = X3 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(singleton(X3),X4,X2),X1),singleton(sK1(singleton(X3),X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_32955]) ).
tcf(c_33093,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK1(X2,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK2(X2,X3,singleton(X4)),X1),singleton(sK2(X2,X3,singleton(X4))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_32955]) ).
tcf(c_33094,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X2 )
| ( sK3(X3,singleton(X4),X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,singleton(X4),X2),X1),singleton(sK1(X3,singleton(X4),X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_32955]) ).
tcf(c_33095,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X2) = singleton(X4) )
| ( sK1(X3,X2,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK3(X3,X2,singleton(X4)),X1),singleton(sK3(X3,X2,singleton(X4))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_32955]) ).
tcf(c_33096,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(sK3(X3,X2,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_32955]) ).
tcf(c_33097,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(sK3(X3,X2,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_32955]) ).
tcf(c_33098,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(sK3(X3,X2,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_32955]) ).
tcf(c_33099,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X2,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(sK3(X3,X2,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_32955]) ).
tcf(c_33100,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(sK2(X2,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_32955]) ).
tcf(c_33101,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(sK2(X2,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_32955]) ).
tcf(c_33102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(sK2(X2,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_32955]) ).
tcf(c_33103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X2,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(sK2(X2,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_32955]) ).
tcf(c_33104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_32955]) ).
tcf(c_33105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_32955]) ).
tcf(c_33106,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_32955]) ).
tcf(c_33107,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_32955]) ).
tcf(c_33108,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_32955]) ).
tcf(c_33109,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_32955]) ).
tcf(c_33110,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_32955]) ).
tcf(c_33111,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_32955]) ).
tcf(c_33513,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X3),unordered_pair(singleton(X0),unordered_pair(X3,X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2678]) ).
tcf(c_33514,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2678]) ).
tcf(c_33515,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2678]) ).
tcf(c_33516,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2678]) ).
tcf(c_33517,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2678]) ).
tcf(c_33518,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2678]) ).
tcf(c_33519,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK4(X4,X1,unordered_pair(singleton(X3),unordered_pair(sK4(X1,X2,X0),X3))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2678]) ).
tcf(c_33520,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK4(X4,X2,unordered_pair(singleton(X3),unordered_pair(sK5(X1,X2,X0),X3))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2678]) ).
tcf(c_33521,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK4(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X4))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2678]) ).
tcf(c_33522,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK4(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X4))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2678]) ).
tcf(c_33523,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK4(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X4))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2678]) ).
tcf(c_33524,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK4(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X4))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2678]) ).
tcf(c_33525,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK4(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X4))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2678]) ).
tcf(c_33526,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK4(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X4))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2678]) ).
tcf(c_33528,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(singleton(X4),X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2678]) ).
tcf(c_33529,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,singleton(X5)),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2678]) ).
tcf(c_33530,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,singleton(X5),X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2678]) ).
tcf(c_33531,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,singleton(X5)),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2678]) ).
tcf(c_33532,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2678]) ).
tcf(c_33533,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2678]) ).
tcf(c_33534,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2678]) ).
tcf(c_33535,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2678]) ).
tcf(c_33536,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2678]) ).
tcf(c_33537,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2678]) ).
tcf(c_33538,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2678]) ).
tcf(c_33539,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2678]) ).
tcf(c_33540,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2678]) ).
tcf(c_33541,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2678]) ).
tcf(c_33542,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2678]) ).
tcf(c_33543,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2678]) ).
tcf(c_33544,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2678]) ).
tcf(c_33545,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2678]) ).
tcf(c_33546,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2678]) ).
tcf(c_33547,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2678]) ).
tcf(c_33601,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X1),sK3(X3,X4,X1)),singleton(sK2(X3,X4,X1))) = sK1(X3,X4,X1) )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_33513]) ).
tcf(c_33602,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X1),X4)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_33513]) ).
tcf(c_33603,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X1),X3)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_33513]) ).
tcf(c_33604,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X1,X3,X4),X4)
| ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_33513]) ).
tcf(c_33605,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X1,X4),X4)
| ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_33513]) ).
tcf(c_33606,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X4),unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(X4,sK4(X1,X2,X0)))),X3),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_33513]) ).
tcf(c_33607,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X2,unordered_pair(unordered_pair(sK4(X2,singleton(X4),unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(X4,sK5(X1,X2,X0)))),X3),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_33513]) ).
tcf(c_33608,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(sK4(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X2))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_33513]) ).
tcf(c_33609,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(sK4(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X0,X2))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_33513]) ).
tcf(c_33610,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(sK4(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X0))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_33513]) ).
tcf(c_33611,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(sK4(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X2,X0))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_33513]) ).
tcf(c_33612,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(sK4(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X0,X2))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_33513]) ).
tcf(c_33613,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(sK4(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X2,X0))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_33513]) ).
tcf(c_33615,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X1 )
| ( sK2(singleton(X3),X4,X1) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(singleton(X3),X4,X1)),unordered_pair(X2,sK1(singleton(X3),X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_33513]) ).
tcf(c_33616,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X3) = singleton(X4) )
| ( sK1(X1,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,singleton(X4))),unordered_pair(X2,sK2(X1,X3,singleton(X4))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_33513]) ).
tcf(c_33617,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X1 )
| ( sK3(X3,singleton(X4),X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,singleton(X4),X1)),unordered_pair(X2,sK1(X3,singleton(X4),X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_33513]) ).
tcf(c_33618,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X1) = singleton(X4) )
| ( sK1(X3,X1,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,singleton(X4))),unordered_pair(X2,sK3(X3,X1,singleton(X4))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_33513]) ).
tcf(c_33619,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_33513]) ).
tcf(c_33620,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_33513]) ).
tcf(c_33621,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_33513]) ).
tcf(c_33622,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X1,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_33513]) ).
tcf(c_33623,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_33513]) ).
tcf(c_33624,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_33513]) ).
tcf(c_33625,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_33513]) ).
tcf(c_33626,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X1,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_33513]) ).
tcf(c_33627,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_33513]) ).
tcf(c_33628,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_33513]) ).
tcf(c_33629,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_33513]) ).
tcf(c_33630,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_33513]) ).
tcf(c_33631,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_33513]) ).
tcf(c_33632,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_33513]) ).
tcf(c_33633,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_33513]) ).
tcf(c_33634,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_33513]) ).
tcf(c_33912,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X3),unordered_pair(singleton(X0),unordered_pair(X0,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2679]) ).
tcf(c_33913,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2679]) ).
tcf(c_33914,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2679]) ).
tcf(c_33915,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2679]) ).
tcf(c_33916,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2679]) ).
tcf(c_33917,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2679]) ).
tcf(c_33918,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK4(X4,X1,unordered_pair(singleton(X3),unordered_pair(X3,sK4(X1,X2,X0)))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2679]) ).
tcf(c_33919,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK4(X4,X2,unordered_pair(singleton(X3),unordered_pair(X3,sK5(X1,X2,X0)))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2679]) ).
tcf(c_33920,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK4(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2679]) ).
tcf(c_33921,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK4(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2679]) ).
tcf(c_33922,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK4(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2679]) ).
tcf(c_33923,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK4(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2679]) ).
tcf(c_33924,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK4(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2679]) ).
tcf(c_33925,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK4(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2679]) ).
tcf(c_33927,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(singleton(X4),X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2679]) ).
tcf(c_33928,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,singleton(X5))))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2679]) ).
tcf(c_33929,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,singleton(X5),X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2679]) ).
tcf(c_33930,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,singleton(X5))))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2679]) ).
tcf(c_33931,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2679]) ).
tcf(c_33932,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2679]) ).
tcf(c_33933,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2679]) ).
tcf(c_33934,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2679]) ).
tcf(c_33935,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2679]) ).
tcf(c_33936,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2679]) ).
tcf(c_33937,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2679]) ).
tcf(c_33938,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2679]) ).
tcf(c_33939,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2679]) ).
tcf(c_33940,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2679]) ).
tcf(c_33941,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2679]) ).
tcf(c_33942,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2679]) ).
tcf(c_33943,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2679]) ).
tcf(c_33944,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2679]) ).
tcf(c_33945,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2679]) ).
tcf(c_33946,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2679]) ).
tcf(c_34054,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X1),sK3(X3,X4,X1)),singleton(sK2(X3,X4,X1))) = sK1(X3,X4,X1) )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_33912]) ).
tcf(c_34055,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X1),X4)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_33912]) ).
tcf(c_34056,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X1),X3)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_33912]) ).
tcf(c_34057,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X1,X3,X4),X4)
| ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_33912]) ).
tcf(c_34058,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X1,X4),X4)
| ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_33912]) ).
tcf(c_34059,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X4),unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(sK4(X1,X2,X0),X4))),X3),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_33912]) ).
tcf(c_34060,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X2,unordered_pair(unordered_pair(sK4(X2,singleton(X4),unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(sK5(X1,X2,X0),X4))),X3),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_33912]) ).
tcf(c_34061,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(sK4(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_33912]) ).
tcf(c_34062,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(sK4(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_33912]) ).
tcf(c_34063,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(sK4(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_33912]) ).
tcf(c_34064,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(sK4(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_33912]) ).
tcf(c_34065,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(sK4(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_33912]) ).
tcf(c_34066,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(sK4(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_33912]) ).
tcf(c_34068,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X1 )
| ( sK2(singleton(X3),X4,X1) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(singleton(X3),X4,X1)),unordered_pair(sK1(singleton(X3),X4,X1),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_33912]) ).
tcf(c_34069,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X3) = singleton(X4) )
| ( sK1(X1,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,singleton(X4))),unordered_pair(sK2(X1,X3,singleton(X4)),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_33912]) ).
tcf(c_34070,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X1 )
| ( sK3(X3,singleton(X4),X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,singleton(X4),X1)),unordered_pair(sK1(X3,singleton(X4),X1),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_33912]) ).
tcf(c_34071,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X1) = singleton(X4) )
| ( sK1(X3,X1,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,singleton(X4))),unordered_pair(sK3(X3,X1,singleton(X4)),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_33912]) ).
tcf(c_34072,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_33912]) ).
tcf(c_34073,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_33912]) ).
tcf(c_34074,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_33912]) ).
tcf(c_34075,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X1,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_33912]) ).
tcf(c_34076,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_33912]) ).
tcf(c_34077,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_33912]) ).
tcf(c_34078,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_33912]) ).
tcf(c_34079,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X1,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_33912]) ).
tcf(c_34080,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_33912]) ).
tcf(c_34081,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_33912]) ).
tcf(c_34082,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_33912]) ).
tcf(c_34083,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_33912]) ).
tcf(c_34084,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_33912]) ).
tcf(c_34085,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_33912]) ).
tcf(c_34086,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_33912]) ).
tcf(c_34087,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_33912]) ).
tcf(c_34285,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(singleton(X3),X1,unordered_pair(singleton(X3),unordered_pair(X3,X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2732]) ).
tcf(c_34286,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2732]) ).
tcf(c_34287,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2732]) ).
tcf(c_34288,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2732]) ).
tcf(c_34289,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2732]) ).
tcf(c_34290,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2732]) ).
tcf(c_34291,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK5(X1,X4,unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(sK4(X1,X2,X0),X3))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2732]) ).
tcf(c_34292,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK5(X2,X4,unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(sK5(X1,X2,X0),X3))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2732]) ).
tcf(c_34293,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK5(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X4))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2732]) ).
tcf(c_34294,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK5(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X4))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2732]) ).
tcf(c_34295,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK5(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X4))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2732]) ).
tcf(c_34296,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK5(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X4))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2732]) ).
tcf(c_34297,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK5(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X4))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2732]) ).
tcf(c_34298,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK5(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X4))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2732]) ).
tcf(c_34300,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(singleton(X4),X5,X3)),unordered_pair(sK1(singleton(X4),X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2732]) ).
tcf(c_34301,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,singleton(X5))),unordered_pair(sK2(X3,X4,singleton(X5)),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2732]) ).
tcf(c_34302,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,singleton(X5),X3)),unordered_pair(sK1(X4,singleton(X5),X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2732]) ).
tcf(c_34303,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,singleton(X5))),unordered_pair(sK3(X4,X3,singleton(X5)),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2732]) ).
tcf(c_34304,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2732]) ).
tcf(c_34305,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2732]) ).
tcf(c_34306,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2732]) ).
tcf(c_34307,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2732]) ).
tcf(c_34308,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2732]) ).
tcf(c_34309,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2732]) ).
tcf(c_34310,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2732]) ).
tcf(c_34311,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2732]) ).
tcf(c_34312,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2732]) ).
tcf(c_34313,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2732]) ).
tcf(c_34314,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2732]) ).
tcf(c_34315,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2732]) ).
tcf(c_34316,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2732]) ).
tcf(c_34317,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2732]) ).
tcf(c_34318,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2732]) ).
tcf(c_34319,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2732]) ).
tcf(c_34399,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X1),sK3(X3,X4,X1)),singleton(sK2(X3,X4,X1))) = sK1(X3,X4,X1) )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_34285]) ).
tcf(c_34400,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X1),X4)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_34285]) ).
tcf(c_34401,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X1),X3)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_34285]) ).
tcf(c_34402,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X1,X3,X4),X4)
| ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK2(X1,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_34285]) ).
tcf(c_34403,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X1,X4),X4)
| ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK3(X3,X1,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_34285]) ).
tcf(c_34404,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X1,unordered_pair(unordered_pair(sK5(singleton(X4),X1,unordered_pair(singleton(X4),unordered_pair(X4,sK4(X1,X2,X0)))),X3),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_34285]) ).
tcf(c_34405,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X2,unordered_pair(unordered_pair(sK5(singleton(X4),X2,unordered_pair(singleton(X4),unordered_pair(X4,sK5(X1,X2,X0)))),X3),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_34285]) ).
tcf(c_34406,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(sK5(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X2))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_34285]) ).
tcf(c_34407,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(sK5(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X0,X2))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_34285]) ).
tcf(c_34408,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(sK5(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X0))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_34285]) ).
tcf(c_34409,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(sK5(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X2,X0))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_34285]) ).
tcf(c_34410,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(sK5(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X0,X2))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_34285]) ).
tcf(c_34411,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(sK5(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X2,X0))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_34285]) ).
tcf(c_34413,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X1 )
| ( sK2(singleton(X3),X4,X1) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(singleton(X3),X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_34285]) ).
tcf(c_34414,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X3) = singleton(X4) )
| ( sK1(X1,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK2(X1,X3,singleton(X4))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_34285]) ).
tcf(c_34415,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X1 )
| ( sK3(X3,singleton(X4),X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,singleton(X4),X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_34285]) ).
tcf(c_34416,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X1) = singleton(X4) )
| ( sK1(X3,X1,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK3(X3,X1,singleton(X4))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_34285]) ).
tcf(c_34417,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK3(X3,X1,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_34285]) ).
tcf(c_34418,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK3(X3,X1,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_34285]) ).
tcf(c_34419,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK3(X3,X1,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_34285]) ).
tcf(c_34420,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X1,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK3(X3,X1,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_34285]) ).
tcf(c_34421,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK2(X1,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_34285]) ).
tcf(c_34422,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK2(X1,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_34285]) ).
tcf(c_34423,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK2(X1,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_34285]) ).
tcf(c_34424,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X1,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK2(X1,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_34285]) ).
tcf(c_34425,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_34285]) ).
tcf(c_34426,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_34285]) ).
tcf(c_34427,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_34285]) ).
tcf(c_34428,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_34285]) ).
tcf(c_34429,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_34285]) ).
tcf(c_34430,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_34285]) ).
tcf(c_34431,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_34285]) ).
tcf(c_34432,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_34285]) ).
tcf(c_34537,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(singleton(X3),X1,unordered_pair(unordered_pair(X0,X3),singleton(X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2733]) ).
tcf(c_34538,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2733]) ).
tcf(c_34539,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2733]) ).
tcf(c_34540,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2733]) ).
tcf(c_34541,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2733]) ).
tcf(c_34542,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2733]) ).
tcf(c_34543,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK5(X1,X4,unordered_pair(unordered_pair(X3,sK4(X1,X2,X0)),singleton(sK4(X1,X2,X0)))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2733]) ).
tcf(c_34544,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK5(X2,X4,unordered_pair(unordered_pair(X3,sK5(X1,X2,X0)),singleton(sK5(X1,X2,X0)))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2733]) ).
tcf(c_34545,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK5(cartesian_product2(X3,X1),X5,unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2733]) ).
tcf(c_34546,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK5(cartesian_product2(X1,X3),X5,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))),singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2733]) ).
tcf(c_34547,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK5(cartesian_product2(X1,X3),X5,unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2733]) ).
tcf(c_34548,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK5(cartesian_product2(X1,X3),X5,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))),singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2733]) ).
tcf(c_34549,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK5(cartesian_product2(X3,X1),X5,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))),singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2733]) ).
tcf(c_34550,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK5(cartesian_product2(X3,X1),X5,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))),singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2733]) ).
tcf(c_34552,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(singleton(X4),X5,X3)),singleton(sK1(singleton(X4),X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2733]) ).
tcf(c_34553,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,singleton(X5))),singleton(sK2(X3,X4,singleton(X5))))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2733]) ).
tcf(c_34554,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,singleton(X5),X3)),singleton(sK1(X4,singleton(X5),X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2733]) ).
tcf(c_34555,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,singleton(X5))),singleton(sK3(X4,X3,singleton(X5))))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2733]) ).
tcf(c_34556,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2733]) ).
tcf(c_34557,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2733]) ).
tcf(c_34558,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2733]) ).
tcf(c_34559,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2733]) ).
tcf(c_34560,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2733]) ).
tcf(c_34561,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2733]) ).
tcf(c_34562,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2733]) ).
tcf(c_34563,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2733]) ).
tcf(c_34564,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2733]) ).
tcf(c_34565,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2733]) ).
tcf(c_34566,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2733]) ).
tcf(c_34567,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2733]) ).
tcf(c_34568,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2733]) ).
tcf(c_34569,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2733]) ).
tcf(c_34570,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2733]) ).
tcf(c_34571,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2733]) ).
tcf(c_34650,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X1),sK3(X3,X4,X1)),singleton(sK2(X3,X4,X1))) = sK1(X3,X4,X1) )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_34537]) ).
tcf(c_34651,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X1),X4)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_34537]) ).
tcf(c_34652,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X1),X3)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_34537]) ).
tcf(c_34653,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X1,X3,X4),X4)
| ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_34537]) ).
tcf(c_34654,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X1,X4),X4)
| ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_34537]) ).
tcf(c_34655,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X1,unordered_pair(unordered_pair(sK5(singleton(X4),X1,unordered_pair(unordered_pair(sK4(X1,X2,X0),X4),singleton(X4))),X3),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_34537]) ).
tcf(c_34656,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X2,unordered_pair(unordered_pair(sK5(singleton(X4),X2,unordered_pair(unordered_pair(sK5(X1,X2,X0),X4),singleton(X4))),X3),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_34537]) ).
tcf(c_34657,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(sK5(singleton(X5),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5),singleton(X5))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_34537]) ).
tcf(c_34658,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(sK5(singleton(X5),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5),singleton(X5))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_34537]) ).
tcf(c_34659,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(sK5(singleton(X5),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5),singleton(X5))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_34537]) ).
tcf(c_34660,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(sK5(singleton(X5),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5),singleton(X5))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_34537]) ).
tcf(c_34661,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(sK5(singleton(X5),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5),singleton(X5))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_34537]) ).
tcf(c_34662,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(sK5(singleton(X5),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5),singleton(X5))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_34537]) ).
tcf(c_34664,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X1 )
| ( sK2(singleton(X3),X4,X1) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(singleton(X3),X4,X1),X2),singleton(X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_34537]) ).
tcf(c_34665,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X3) = singleton(X4) )
| ( sK1(X1,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK2(X1,X3,singleton(X4)),X2),singleton(X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_34537]) ).
tcf(c_34666,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X1 )
| ( sK3(X3,singleton(X4),X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,singleton(X4),X1),X2),singleton(X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_34537]) ).
tcf(c_34667,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X1) = singleton(X4) )
| ( sK1(X3,X1,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK3(X3,X1,singleton(X4)),X2),singleton(X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_34537]) ).
tcf(c_34668,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_34537]) ).
tcf(c_34669,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_34537]) ).
tcf(c_34670,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_34537]) ).
tcf(c_34671,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X1,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_34537]) ).
tcf(c_34672,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_34537]) ).
tcf(c_34673,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_34537]) ).
tcf(c_34674,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_34537]) ).
tcf(c_34675,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X1,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_34537]) ).
tcf(c_34676,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_34537]) ).
tcf(c_34677,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_34537]) ).
tcf(c_34678,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_34537]) ).
tcf(c_34679,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_34537]) ).
tcf(c_34680,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_34537]) ).
tcf(c_34681,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_34537]) ).
tcf(c_34682,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_34537]) ).
tcf(c_34683,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_34537]) ).
tcf(c_34740,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(singleton(X3),X1,unordered_pair(singleton(X3),unordered_pair(X0,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2734]) ).
tcf(c_34741,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2734]) ).
tcf(c_34742,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2734]) ).
tcf(c_34743,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2734]) ).
tcf(c_34744,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2734]) ).
tcf(c_34745,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2734]) ).
tcf(c_34746,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK5(X1,X4,unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(X3,sK4(X1,X2,X0)))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2734]) ).
tcf(c_34747,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK5(X2,X4,unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(X3,sK5(X1,X2,X0)))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2734]) ).
tcf(c_34748,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK5(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2734]) ).
tcf(c_34749,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK5(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2734]) ).
tcf(c_34750,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK5(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2734]) ).
tcf(c_34751,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK5(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2734]) ).
tcf(c_34752,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK5(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2734]) ).
tcf(c_34753,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK5(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2734]) ).
tcf(c_34755,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(singleton(X4),X5,X3)),unordered_pair(X0,sK1(singleton(X4),X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2734]) ).
tcf(c_34756,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,singleton(X5))),unordered_pair(X0,sK2(X3,X4,singleton(X5))))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2734]) ).
tcf(c_34757,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,singleton(X5),X3)),unordered_pair(X0,sK1(X4,singleton(X5),X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2734]) ).
tcf(c_34758,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,singleton(X5))),unordered_pair(X0,sK3(X4,X3,singleton(X5))))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2734]) ).
tcf(c_34759,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2734]) ).
tcf(c_34760,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2734]) ).
tcf(c_34761,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2734]) ).
tcf(c_34762,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2734]) ).
tcf(c_34763,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2734]) ).
tcf(c_34764,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2734]) ).
tcf(c_34765,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2734]) ).
tcf(c_34766,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2734]) ).
tcf(c_34767,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2734]) ).
tcf(c_34768,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2734]) ).
tcf(c_34769,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2734]) ).
tcf(c_34770,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2734]) ).
tcf(c_34771,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2734]) ).
tcf(c_34772,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2734]) ).
tcf(c_34773,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2734]) ).
tcf(c_34774,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2734]) ).
tcf(c_34944,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X1),sK3(X3,X4,X1)),singleton(sK2(X3,X4,X1))) = sK1(X3,X4,X1) )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_34740]) ).
tcf(c_34945,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X1),X4)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_34740]) ).
tcf(c_34946,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X1),X3)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_34740]) ).
tcf(c_34947,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X1,X3,X4),X4)
| ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK2(X1,X3,X4),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_34740]) ).
tcf(c_34948,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X1,X4),X4)
| ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK3(X3,X1,X4),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_34740]) ).
tcf(c_34949,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X1,unordered_pair(unordered_pair(sK5(singleton(X4),X1,unordered_pair(singleton(X4),unordered_pair(sK4(X1,X2,X0),X4))),X3),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_34740]) ).
tcf(c_34950,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X2,unordered_pair(unordered_pair(sK5(singleton(X4),X2,unordered_pair(singleton(X4),unordered_pair(sK5(X1,X2,X0),X4))),X3),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_34740]) ).
tcf(c_34951,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(sK5(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_34740]) ).
tcf(c_34952,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(sK5(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_34740]) ).
tcf(c_34953,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(sK5(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_34740]) ).
tcf(c_34954,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(unordered_pair(sK5(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_34740]) ).
tcf(c_34955,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(sK5(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_34740]) ).
tcf(c_34956,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(unordered_pair(sK5(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_34740]) ).
tcf(c_34958,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X1 )
| ( sK2(singleton(X3),X4,X1) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(singleton(X3),X4,X1),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_34740]) ).
tcf(c_34959,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X3) = singleton(X4) )
| ( sK1(X1,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK2(X1,X3,singleton(X4)),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_34740]) ).
tcf(c_34960,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X1 )
| ( sK3(X3,singleton(X4),X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,singleton(X4),X1),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_34740]) ).
tcf(c_34961,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X1) = singleton(X4) )
| ( sK1(X3,X1,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK3(X3,X1,singleton(X4)),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_34740]) ).
tcf(c_34962,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK3(X3,X1,X4),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_34740]) ).
tcf(c_34963,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK3(X3,X1,X4),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_34740]) ).
tcf(c_34964,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK3(X3,X1,X4),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_34740]) ).
tcf(c_34965,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X1,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK3(X3,X1,X4),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_34740]) ).
tcf(c_34966,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK2(X1,X3,X4),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_34740]) ).
tcf(c_34967,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK2(X1,X3,X4),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_34740]) ).
tcf(c_34968,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK2(X1,X3,X4),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_34740]) ).
tcf(c_34969,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X1,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK2(X1,X3,X4),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_34740]) ).
tcf(c_34970,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_34740]) ).
tcf(c_34971,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_34740]) ).
tcf(c_34972,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_34740]) ).
tcf(c_34973,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_34740]) ).
tcf(c_34974,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_34740]) ).
tcf(c_34975,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_34740]) ).
tcf(c_34976,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_34740]) ).
tcf(c_34977,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_34740]) ).
tcf(c_35157,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),singleton(X3),unordered_pair(unordered_pair(sK5(X1,singleton(X3),unordered_pair(singleton(X0),unordered_pair(X3,X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2735]) ).
tcf(c_35158,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2735]) ).
tcf(c_35159,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2735]) ).
tcf(c_35160,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2735]) ).
tcf(c_35161,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2735]) ).
tcf(c_35162,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2735]) ).
tcf(c_35163,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(unordered_pair(sK5(X4,X1,unordered_pair(singleton(X3),unordered_pair(sK4(X1,X2,X0),X3))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2735]) ).
tcf(c_35164,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(unordered_pair(sK5(X4,X2,unordered_pair(singleton(X3),unordered_pair(sK5(X1,X2,X0),X3))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2735]) ).
tcf(c_35165,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(unordered_pair(sK5(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X4))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2735]) ).
tcf(c_35166,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(unordered_pair(sK5(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X4))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2735]) ).
tcf(c_35167,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(unordered_pair(sK5(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X4))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2735]) ).
tcf(c_35168,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(unordered_pair(sK5(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X4))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2735]) ).
tcf(c_35169,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(unordered_pair(sK5(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X4))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2735]) ).
tcf(c_35170,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(unordered_pair(sK5(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X4))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2735]) ).
tcf(c_35172,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(singleton(X4),X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2735]) ).
tcf(c_35173,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,singleton(X5)),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2735]) ).
tcf(c_35174,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,singleton(X5),X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2735]) ).
tcf(c_35175,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,singleton(X5)),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2735]) ).
tcf(c_35176,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2735]) ).
tcf(c_35177,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2735]) ).
tcf(c_35178,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2735]) ).
tcf(c_35179,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2735]) ).
tcf(c_35180,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2735]) ).
tcf(c_35181,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2735]) ).
tcf(c_35182,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2735]) ).
tcf(c_35183,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2735]) ).
tcf(c_35184,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2735]) ).
tcf(c_35185,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2735]) ).
tcf(c_35186,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2735]) ).
tcf(c_35187,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2735]) ).
tcf(c_35188,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2735]) ).
tcf(c_35189,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2735]) ).
tcf(c_35190,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2735]) ).
tcf(c_35191,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2735]) ).
tcf(c_35400,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X2),sK3(X3,X4,X2)),singleton(sK2(X3,X4,X2))) = sK1(X3,X4,X2) )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_35157]) ).
tcf(c_35401,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X2),X4)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_35157]) ).
tcf(c_35402,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X2),X3)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_35157]) ).
tcf(c_35403,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X2,X3,X4),X4)
| ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(X1,sK2(X2,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_35157]) ).
tcf(c_35404,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X2,X4),X4)
| ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(X1,sK3(X3,X2,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_35157]) ).
tcf(c_35405,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(unordered_pair(sK5(X1,singleton(X4),unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(X4,sK4(X1,X2,X0)))),X3),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_35157]) ).
tcf(c_35406,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(unordered_pair(sK5(X2,singleton(X4),unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(X4,sK5(X1,X2,X0)))),X3),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_35157]) ).
tcf(c_35407,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(sK5(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X2))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_35157]) ).
tcf(c_35408,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(sK5(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X0,X2))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_35157]) ).
tcf(c_35409,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(sK5(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X0))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_35157]) ).
tcf(c_35410,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(sK5(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X2,X0))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_35157]) ).
tcf(c_35411,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(sK5(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X0,X2))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_35157]) ).
tcf(c_35412,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(sK5(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X2,X0))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_35157]) ).
tcf(c_35414,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X2 )
| ( sK2(singleton(X3),X4,X2) = X3 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(singleton(X3),X4,X2)),unordered_pair(X1,sK1(singleton(X3),X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_35157]) ).
tcf(c_35415,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK1(X2,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,singleton(X4))),unordered_pair(X1,sK2(X2,X3,singleton(X4))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_35157]) ).
tcf(c_35416,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X2 )
| ( sK3(X3,singleton(X4),X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,singleton(X4),X2)),unordered_pair(X1,sK1(X3,singleton(X4),X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_35157]) ).
tcf(c_35417,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X2) = singleton(X4) )
| ( sK1(X3,X2,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,singleton(X4))),unordered_pair(X1,sK3(X3,X2,singleton(X4))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_35157]) ).
tcf(c_35418,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(X1,sK3(X3,X2,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_35157]) ).
tcf(c_35419,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(X1,sK3(X3,X2,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_35157]) ).
tcf(c_35420,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(X1,sK3(X3,X2,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_35157]) ).
tcf(c_35421,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X2,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(X1,sK3(X3,X2,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_35157]) ).
tcf(c_35422,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(X1,sK2(X2,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_35157]) ).
tcf(c_35423,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(X1,sK2(X2,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_35157]) ).
tcf(c_35424,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(X1,sK2(X2,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_35157]) ).
tcf(c_35425,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X2,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(X1,sK2(X2,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_35157]) ).
tcf(c_35426,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_35157]) ).
tcf(c_35427,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_35157]) ).
tcf(c_35428,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_35157]) ).
tcf(c_35429,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_35157]) ).
tcf(c_35430,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_35157]) ).
tcf(c_35431,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_35157]) ).
tcf(c_35432,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_35157]) ).
tcf(c_35433,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_35157]) ).
tcf(c_35616,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = cartesian_product2(X0,X1) )
| ( sK4(singleton(X5),X2,unordered_pair(singleton(X5),unordered_pair(sK4(X2,X3,sK4(cartesian_product2(X2,X3),X4,sK1(X0,X1,cartesian_product2(cartesian_product2(X2,X3),X4)))),X5))) = X5 )
| ( unordered_pair(unordered_pair(sK2(X0,X1,cartesian_product2(cartesian_product2(X2,X3),X4)),sK3(X0,X1,cartesian_product2(cartesian_product2(X2,X3),X4))),singleton(sK2(X0,X1,cartesian_product2(cartesian_product2(X2,X3),X4)))) = sK1(X0,X1,cartesian_product2(cartesian_product2(X2,X3),X4)) ) ),
inference(superposition,[status(thm)],[c_58,c_2820]) ).
tcf(c_35617,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)),X5)
| ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_2820]) ).
tcf(c_35618,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)),X4)
| ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_2820]) ).
tcf(c_35619,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X3),X4) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK2(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_2820]) ).
tcf(c_35620,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X1,X2),X3)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK3(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_2820]) ).
tcf(c_35621,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(singleton(X5),unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK4(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X0))),X5))) = X5 )
| ~ in(X0,cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X3),X4)) ),
inference(superposition,[status(thm)],[c_60,c_2820]) ).
tcf(c_35622,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(singleton(X5),unordered_pair(sK4(X2,X3,sK4(cartesian_product2(X2,X3),X4,sK5(X1,cartesian_product2(cartesian_product2(X2,X3),X4),X0))),X5))) = X5 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(cartesian_product2(X2,X3),X4))) ),
inference(superposition,[status(thm)],[c_61,c_2820]) ).
tcf(c_35623,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(singleton(X5),unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X4,unordered_pair(unordered_pair(X0,X3),singleton(X0)))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_64,c_2820]) ).
tcf(c_35625,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(singleton(X5),unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X4,unordered_pair(unordered_pair(X3,X0),singleton(X0)))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_809,c_2820]) ).
tcf(c_35626,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(singleton(X5),unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X4,unordered_pair(singleton(X0),unordered_pair(X3,X0)))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_882,c_2820]) ).
tcf(c_35628,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(singleton(X5),unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X4,unordered_pair(singleton(X0),unordered_pair(X0,X3)))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_900,c_2820]) ).
tcf(c_35629,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(singleton(X4),X5) )
| ( sK2(singleton(X4),X5,cartesian_product2(cartesian_product2(X1,X2),X3)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(singleton(X4),X5,cartesian_product2(cartesian_product2(X1,X2),X3)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_2820]) ).
tcf(c_35630,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X3),X4) = singleton(X5) )
| ( sK1(cartesian_product2(cartesian_product2(X1,X2),X3),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK2(cartesian_product2(cartesian_product2(X1,X2),X3),X4,singleton(X5)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_2820]) ).
tcf(c_35631,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,singleton(X5)) )
| ( sK3(X4,singleton(X5),cartesian_product2(cartesian_product2(X1,X2),X3)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,singleton(X5),cartesian_product2(cartesian_product2(X1,X2),X3)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_2820]) ).
tcf(c_35632,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X1,X2),X3)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(cartesian_product2(X1,X2),X3),singleton(X5)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK3(X4,cartesian_product2(cartesian_product2(X1,X2),X3),singleton(X5)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_2820]) ).
tcf(c_35633,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X1,X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK3(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_2820]) ).
tcf(c_35634,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X1,X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK3(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_2820]) ).
tcf(c_35635,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X1,X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK3(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_2820]) ).
tcf(c_35636,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X1,X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK3(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_2820]) ).
tcf(c_35637,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK2(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_2820]) ).
tcf(c_35638,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK2(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_2820]) ).
tcf(c_35639,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK2(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_2820]) ).
tcf(c_35640,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK2(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_2820]) ).
tcf(c_35641,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_2820]) ).
tcf(c_35642,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_2820]) ).
tcf(c_35643,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_2820]) ).
tcf(c_35644,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_2820]) ).
tcf(c_35645,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_2820]) ).
tcf(c_35646,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_2820]) ).
tcf(c_35647,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_2820]) ).
tcf(c_35648,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_2820]) ).
tcf(c_35813,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(X3,X4)) = cartesian_product2(X0,X1) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK4(X3,X4,sK5(X2,cartesian_product2(X3,X4),sK1(X0,X1,cartesian_product2(X2,cartesian_product2(X3,X4))))),X5))) = X5 )
| ( unordered_pair(unordered_pair(sK2(X0,X1,cartesian_product2(X2,cartesian_product2(X3,X4))),sK3(X0,X1,cartesian_product2(X2,cartesian_product2(X3,X4)))),singleton(sK2(X0,X1,cartesian_product2(X2,cartesian_product2(X3,X4))))) = sK1(X0,X1,cartesian_product2(X2,cartesian_product2(X3,X4))) ) ),
inference(superposition,[status(thm)],[c_58,c_2821]) ).
tcf(c_35814,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))),X5)
| ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_2821]) ).
tcf(c_35815,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))),X4)
| ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_2821]) ).
tcf(c_35816,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_2821]) ).
tcf(c_35817,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X1,X2))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK3(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_2821]) ).
tcf(c_35818,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(singleton(X5),unordered_pair(sK4(X2,X3,sK5(X1,cartesian_product2(X2,X3),sK4(cartesian_product2(X1,cartesian_product2(X2,X3)),X4,X0))),X5))) = X5 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,cartesian_product2(X2,X3)),X4)) ),
inference(superposition,[status(thm)],[c_60,c_2821]) ).
tcf(c_35819,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK4(X3,X4,sK5(X2,cartesian_product2(X3,X4),sK5(X1,cartesian_product2(X2,cartesian_product2(X3,X4)),X0))),X5))) = X5 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,cartesian_product2(X3,X4)))) ),
inference(superposition,[status(thm)],[c_61,c_2821]) ).
tcf(c_35820,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(singleton(X5),unordered_pair(sK4(X1,X2,sK5(X4,cartesian_product2(X1,X2),unordered_pair(unordered_pair(X3,X0),singleton(X3)))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_64,c_2821]) ).
tcf(c_35822,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(singleton(X5),unordered_pair(sK4(X1,X2,sK5(X4,cartesian_product2(X1,X2),unordered_pair(unordered_pair(X0,X3),singleton(X3)))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_809,c_2821]) ).
tcf(c_35823,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(singleton(X5),unordered_pair(sK4(X1,X2,sK5(X4,cartesian_product2(X1,X2),unordered_pair(singleton(X3),unordered_pair(X0,X3)))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_882,c_2821]) ).
tcf(c_35825,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(singleton(X5),unordered_pair(sK4(X1,X2,sK5(X4,cartesian_product2(X1,X2),unordered_pair(singleton(X3),unordered_pair(X3,X0)))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_900,c_2821]) ).
tcf(c_35826,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(singleton(X4),X5) )
| ( sK2(singleton(X4),X5,cartesian_product2(X3,cartesian_product2(X1,X2))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(singleton(X4),X5,cartesian_product2(X3,cartesian_product2(X1,X2))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_2821]) ).
tcf(c_35827,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,singleton(X5)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_2821]) ).
tcf(c_35828,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,singleton(X5)) )
| ( sK3(X4,singleton(X5),cartesian_product2(X3,cartesian_product2(X1,X2))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,singleton(X5),cartesian_product2(X3,cartesian_product2(X1,X2))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_2821]) ).
tcf(c_35829,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X1,X2))) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),singleton(X5)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK3(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),singleton(X5)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_2821]) ).
tcf(c_35830,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X1,X2))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK3(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_2821]) ).
tcf(c_35831,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X1,X2))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK3(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_2821]) ).
tcf(c_35832,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X1,X2))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK3(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_2821]) ).
tcf(c_35833,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X1,X2))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK3(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_2821]) ).
tcf(c_35834,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_2821]) ).
tcf(c_35835,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_2821]) ).
tcf(c_35836,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_2821]) ).
tcf(c_35837,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_2821]) ).
tcf(c_35838,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_2821]) ).
tcf(c_35839,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_2821]) ).
tcf(c_35840,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_2821]) ).
tcf(c_35841,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_2821]) ).
tcf(c_35842,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_2821]) ).
tcf(c_35843,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_2821]) ).
tcf(c_35844,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_2821]) ).
tcf(c_35845,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_2821]) ).
tcf(c_35937,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,singleton(X3),unordered_pair(unordered_pair(X0,X3),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2822]) ).
tcf(c_35938,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2822]) ).
tcf(c_35939,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2822]) ).
tcf(c_35940,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2822]) ).
tcf(c_35941,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2822]) ).
tcf(c_35942,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2822]) ).
tcf(c_35943,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK4(X4,X1,unordered_pair(unordered_pair(X3,sK4(X1,X2,X0)),singleton(X3))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2822]) ).
tcf(c_35944,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK4(X4,X2,unordered_pair(unordered_pair(X3,sK5(X1,X2,X0)),singleton(X3))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2822]) ).
tcf(c_35945,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK4(X5,cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))),singleton(X4))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2822]) ).
tcf(c_35946,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK4(X5,cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))),singleton(X4))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2822]) ).
tcf(c_35947,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK4(X5,cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))),singleton(X4))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2822]) ).
tcf(c_35948,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK4(X5,cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))),singleton(X4))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2822]) ).
tcf(c_35949,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK4(X5,cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))),singleton(X4))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2822]) ).
tcf(c_35950,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK4(X5,cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))),singleton(X4))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2822]) ).
tcf(c_35952,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(singleton(X4),X5,X3)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2822]) ).
tcf(c_35953,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,singleton(X5))),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2822]) ).
tcf(c_35954,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,singleton(X5),X3)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2822]) ).
tcf(c_35955,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,singleton(X5))),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2822]) ).
tcf(c_35956,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2822]) ).
tcf(c_35957,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2822]) ).
tcf(c_35958,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2822]) ).
tcf(c_35959,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2822]) ).
tcf(c_35960,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2822]) ).
tcf(c_35961,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2822]) ).
tcf(c_35962,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2822]) ).
tcf(c_35963,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2822]) ).
tcf(c_35964,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2822]) ).
tcf(c_35965,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2822]) ).
tcf(c_35966,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2822]) ).
tcf(c_35967,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2822]) ).
tcf(c_35968,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2822]) ).
tcf(c_35969,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2822]) ).
tcf(c_35970,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2822]) ).
tcf(c_35971,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2822]) ).
tcf(c_36182,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X1),sK3(X3,X4,X1)),singleton(sK2(X3,X4,X1))) = sK1(X3,X4,X1) )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_35937]) ).
tcf(c_36183,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X1),X4)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_35937]) ).
tcf(c_36184,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X1),X3)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_35937]) ).
tcf(c_36185,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X1,X3,X4),X4)
| ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_35937]) ).
tcf(c_36186,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X1,X4),X4)
| ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_35937]) ).
tcf(c_36187,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X1,unordered_pair(singleton(X3),unordered_pair(sK4(X1,singleton(X4),unordered_pair(unordered_pair(sK4(X1,X2,X0),X4),singleton(sK4(X1,X2,X0)))),X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_35937]) ).
tcf(c_36188,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X2,unordered_pair(singleton(X3),unordered_pair(sK4(X2,singleton(X4),unordered_pair(unordered_pair(sK5(X1,X2,X0),X4),singleton(sK5(X1,X2,X0)))),X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_35937]) ).
tcf(c_36189,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(sK4(cartesian_product2(X3,X1),singleton(X5),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_35937]) ).
tcf(c_36190,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(sK4(cartesian_product2(X1,X3),singleton(X5),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5),singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_35937]) ).
tcf(c_36191,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(sK4(cartesian_product2(X1,X3),singleton(X5),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_35937]) ).
tcf(c_36192,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(sK4(cartesian_product2(X1,X3),singleton(X5),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5),singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_35937]) ).
tcf(c_36193,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(sK4(cartesian_product2(X3,X1),singleton(X5),unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5),singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_35937]) ).
tcf(c_36194,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(sK4(cartesian_product2(X3,X1),singleton(X5),unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5),singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_35937]) ).
tcf(c_36196,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X1 )
| ( sK2(singleton(X3),X4,X1) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(singleton(X3),X4,X1),X2),singleton(sK1(singleton(X3),X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_35937]) ).
tcf(c_36197,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X3) = singleton(X4) )
| ( sK1(X1,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK2(X1,X3,singleton(X4)),X2),singleton(sK2(X1,X3,singleton(X4))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_35937]) ).
tcf(c_36198,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X1 )
| ( sK3(X3,singleton(X4),X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,singleton(X4),X1),X2),singleton(sK1(X3,singleton(X4),X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_35937]) ).
tcf(c_36199,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X1) = singleton(X4) )
| ( sK1(X3,X1,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK3(X3,X1,singleton(X4)),X2),singleton(sK3(X3,X1,singleton(X4))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_35937]) ).
tcf(c_36200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_35937]) ).
tcf(c_36201,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_35937]) ).
tcf(c_36202,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_35937]) ).
tcf(c_36203,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X1,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_35937]) ).
tcf(c_36204,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_35937]) ).
tcf(c_36205,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_35937]) ).
tcf(c_36206,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_35937]) ).
tcf(c_36207,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X1,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_35937]) ).
tcf(c_36208,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_35937]) ).
tcf(c_36209,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_35937]) ).
tcf(c_36210,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_35937]) ).
tcf(c_36211,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_35937]) ).
tcf(c_36212,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_35937]) ).
tcf(c_36213,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_35937]) ).
tcf(c_36214,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_35937]) ).
tcf(c_36215,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_35937]) ).
tcf(c_36554,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),singleton(X3),unordered_pair(unordered_pair(sK5(X1,singleton(X3),unordered_pair(singleton(X0),unordered_pair(X0,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2736]) ).
tcf(c_36555,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2736]) ).
tcf(c_36556,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2736]) ).
tcf(c_36557,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2736]) ).
tcf(c_36558,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2736]) ).
tcf(c_36559,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2736]) ).
tcf(c_36560,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(unordered_pair(sK5(X4,X1,unordered_pair(singleton(X3),unordered_pair(X3,sK4(X1,X2,X0)))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2736]) ).
tcf(c_36561,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(unordered_pair(sK5(X4,X2,unordered_pair(singleton(X3),unordered_pair(X3,sK5(X1,X2,X0)))),X5),singleton(X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2736]) ).
tcf(c_36562,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(unordered_pair(sK5(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2736]) ).
tcf(c_36563,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(unordered_pair(sK5(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2736]) ).
tcf(c_36564,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(unordered_pair(sK5(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2736]) ).
tcf(c_36565,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(unordered_pair(sK5(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2736]) ).
tcf(c_36566,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(unordered_pair(sK5(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2736]) ).
tcf(c_36567,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(unordered_pair(sK5(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))))),X6),singleton(X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2736]) ).
tcf(c_36569,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(singleton(X4),X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2736]) ).
tcf(c_36570,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,singleton(X5))))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2736]) ).
tcf(c_36571,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,singleton(X5),X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2736]) ).
tcf(c_36572,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,singleton(X5))))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2736]) ).
tcf(c_36573,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2736]) ).
tcf(c_36574,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2736]) ).
tcf(c_36575,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2736]) ).
tcf(c_36576,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2736]) ).
tcf(c_36577,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2736]) ).
tcf(c_36578,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2736]) ).
tcf(c_36579,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2736]) ).
tcf(c_36580,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2736]) ).
tcf(c_36581,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2736]) ).
tcf(c_36582,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2736]) ).
tcf(c_36583,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2736]) ).
tcf(c_36584,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2736]) ).
tcf(c_36585,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2736]) ).
tcf(c_36586,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2736]) ).
tcf(c_36587,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2736]) ).
tcf(c_36588,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2736]) ).
tcf(c_37070,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X2),sK3(X3,X4,X2)),singleton(sK2(X3,X4,X2))) = sK1(X3,X4,X2) )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_36554]) ).
tcf(c_37071,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X2),X4)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_36554]) ).
tcf(c_37072,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X2),X3)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_36554]) ).
tcf(c_37073,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X2,X3,X4),X4)
| ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(sK2(X2,X3,X4),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_36554]) ).
tcf(c_37074,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X2,X4),X4)
| ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(sK3(X3,X2,X4),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_36554]) ).
tcf(c_37075,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(unordered_pair(sK5(X1,singleton(X4),unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(sK4(X1,X2,X0),X4))),X3),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_36554]) ).
tcf(c_37076,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(unordered_pair(sK5(X2,singleton(X4),unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(sK5(X1,X2,X0),X4))),X3),singleton(X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_36554]) ).
tcf(c_37077,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(sK5(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_36554]) ).
tcf(c_37078,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(sK5(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_36554]) ).
tcf(c_37079,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(sK5(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_36554]) ).
tcf(c_37080,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(sK5(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_36554]) ).
tcf(c_37081,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(sK5(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_36554]) ).
tcf(c_37082,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(unordered_pair(sK5(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_36554]) ).
tcf(c_37084,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X2 )
| ( sK2(singleton(X3),X4,X2) = X3 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(singleton(X3),X4,X2)),unordered_pair(sK1(singleton(X3),X4,X2),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_36554]) ).
tcf(c_37085,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK1(X2,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,singleton(X4))),unordered_pair(sK2(X2,X3,singleton(X4)),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_36554]) ).
tcf(c_37086,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X2 )
| ( sK3(X3,singleton(X4),X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,singleton(X4),X2)),unordered_pair(sK1(X3,singleton(X4),X2),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_36554]) ).
tcf(c_37087,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X2) = singleton(X4) )
| ( sK1(X3,X2,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,singleton(X4))),unordered_pair(sK3(X3,X2,singleton(X4)),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_36554]) ).
tcf(c_37088,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(sK3(X3,X2,X4),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_36554]) ).
tcf(c_37089,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(sK3(X3,X2,X4),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_36554]) ).
tcf(c_37090,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(sK3(X3,X2,X4),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_36554]) ).
tcf(c_37091,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X2,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(sK3(X3,X2,X4),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_36554]) ).
tcf(c_37092,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(sK2(X2,X3,X4),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_36554]) ).
tcf(c_37093,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(sK2(X2,X3,X4),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_36554]) ).
tcf(c_37094,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(sK2(X2,X3,X4),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_36554]) ).
tcf(c_37095,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X2,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(sK2(X2,X3,X4),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_36554]) ).
tcf(c_37096,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_36554]) ).
tcf(c_37097,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_36554]) ).
tcf(c_37098,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_36554]) ).
tcf(c_37099,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_36554]) ).
tcf(c_37100,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_36554]) ).
tcf(c_37101,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_36554]) ).
tcf(c_37102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_36554]) ).
tcf(c_37103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_36554]) ).
tcf(c_37625,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),singleton(X3),unordered_pair(singleton(X2),unordered_pair(sK4(singleton(X3),X1,unordered_pair(singleton(X3),unordered_pair(X3,X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2823]) ).
tcf(c_37626,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2823]) ).
tcf(c_37627,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2823]) ).
tcf(c_37628,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2823]) ).
tcf(c_37629,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2823]) ).
tcf(c_37630,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2823]) ).
tcf(c_37631,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(singleton(X5),unordered_pair(sK4(X1,X4,unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(sK4(X1,X2,X0),X3))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2823]) ).
tcf(c_37632,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(singleton(X5),unordered_pair(sK4(X2,X4,unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(sK5(X1,X2,X0),X3))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2823]) ).
tcf(c_37633,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(singleton(X6),unordered_pair(sK4(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X4))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2823]) ).
tcf(c_37634,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(singleton(X6),unordered_pair(sK4(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X4))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2823]) ).
tcf(c_37635,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(singleton(X6),unordered_pair(sK4(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X4))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2823]) ).
tcf(c_37636,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(singleton(X6),unordered_pair(sK4(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X4))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2823]) ).
tcf(c_37637,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(singleton(X6),unordered_pair(sK4(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X4))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2823]) ).
tcf(c_37638,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(singleton(X6),unordered_pair(sK4(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X4))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2823]) ).
tcf(c_37640,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(singleton(X4),X5,X3)),unordered_pair(sK1(singleton(X4),X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2823]) ).
tcf(c_37641,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,singleton(X5))),unordered_pair(sK2(X3,X4,singleton(X5)),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2823]) ).
tcf(c_37642,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,singleton(X5),X3)),unordered_pair(sK1(X4,singleton(X5),X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2823]) ).
tcf(c_37643,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,singleton(X5))),unordered_pair(sK3(X4,X3,singleton(X5)),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2823]) ).
tcf(c_37644,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2823]) ).
tcf(c_37645,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2823]) ).
tcf(c_37646,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2823]) ).
tcf(c_37647,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2823]) ).
tcf(c_37648,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2823]) ).
tcf(c_37649,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2823]) ).
tcf(c_37650,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2823]) ).
tcf(c_37651,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2823]) ).
tcf(c_37652,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2823]) ).
tcf(c_37653,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2823]) ).
tcf(c_37654,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2823]) ).
tcf(c_37655,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2823]) ).
tcf(c_37656,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2823]) ).
tcf(c_37657,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2823]) ).
tcf(c_37658,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2823]) ).
tcf(c_37659,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2823]) ).
tcf(c_37823,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X2),sK3(X3,X4,X2)),singleton(sK2(X3,X4,X2))) = sK1(X3,X4,X2) )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_37625]) ).
tcf(c_37824,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X2),X4)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_37625]) ).
tcf(c_37825,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X2),X3)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_37625]) ).
tcf(c_37826,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X2,X3,X4),X4)
| ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_37625]) ).
tcf(c_37827,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X2,X4),X4)
| ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_37625]) ).
tcf(c_37828,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(singleton(X3),unordered_pair(sK4(singleton(X4),X1,unordered_pair(singleton(X4),unordered_pair(X4,sK4(X1,X2,X0)))),X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_37625]) ).
tcf(c_37829,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(singleton(X3),unordered_pair(sK4(singleton(X4),X2,unordered_pair(singleton(X4),unordered_pair(X4,sK5(X1,X2,X0)))),X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_37625]) ).
tcf(c_37830,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(sK4(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X2))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_37625]) ).
tcf(c_37831,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(sK4(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X0,X2))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_37625]) ).
tcf(c_37832,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(sK4(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X0))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_37625]) ).
tcf(c_37833,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(sK4(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X2,X0))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_37625]) ).
tcf(c_37834,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(sK4(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X0,X2))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_37625]) ).
tcf(c_37835,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(sK4(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X2,X0))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_37625]) ).
tcf(c_37837,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X2 )
| ( sK2(singleton(X3),X4,X2) = X3 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(singleton(X3),X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_37625]) ).
tcf(c_37838,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK1(X2,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,singleton(X4))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_37625]) ).
tcf(c_37839,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X2 )
| ( sK3(X3,singleton(X4),X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,singleton(X4),X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_37625]) ).
tcf(c_37840,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X2) = singleton(X4) )
| ( sK1(X3,X2,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,singleton(X4))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_37625]) ).
tcf(c_37841,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_37625]) ).
tcf(c_37842,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_37625]) ).
tcf(c_37843,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_37625]) ).
tcf(c_37844,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X2,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_37625]) ).
tcf(c_37845,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_37625]) ).
tcf(c_37846,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_37625]) ).
tcf(c_37847,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_37625]) ).
tcf(c_37848,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X2,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_37625]) ).
tcf(c_37849,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_37625]) ).
tcf(c_37850,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_37625]) ).
tcf(c_37851,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_37625]) ).
tcf(c_37852,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_37625]) ).
tcf(c_37853,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_37625]) ).
tcf(c_37854,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_37625]) ).
tcf(c_37855,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_37625]) ).
tcf(c_37856,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_37625]) ).
tcf(c_37946,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),singleton(X3),unordered_pair(singleton(X2),unordered_pair(sK4(singleton(X3),X1,unordered_pair(unordered_pair(X0,X3),singleton(X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2824]) ).
tcf(c_37947,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2824]) ).
tcf(c_37948,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2824]) ).
tcf(c_37949,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2824]) ).
tcf(c_37950,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2824]) ).
tcf(c_37951,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2824]) ).
tcf(c_37952,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(singleton(X5),unordered_pair(sK4(X1,X4,unordered_pair(unordered_pair(X3,sK4(X1,X2,X0)),singleton(sK4(X1,X2,X0)))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2824]) ).
tcf(c_37953,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(singleton(X5),unordered_pair(sK4(X2,X4,unordered_pair(unordered_pair(X3,sK5(X1,X2,X0)),singleton(sK5(X1,X2,X0)))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2824]) ).
tcf(c_37954,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(singleton(X6),unordered_pair(sK4(cartesian_product2(X3,X1),X5,unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2824]) ).
tcf(c_37955,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(singleton(X6),unordered_pair(sK4(cartesian_product2(X1,X3),X5,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))),singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2824]) ).
tcf(c_37956,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(singleton(X6),unordered_pair(sK4(cartesian_product2(X1,X3),X5,unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2824]) ).
tcf(c_37957,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(singleton(X6),unordered_pair(sK4(cartesian_product2(X1,X3),X5,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))),singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2824]) ).
tcf(c_37958,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(singleton(X6),unordered_pair(sK4(cartesian_product2(X3,X1),X5,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))),singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2824]) ).
tcf(c_37959,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(singleton(X6),unordered_pair(sK4(cartesian_product2(X3,X1),X5,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))),singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2824]) ).
tcf(c_37961,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(singleton(X4),X5,X3)),singleton(sK1(singleton(X4),X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2824]) ).
tcf(c_37962,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,singleton(X5))),singleton(sK2(X3,X4,singleton(X5))))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2824]) ).
tcf(c_37963,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,singleton(X5),X3)),singleton(sK1(X4,singleton(X5),X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2824]) ).
tcf(c_37964,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,singleton(X5))),singleton(sK3(X4,X3,singleton(X5))))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2824]) ).
tcf(c_37965,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2824]) ).
tcf(c_37966,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2824]) ).
tcf(c_37967,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2824]) ).
tcf(c_37968,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2824]) ).
tcf(c_37969,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2824]) ).
tcf(c_37970,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2824]) ).
tcf(c_37971,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2824]) ).
tcf(c_37972,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2824]) ).
tcf(c_37973,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2824]) ).
tcf(c_37974,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2824]) ).
tcf(c_37975,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2824]) ).
tcf(c_37976,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2824]) ).
tcf(c_37977,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2824]) ).
tcf(c_37978,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2824]) ).
tcf(c_37979,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2824]) ).
tcf(c_37980,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2824]) ).
tcf(c_38052,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X2),sK3(X3,X4,X2)),singleton(sK2(X3,X4,X2))) = sK1(X3,X4,X2) )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_37946]) ).
tcf(c_38053,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X2),X4)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_37946]) ).
tcf(c_38054,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X2),X3)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_37946]) ).
tcf(c_38055,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X2,X3,X4),X4)
| ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_37946]) ).
tcf(c_38056,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X2,X4),X4)
| ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_37946]) ).
tcf(c_38057,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(singleton(X3),unordered_pair(sK4(singleton(X4),X1,unordered_pair(unordered_pair(sK4(X1,X2,X0),X4),singleton(X4))),X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_37946]) ).
tcf(c_38058,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(singleton(X3),unordered_pair(sK4(singleton(X4),X2,unordered_pair(unordered_pair(sK5(X1,X2,X0),X4),singleton(X4))),X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_37946]) ).
tcf(c_38059,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(sK4(singleton(X5),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5),singleton(X5))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_37946]) ).
tcf(c_38060,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(sK4(singleton(X5),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5),singleton(X5))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_37946]) ).
tcf(c_38061,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(sK4(singleton(X5),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5),singleton(X5))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_37946]) ).
tcf(c_38062,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(sK4(singleton(X5),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5),singleton(X5))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_37946]) ).
tcf(c_38063,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(sK4(singleton(X5),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5),singleton(X5))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_37946]) ).
tcf(c_38064,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(sK4(singleton(X5),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5),singleton(X5))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_37946]) ).
tcf(c_38066,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X2 )
| ( sK2(singleton(X3),X4,X2) = X3 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(singleton(X3),X4,X2),X1),singleton(X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_37946]) ).
tcf(c_38067,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK1(X2,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK2(X2,X3,singleton(X4)),X1),singleton(X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_37946]) ).
tcf(c_38068,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X2 )
| ( sK3(X3,singleton(X4),X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,singleton(X4),X2),X1),singleton(X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_37946]) ).
tcf(c_38069,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X2) = singleton(X4) )
| ( sK1(X3,X2,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK3(X3,X2,singleton(X4)),X1),singleton(X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_37946]) ).
tcf(c_38070,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_37946]) ).
tcf(c_38071,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_37946]) ).
tcf(c_38072,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_37946]) ).
tcf(c_38073,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X2,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_37946]) ).
tcf(c_38074,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_37946]) ).
tcf(c_38075,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_37946]) ).
tcf(c_38076,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_37946]) ).
tcf(c_38077,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X2,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_37946]) ).
tcf(c_38078,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_37946]) ).
tcf(c_38079,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_37946]) ).
tcf(c_38080,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_37946]) ).
tcf(c_38081,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_37946]) ).
tcf(c_38082,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_37946]) ).
tcf(c_38083,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_37946]) ).
tcf(c_38084,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_37946]) ).
tcf(c_38085,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_37946]) ).
tcf(c_38387,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),singleton(X3),unordered_pair(singleton(X2),unordered_pair(sK4(singleton(X3),X1,unordered_pair(singleton(X3),unordered_pair(X0,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2825]) ).
tcf(c_38388,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2825]) ).
tcf(c_38389,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2825]) ).
tcf(c_38390,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2825]) ).
tcf(c_38391,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2825]) ).
tcf(c_38392,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2825]) ).
tcf(c_38393,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(singleton(X5),unordered_pair(sK4(X1,X4,unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(X3,sK4(X1,X2,X0)))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2825]) ).
tcf(c_38394,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(singleton(X5),unordered_pair(sK4(X2,X4,unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(X3,sK5(X1,X2,X0)))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2825]) ).
tcf(c_38395,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(singleton(X6),unordered_pair(sK4(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2825]) ).
tcf(c_38396,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(singleton(X6),unordered_pair(sK4(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2825]) ).
tcf(c_38397,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(singleton(X6),unordered_pair(sK4(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2825]) ).
tcf(c_38398,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(singleton(X6),unordered_pair(sK4(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2825]) ).
tcf(c_38399,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(singleton(X6),unordered_pair(sK4(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2825]) ).
tcf(c_38400,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(singleton(X6),unordered_pair(sK4(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2825]) ).
tcf(c_38402,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(singleton(X4),X5,X3)),unordered_pair(X0,sK1(singleton(X4),X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2825]) ).
tcf(c_38403,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,singleton(X5))),unordered_pair(X0,sK2(X3,X4,singleton(X5))))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2825]) ).
tcf(c_38404,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,singleton(X5),X3)),unordered_pair(X0,sK1(X4,singleton(X5),X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2825]) ).
tcf(c_38405,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,singleton(X5))),unordered_pair(X0,sK3(X4,X3,singleton(X5))))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2825]) ).
tcf(c_38406,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2825]) ).
tcf(c_38407,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2825]) ).
tcf(c_38408,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2825]) ).
tcf(c_38409,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2825]) ).
tcf(c_38410,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2825]) ).
tcf(c_38411,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2825]) ).
tcf(c_38412,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2825]) ).
tcf(c_38413,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2825]) ).
tcf(c_38414,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2825]) ).
tcf(c_38415,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2825]) ).
tcf(c_38416,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2825]) ).
tcf(c_38417,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2825]) ).
tcf(c_38418,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2825]) ).
tcf(c_38419,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2825]) ).
tcf(c_38420,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2825]) ).
tcf(c_38421,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2825]) ).
tcf(c_38889,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X2),sK3(X3,X4,X2)),singleton(sK2(X3,X4,X2))) = sK1(X3,X4,X2) )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_38387]) ).
tcf(c_38890,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X2),X4)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_38387]) ).
tcf(c_38891,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X2),X3)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_38387]) ).
tcf(c_38892,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X2,X3,X4),X4)
| ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_38387]) ).
tcf(c_38893,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X2,X4),X4)
| ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_38387]) ).
tcf(c_38894,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(singleton(X3),unordered_pair(sK4(singleton(X4),X1,unordered_pair(singleton(X4),unordered_pair(sK4(X1,X2,X0),X4))),X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_38387]) ).
tcf(c_38895,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(singleton(X3),unordered_pair(sK4(singleton(X4),X2,unordered_pair(singleton(X4),unordered_pair(sK5(X1,X2,X0),X4))),X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_38387]) ).
tcf(c_38896,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(sK4(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_38387]) ).
tcf(c_38897,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(sK4(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_38387]) ).
tcf(c_38898,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(sK4(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_38387]) ).
tcf(c_38899,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(sK4(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_38387]) ).
tcf(c_38900,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(sK4(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_38387]) ).
tcf(c_38901,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(sK4(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_38387]) ).
tcf(c_38903,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X2 )
| ( sK2(singleton(X3),X4,X2) = X3 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(singleton(X3),X4,X2),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_38387]) ).
tcf(c_38904,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK1(X2,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,singleton(X4)),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_38387]) ).
tcf(c_38905,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X2 )
| ( sK3(X3,singleton(X4),X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,singleton(X4),X2),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_38387]) ).
tcf(c_38906,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X2) = singleton(X4) )
| ( sK1(X3,X2,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,singleton(X4)),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_38387]) ).
tcf(c_38907,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_38387]) ).
tcf(c_38908,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_38387]) ).
tcf(c_38909,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_38387]) ).
tcf(c_38910,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X2,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_38387]) ).
tcf(c_38911,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_38387]) ).
tcf(c_38912,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_38387]) ).
tcf(c_38913,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_38387]) ).
tcf(c_38914,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X2,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_38387]) ).
tcf(c_38915,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_38387]) ).
tcf(c_38916,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_38387]) ).
tcf(c_38917,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_38387]) ).
tcf(c_38918,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_38387]) ).
tcf(c_38919,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_38387]) ).
tcf(c_38920,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_38387]) ).
tcf(c_38921,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_38387]) ).
tcf(c_38922,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_38387]) ).
tcf(c_39078,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,singleton(X3),unordered_pair(singleton(X0),unordered_pair(X3,X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2826]) ).
tcf(c_39079,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2826]) ).
tcf(c_39080,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2826]) ).
tcf(c_39081,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2826]) ).
tcf(c_39082,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2826]) ).
tcf(c_39083,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2826]) ).
tcf(c_39084,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK4(X4,X1,unordered_pair(singleton(X3),unordered_pair(sK4(X1,X2,X0),X3))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2826]) ).
tcf(c_39085,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK4(X4,X2,unordered_pair(singleton(X3),unordered_pair(sK5(X1,X2,X0),X3))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2826]) ).
tcf(c_39086,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK4(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X4))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2826]) ).
tcf(c_39087,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK4(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X4))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2826]) ).
tcf(c_39088,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK4(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X4))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2826]) ).
tcf(c_39089,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK4(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X4))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2826]) ).
tcf(c_39090,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK4(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X4))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2826]) ).
tcf(c_39091,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK4(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X4))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2826]) ).
tcf(c_39093,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(singleton(X4),X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2826]) ).
tcf(c_39094,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,singleton(X5)),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2826]) ).
tcf(c_39095,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,singleton(X5),X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2826]) ).
tcf(c_39096,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,singleton(X5)),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2826]) ).
tcf(c_39097,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2826]) ).
tcf(c_39098,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2826]) ).
tcf(c_39099,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2826]) ).
tcf(c_39100,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2826]) ).
tcf(c_39101,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2826]) ).
tcf(c_39102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2826]) ).
tcf(c_39103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2826]) ).
tcf(c_39104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2826]) ).
tcf(c_39105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2826]) ).
tcf(c_39106,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2826]) ).
tcf(c_39107,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2826]) ).
tcf(c_39108,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2826]) ).
tcf(c_39109,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2826]) ).
tcf(c_39110,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2826]) ).
tcf(c_39111,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2826]) ).
tcf(c_39112,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2826]) ).
tcf(c_39608,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X1),sK3(X3,X4,X1)),singleton(sK2(X3,X4,X1))) = sK1(X3,X4,X1) )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_39078]) ).
tcf(c_39609,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X1),X4)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_39078]) ).
tcf(c_39610,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X1),X3)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_39078]) ).
tcf(c_39611,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X1,X3,X4),X4)
| ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_39078]) ).
tcf(c_39612,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X1,X4),X4)
| ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_39078]) ).
tcf(c_39613,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X1,unordered_pair(singleton(X3),unordered_pair(sK4(X1,singleton(X4),unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(X4,sK4(X1,X2,X0)))),X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_39078]) ).
tcf(c_39614,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X2,unordered_pair(singleton(X3),unordered_pair(sK4(X2,singleton(X4),unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(X4,sK5(X1,X2,X0)))),X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_39078]) ).
tcf(c_39615,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(sK4(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X2))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_39078]) ).
tcf(c_39616,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(sK4(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X0,X2))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_39078]) ).
tcf(c_39617,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(sK4(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X0))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_39078]) ).
tcf(c_39618,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(sK4(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X2,X0))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_39078]) ).
tcf(c_39619,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(sK4(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X0,X2))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_39078]) ).
tcf(c_39620,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(sK4(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X2,X0))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_39078]) ).
tcf(c_39622,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X1 )
| ( sK2(singleton(X3),X4,X1) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(singleton(X3),X4,X1)),unordered_pair(X2,sK1(singleton(X3),X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_39078]) ).
tcf(c_39623,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X3) = singleton(X4) )
| ( sK1(X1,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,singleton(X4))),unordered_pair(X2,sK2(X1,X3,singleton(X4))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_39078]) ).
tcf(c_39624,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X1 )
| ( sK3(X3,singleton(X4),X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,singleton(X4),X1)),unordered_pair(X2,sK1(X3,singleton(X4),X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_39078]) ).
tcf(c_39625,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X1) = singleton(X4) )
| ( sK1(X3,X1,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,singleton(X4))),unordered_pair(X2,sK3(X3,X1,singleton(X4))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_39078]) ).
tcf(c_39626,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_39078]) ).
tcf(c_39627,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_39078]) ).
tcf(c_39628,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_39078]) ).
tcf(c_39629,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X1,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_39078]) ).
tcf(c_39630,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_39078]) ).
tcf(c_39631,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_39078]) ).
tcf(c_39632,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_39078]) ).
tcf(c_39633,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X1,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_39078]) ).
tcf(c_39634,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_39078]) ).
tcf(c_39635,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_39078]) ).
tcf(c_39636,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_39078]) ).
tcf(c_39637,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_39078]) ).
tcf(c_39638,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_39078]) ).
tcf(c_39639,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_39078]) ).
tcf(c_39640,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_39078]) ).
tcf(c_39641,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_39078]) ).
tcf(c_40020,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,singleton(X3),unordered_pair(singleton(X0),unordered_pair(X0,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2827]) ).
tcf(c_40021,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2827]) ).
tcf(c_40022,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2827]) ).
tcf(c_40023,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2827]) ).
tcf(c_40024,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2827]) ).
tcf(c_40025,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2827]) ).
tcf(c_40026,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK4(X4,X1,unordered_pair(singleton(X3),unordered_pair(X3,sK4(X1,X2,X0)))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2827]) ).
tcf(c_40027,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK4(X4,X2,unordered_pair(singleton(X3),unordered_pair(X3,sK5(X1,X2,X0)))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2827]) ).
tcf(c_40028,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK4(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2827]) ).
tcf(c_40029,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK4(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2827]) ).
tcf(c_40030,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK4(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2827]) ).
tcf(c_40031,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK4(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2827]) ).
tcf(c_40032,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK4(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2827]) ).
tcf(c_40033,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK4(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2827]) ).
tcf(c_40035,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(singleton(X4),X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2827]) ).
tcf(c_40036,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,singleton(X5))))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2827]) ).
tcf(c_40037,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,singleton(X5),X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2827]) ).
tcf(c_40038,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,singleton(X5))))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2827]) ).
tcf(c_40039,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2827]) ).
tcf(c_40040,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2827]) ).
tcf(c_40041,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2827]) ).
tcf(c_40042,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2827]) ).
tcf(c_40043,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2827]) ).
tcf(c_40044,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2827]) ).
tcf(c_40045,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2827]) ).
tcf(c_40046,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2827]) ).
tcf(c_40047,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2827]) ).
tcf(c_40048,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2827]) ).
tcf(c_40049,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2827]) ).
tcf(c_40050,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2827]) ).
tcf(c_40051,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2827]) ).
tcf(c_40052,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2827]) ).
tcf(c_40053,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2827]) ).
tcf(c_40054,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2827]) ).
tcf(c_40377,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X1),sK3(X3,X4,X1)),singleton(sK2(X3,X4,X1))) = sK1(X3,X4,X1) )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_40020]) ).
tcf(c_40378,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X1),X4)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_40020]) ).
tcf(c_40379,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X1),X3)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_40020]) ).
tcf(c_40380,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X1,X3,X4),X4)
| ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_40020]) ).
tcf(c_40381,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X1,X4),X4)
| ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_40020]) ).
tcf(c_40382,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X1,unordered_pair(singleton(X3),unordered_pair(sK4(X1,singleton(X4),unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(sK4(X1,X2,X0),X4))),X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_40020]) ).
tcf(c_40383,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X2,unordered_pair(singleton(X3),unordered_pair(sK4(X2,singleton(X4),unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(sK5(X1,X2,X0),X4))),X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_40020]) ).
tcf(c_40384,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(sK4(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_40020]) ).
tcf(c_40385,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(sK4(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_40020]) ).
tcf(c_40386,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(sK4(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_40020]) ).
tcf(c_40387,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(sK4(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_40020]) ).
tcf(c_40388,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(sK4(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_40020]) ).
tcf(c_40389,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(sK4(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_40020]) ).
tcf(c_40391,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X1 )
| ( sK2(singleton(X3),X4,X1) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(singleton(X3),X4,X1)),unordered_pair(sK1(singleton(X3),X4,X1),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_40020]) ).
tcf(c_40392,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X3) = singleton(X4) )
| ( sK1(X1,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,singleton(X4))),unordered_pair(sK2(X1,X3,singleton(X4)),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_40020]) ).
tcf(c_40393,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X1 )
| ( sK3(X3,singleton(X4),X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,singleton(X4),X1)),unordered_pair(sK1(X3,singleton(X4),X1),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_40020]) ).
tcf(c_40394,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X1) = singleton(X4) )
| ( sK1(X3,X1,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,singleton(X4))),unordered_pair(sK3(X3,X1,singleton(X4)),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_40020]) ).
tcf(c_40395,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_40020]) ).
tcf(c_40396,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_40020]) ).
tcf(c_40397,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_40020]) ).
tcf(c_40398,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X1,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_40020]) ).
tcf(c_40399,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_40020]) ).
tcf(c_40400,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_40020]) ).
tcf(c_40401,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_40020]) ).
tcf(c_40402,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X1,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_40020]) ).
tcf(c_40403,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_40020]) ).
tcf(c_40404,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_40020]) ).
tcf(c_40405,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_40020]) ).
tcf(c_40406,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_40020]) ).
tcf(c_40407,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_40020]) ).
tcf(c_40408,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_40020]) ).
tcf(c_40409,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_40020]) ).
tcf(c_40410,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_40020]) ).
tcf(c_40565,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = cartesian_product2(X0,X1) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK5(X2,X3,sK4(cartesian_product2(X2,X3),X4,sK1(X0,X1,cartesian_product2(cartesian_product2(X2,X3),X4)))),X5))) = X5 )
| ( unordered_pair(unordered_pair(sK2(X0,X1,cartesian_product2(cartesian_product2(X2,X3),X4)),sK3(X0,X1,cartesian_product2(cartesian_product2(X2,X3),X4))),singleton(sK2(X0,X1,cartesian_product2(cartesian_product2(X2,X3),X4)))) = sK1(X0,X1,cartesian_product2(cartesian_product2(X2,X3),X4)) ) ),
inference(superposition,[status(thm)],[c_58,c_2896]) ).
tcf(c_40566,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)),X5)
| ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_2896]) ).
tcf(c_40567,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)),X4)
| ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_2896]) ).
tcf(c_40568,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(cartesian_product2(X2,X1),X3),X4) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK2(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_2896]) ).
tcf(c_40569,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X2,X1),X3)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK3(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_2896]) ).
tcf(c_40570,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(singleton(X5),unordered_pair(sK5(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK4(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X0))),X5))) = X5 )
| ~ in(X0,cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X3),X4)) ),
inference(superposition,[status(thm)],[c_60,c_2896]) ).
tcf(c_40571,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK5(X2,X3,sK4(cartesian_product2(X2,X3),X4,sK5(X1,cartesian_product2(cartesian_product2(X2,X3),X4),X0))),X5))) = X5 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(cartesian_product2(X2,X3),X4))) ),
inference(superposition,[status(thm)],[c_61,c_2896]) ).
tcf(c_40572,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(singleton(X5),unordered_pair(sK5(X1,X2,sK4(cartesian_product2(X1,X2),X4,unordered_pair(unordered_pair(X0,X3),singleton(X0)))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_64,c_2896]) ).
tcf(c_40574,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(singleton(X5),unordered_pair(sK5(X1,X2,sK4(cartesian_product2(X1,X2),X4,unordered_pair(unordered_pair(X3,X0),singleton(X0)))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_809,c_2896]) ).
tcf(c_40575,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(singleton(X5),unordered_pair(sK5(X1,X2,sK4(cartesian_product2(X1,X2),X4,unordered_pair(singleton(X0),unordered_pair(X3,X0)))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_882,c_2896]) ).
tcf(c_40577,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(singleton(X5),unordered_pair(sK5(X1,X2,sK4(cartesian_product2(X1,X2),X4,unordered_pair(singleton(X0),unordered_pair(X0,X3)))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_900,c_2896]) ).
tcf(c_40578,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(singleton(X4),X5) )
| ( sK2(singleton(X4),X5,cartesian_product2(cartesian_product2(X2,X1),X3)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(singleton(X4),X5,cartesian_product2(cartesian_product2(X2,X1),X3)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_2896]) ).
tcf(c_40579,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X2,X1),X3),X4) = singleton(X5) )
| ( sK1(cartesian_product2(cartesian_product2(X2,X1),X3),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK2(cartesian_product2(cartesian_product2(X2,X1),X3),X4,singleton(X5)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_2896]) ).
tcf(c_40580,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,singleton(X5)) )
| ( sK3(X4,singleton(X5),cartesian_product2(cartesian_product2(X2,X1),X3)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,singleton(X5),cartesian_product2(cartesian_product2(X2,X1),X3)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_2896]) ).
tcf(c_40581,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X2,X1),X3)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(cartesian_product2(X2,X1),X3),singleton(X5)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK3(X4,cartesian_product2(cartesian_product2(X2,X1),X3),singleton(X5)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_2896]) ).
tcf(c_40582,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X2,X1),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK3(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_2896]) ).
tcf(c_40583,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X2,X1),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK3(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_2896]) ).
tcf(c_40584,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X2,X1),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK3(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_2896]) ).
tcf(c_40585,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X2,X1),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK3(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_2896]) ).
tcf(c_40586,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X2,X1),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK2(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_2896]) ).
tcf(c_40587,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X2,X1),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK2(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_2896]) ).
tcf(c_40588,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X2,X1),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK2(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_2896]) ).
tcf(c_40589,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X2,X1),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK2(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_2896]) ).
tcf(c_40590,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_2896]) ).
tcf(c_40591,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_2896]) ).
tcf(c_40592,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_2896]) ).
tcf(c_40593,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_2896]) ).
tcf(c_40594,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_2896]) ).
tcf(c_40595,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_2896]) ).
tcf(c_40596,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_2896]) ).
tcf(c_40597,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_2896]) ).
tcf(c_40734,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(X3,X4)) = cartesian_product2(X0,X1) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK5(X3,X4,sK5(X2,cartesian_product2(X3,X4),sK1(X0,X1,cartesian_product2(X2,cartesian_product2(X3,X4))))),X5))) = X5 )
| ( unordered_pair(unordered_pair(sK2(X0,X1,cartesian_product2(X2,cartesian_product2(X3,X4))),sK3(X0,X1,cartesian_product2(X2,cartesian_product2(X3,X4)))),singleton(sK2(X0,X1,cartesian_product2(X2,cartesian_product2(X3,X4))))) = sK1(X0,X1,cartesian_product2(X2,cartesian_product2(X3,X4))) ) ),
inference(superposition,[status(thm)],[c_58,c_2897]) ).
tcf(c_40735,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))),X5)
| ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_2897]) ).
tcf(c_40736,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))),X4)
| ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_2897]) ).
tcf(c_40737,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_2897]) ).
tcf(c_40738,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X2,X1))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK3(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_2897]) ).
tcf(c_40739,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK5(X2,X3,sK5(X1,cartesian_product2(X2,X3),sK4(cartesian_product2(X1,cartesian_product2(X2,X3)),X4,X0))),X5))) = X5 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,cartesian_product2(X2,X3)),X4)) ),
inference(superposition,[status(thm)],[c_60,c_2897]) ).
tcf(c_40740,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK5(X3,X4,sK5(X2,cartesian_product2(X3,X4),sK5(X1,cartesian_product2(X2,cartesian_product2(X3,X4)),X0))),X5))) = X5 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,cartesian_product2(X3,X4)))) ),
inference(superposition,[status(thm)],[c_61,c_2897]) ).
tcf(c_40741,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(singleton(X5),unordered_pair(sK5(X1,X2,sK5(X4,cartesian_product2(X1,X2),unordered_pair(unordered_pair(X3,X0),singleton(X3)))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_64,c_2897]) ).
tcf(c_40743,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(singleton(X5),unordered_pair(sK5(X1,X2,sK5(X4,cartesian_product2(X1,X2),unordered_pair(unordered_pair(X0,X3),singleton(X3)))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_809,c_2897]) ).
tcf(c_40744,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(singleton(X5),unordered_pair(sK5(X1,X2,sK5(X4,cartesian_product2(X1,X2),unordered_pair(singleton(X3),unordered_pair(X0,X3)))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_882,c_2897]) ).
tcf(c_40746,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(singleton(X5),unordered_pair(sK5(X1,X2,sK5(X4,cartesian_product2(X1,X2),unordered_pair(singleton(X3),unordered_pair(X3,X0)))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_900,c_2897]) ).
tcf(c_40747,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(singleton(X4),X5) )
| ( sK2(singleton(X4),X5,cartesian_product2(X3,cartesian_product2(X2,X1))) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(singleton(X4),X5,cartesian_product2(X3,cartesian_product2(X2,X1))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_2897]) ).
tcf(c_40748,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,singleton(X5)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_2897]) ).
tcf(c_40749,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,singleton(X5)) )
| ( sK3(X4,singleton(X5),cartesian_product2(X3,cartesian_product2(X2,X1))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,singleton(X5),cartesian_product2(X3,cartesian_product2(X2,X1))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_2897]) ).
tcf(c_40750,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X2,X1))) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),singleton(X5)) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK3(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),singleton(X5)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_2897]) ).
tcf(c_40751,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X2,X1))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK3(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_2897]) ).
tcf(c_40752,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X2,X1))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK3(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_2897]) ).
tcf(c_40753,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X2,X1))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK3(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_2897]) ).
tcf(c_40754,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X2,X1))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK3(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_2897]) ).
tcf(c_40755,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_2897]) ).
tcf(c_40756,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_2897]) ).
tcf(c_40757,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_2897]) ).
tcf(c_40758,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_2897]) ).
tcf(c_40759,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_2897]) ).
tcf(c_40760,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_2897]) ).
tcf(c_40761,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_2897]) ).
tcf(c_40762,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_2897]) ).
tcf(c_40763,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_2897]) ).
tcf(c_40764,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_2897]) ).
tcf(c_40765,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_2897]) ).
tcf(c_40766,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_2897]) ).
tcf(c_40876,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),singleton(X3),unordered_pair(singleton(X2),unordered_pair(sK5(X1,singleton(X3),unordered_pair(unordered_pair(X0,X3),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2898]) ).
tcf(c_40877,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2898]) ).
tcf(c_40878,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2898]) ).
tcf(c_40879,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2898]) ).
tcf(c_40880,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2898]) ).
tcf(c_40881,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2898]) ).
tcf(c_40882,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(singleton(X5),unordered_pair(sK5(X4,X1,unordered_pair(unordered_pair(X3,sK4(X1,X2,X0)),singleton(X3))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2898]) ).
tcf(c_40883,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(singleton(X5),unordered_pair(sK5(X4,X2,unordered_pair(unordered_pair(X3,sK5(X1,X2,X0)),singleton(X3))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2898]) ).
tcf(c_40884,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(singleton(X6),unordered_pair(sK5(X5,cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))),singleton(X4))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2898]) ).
tcf(c_40885,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(singleton(X6),unordered_pair(sK5(X5,cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))),singleton(X4))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2898]) ).
tcf(c_40886,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(singleton(X6),unordered_pair(sK5(X5,cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))),singleton(X4))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2898]) ).
tcf(c_40887,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(singleton(X6),unordered_pair(sK5(X5,cartesian_product2(X1,X3),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))),singleton(X4))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2898]) ).
tcf(c_40888,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(singleton(X6),unordered_pair(sK5(X5,cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))),singleton(X4))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2898]) ).
tcf(c_40889,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(singleton(X6),unordered_pair(sK5(X5,cartesian_product2(X3,X1),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))),singleton(X4))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2898]) ).
tcf(c_40891,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(singleton(X4),X5,X3)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2898]) ).
tcf(c_40892,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,singleton(X5))),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2898]) ).
tcf(c_40893,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,singleton(X5),X3)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2898]) ).
tcf(c_40894,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,singleton(X5))),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2898]) ).
tcf(c_40895,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2898]) ).
tcf(c_40896,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2898]) ).
tcf(c_40897,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2898]) ).
tcf(c_40898,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2898]) ).
tcf(c_40899,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2898]) ).
tcf(c_40900,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2898]) ).
tcf(c_40901,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2898]) ).
tcf(c_40902,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2898]) ).
tcf(c_40903,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2898]) ).
tcf(c_40904,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2898]) ).
tcf(c_40905,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2898]) ).
tcf(c_40906,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2898]) ).
tcf(c_40907,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2898]) ).
tcf(c_40908,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2898]) ).
tcf(c_40909,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2898]) ).
tcf(c_40910,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2898]) ).
tcf(c_41257,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X2),sK3(X3,X4,X2)),singleton(sK2(X3,X4,X2))) = sK1(X3,X4,X2) )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_40876]) ).
tcf(c_41258,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X2),X4)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_40876]) ).
tcf(c_41259,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X2),X3)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_40876]) ).
tcf(c_41260,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X2,X3,X4),X4)
| ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(sK2(X2,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_40876]) ).
tcf(c_41261,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X2,X4),X4)
| ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(sK3(X3,X2,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_40876]) ).
tcf(c_41262,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(singleton(X3),unordered_pair(sK5(X1,singleton(X4),unordered_pair(unordered_pair(sK4(X1,X2,X0),X4),singleton(sK4(X1,X2,X0)))),X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_40876]) ).
tcf(c_41263,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(singleton(X3),unordered_pair(sK5(X2,singleton(X4),unordered_pair(unordered_pair(sK5(X1,X2,X0),X4),singleton(sK5(X1,X2,X0)))),X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_40876]) ).
tcf(c_41264,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(sK5(cartesian_product2(X3,X1),singleton(X5),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_40876]) ).
tcf(c_41265,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(sK5(cartesian_product2(X1,X3),singleton(X5),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5),singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_40876]) ).
tcf(c_41266,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(sK5(cartesian_product2(X1,X3),singleton(X5),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_40876]) ).
tcf(c_41267,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(sK5(cartesian_product2(X1,X3),singleton(X5),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5),singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_40876]) ).
tcf(c_41268,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(sK5(cartesian_product2(X3,X1),singleton(X5),unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5),singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_40876]) ).
tcf(c_41269,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(sK5(cartesian_product2(X3,X1),singleton(X5),unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5),singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_40876]) ).
tcf(c_41271,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X2 )
| ( sK2(singleton(X3),X4,X2) = X3 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(singleton(X3),X4,X2),X1),singleton(sK1(singleton(X3),X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_40876]) ).
tcf(c_41272,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK1(X2,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK2(X2,X3,singleton(X4)),X1),singleton(sK2(X2,X3,singleton(X4))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_40876]) ).
tcf(c_41273,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X2 )
| ( sK3(X3,singleton(X4),X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,singleton(X4),X2),X1),singleton(sK1(X3,singleton(X4),X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_40876]) ).
tcf(c_41274,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X2) = singleton(X4) )
| ( sK1(X3,X2,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK3(X3,X2,singleton(X4)),X1),singleton(sK3(X3,X2,singleton(X4))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_40876]) ).
tcf(c_41275,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(sK3(X3,X2,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_40876]) ).
tcf(c_41276,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(sK3(X3,X2,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_40876]) ).
tcf(c_41277,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(sK3(X3,X2,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_40876]) ).
tcf(c_41278,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X2,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(sK3(X3,X2,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_40876]) ).
tcf(c_41279,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(sK2(X2,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_40876]) ).
tcf(c_41280,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(sK2(X2,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_40876]) ).
tcf(c_41281,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(sK2(X2,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_40876]) ).
tcf(c_41282,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X2,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(sK2(X2,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_40876]) ).
tcf(c_41283,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_40876]) ).
tcf(c_41284,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_40876]) ).
tcf(c_41285,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_40876]) ).
tcf(c_41286,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_40876]) ).
tcf(c_41287,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_40876]) ).
tcf(c_41288,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_40876]) ).
tcf(c_41289,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_40876]) ).
tcf(c_41290,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_40876]) ).
tcf(c_41683,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(singleton(X3),X1,unordered_pair(singleton(X3),unordered_pair(X3,X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2899]) ).
tcf(c_41684,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2899]) ).
tcf(c_41685,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2899]) ).
tcf(c_41686,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2899]) ).
tcf(c_41687,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2899]) ).
tcf(c_41688,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2899]) ).
tcf(c_41689,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK5(X1,X4,unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(sK4(X1,X2,X0),X3))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2899]) ).
tcf(c_41690,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK5(X2,X4,unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(sK5(X1,X2,X0),X3))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2899]) ).
tcf(c_41691,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK5(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X4))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2899]) ).
tcf(c_41692,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK5(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X4))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2899]) ).
tcf(c_41693,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK5(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X4))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2899]) ).
tcf(c_41694,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK5(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X4))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2899]) ).
tcf(c_41695,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK5(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X4))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2899]) ).
tcf(c_41696,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK5(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X4))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2899]) ).
tcf(c_41698,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(singleton(X4),X5,X3)),unordered_pair(sK1(singleton(X4),X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2899]) ).
tcf(c_41699,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,singleton(X5))),unordered_pair(sK2(X3,X4,singleton(X5)),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2899]) ).
tcf(c_41700,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,singleton(X5),X3)),unordered_pair(sK1(X4,singleton(X5),X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2899]) ).
tcf(c_41701,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,singleton(X5))),unordered_pair(sK3(X4,X3,singleton(X5)),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2899]) ).
tcf(c_41702,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2899]) ).
tcf(c_41703,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2899]) ).
tcf(c_41704,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2899]) ).
tcf(c_41705,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2899]) ).
tcf(c_41706,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2899]) ).
tcf(c_41707,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2899]) ).
tcf(c_41708,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2899]) ).
tcf(c_41709,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2899]) ).
tcf(c_41710,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2899]) ).
tcf(c_41711,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2899]) ).
tcf(c_41712,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2899]) ).
tcf(c_41713,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2899]) ).
tcf(c_41714,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2899]) ).
tcf(c_41715,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2899]) ).
tcf(c_41716,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2899]) ).
tcf(c_41717,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2899]) ).
tcf(c_41978,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X1),sK3(X3,X4,X1)),singleton(sK2(X3,X4,X1))) = sK1(X3,X4,X1) )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_41683]) ).
tcf(c_41979,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X1),X4)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_41683]) ).
tcf(c_41980,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X1),X3)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_41683]) ).
tcf(c_41981,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X1,X3,X4),X4)
| ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK2(X1,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_41683]) ).
tcf(c_41982,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X1,X4),X4)
| ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK3(X3,X1,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_41683]) ).
tcf(c_41983,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X1,unordered_pair(singleton(X3),unordered_pair(sK5(singleton(X4),X1,unordered_pair(singleton(X4),unordered_pair(X4,sK4(X1,X2,X0)))),X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_41683]) ).
tcf(c_41984,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X2,unordered_pair(singleton(X3),unordered_pair(sK5(singleton(X4),X2,unordered_pair(singleton(X4),unordered_pair(X4,sK5(X1,X2,X0)))),X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_41683]) ).
tcf(c_41985,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(sK5(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X2))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_41683]) ).
tcf(c_41986,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(sK5(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X0,X2))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_41683]) ).
tcf(c_41987,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(sK5(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X0))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_41683]) ).
tcf(c_41988,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(sK5(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X2,X0))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_41683]) ).
tcf(c_41989,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(sK5(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X0,X2))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_41683]) ).
tcf(c_41990,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(sK5(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X2,X0))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_41683]) ).
tcf(c_41992,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X1 )
| ( sK2(singleton(X3),X4,X1) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(singleton(X3),X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_41683]) ).
tcf(c_41993,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X3) = singleton(X4) )
| ( sK1(X1,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK2(X1,X3,singleton(X4))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_41683]) ).
tcf(c_41994,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X1 )
| ( sK3(X3,singleton(X4),X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,singleton(X4),X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_41683]) ).
tcf(c_41995,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X1) = singleton(X4) )
| ( sK1(X3,X1,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK3(X3,X1,singleton(X4))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_41683]) ).
tcf(c_41996,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK3(X3,X1,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_41683]) ).
tcf(c_41997,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK3(X3,X1,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_41683]) ).
tcf(c_41998,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK3(X3,X1,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_41683]) ).
tcf(c_41999,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X1,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK3(X3,X1,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_41683]) ).
tcf(c_42000,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK2(X1,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_41683]) ).
tcf(c_42001,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK2(X1,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_41683]) ).
tcf(c_42002,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK2(X1,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_41683]) ).
tcf(c_42003,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X1,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK2(X1,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_41683]) ).
tcf(c_42004,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_41683]) ).
tcf(c_42005,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_41683]) ).
tcf(c_42006,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_41683]) ).
tcf(c_42007,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_41683]) ).
tcf(c_42008,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_41683]) ).
tcf(c_42009,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_41683]) ).
tcf(c_42010,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_41683]) ).
tcf(c_42011,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_41683]) ).
tcf(c_42068,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(singleton(X3),X1,unordered_pair(unordered_pair(X0,X3),singleton(X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2900]) ).
tcf(c_42069,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2900]) ).
tcf(c_42070,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2900]) ).
tcf(c_42071,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2900]) ).
tcf(c_42072,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2900]) ).
tcf(c_42073,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2900]) ).
tcf(c_42074,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK5(X1,X4,unordered_pair(unordered_pair(X3,sK4(X1,X2,X0)),singleton(sK4(X1,X2,X0)))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2900]) ).
tcf(c_42075,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK5(X2,X4,unordered_pair(unordered_pair(X3,sK5(X1,X2,X0)),singleton(sK5(X1,X2,X0)))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2900]) ).
tcf(c_42076,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK5(cartesian_product2(X3,X1),X5,unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2900]) ).
tcf(c_42077,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK5(cartesian_product2(X1,X3),X5,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))),singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2900]) ).
tcf(c_42078,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK5(cartesian_product2(X1,X3),X5,unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2900]) ).
tcf(c_42079,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK5(cartesian_product2(X1,X3),X5,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))),singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2900]) ).
tcf(c_42080,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK5(cartesian_product2(X3,X1),X5,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))),singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2900]) ).
tcf(c_42081,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK5(cartesian_product2(X3,X1),X5,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))),singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2900]) ).
tcf(c_42083,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(singleton(X4),X5,X3)),singleton(sK1(singleton(X4),X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2900]) ).
tcf(c_42084,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,singleton(X5))),singleton(sK2(X3,X4,singleton(X5))))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2900]) ).
tcf(c_42085,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,singleton(X5),X3)),singleton(sK1(X4,singleton(X5),X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2900]) ).
tcf(c_42086,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,singleton(X5))),singleton(sK3(X4,X3,singleton(X5))))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2900]) ).
tcf(c_42087,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2900]) ).
tcf(c_42088,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2900]) ).
tcf(c_42089,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2900]) ).
tcf(c_42090,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2900]) ).
tcf(c_42091,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2900]) ).
tcf(c_42092,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2900]) ).
tcf(c_42093,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2900]) ).
tcf(c_42094,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2900]) ).
tcf(c_42095,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2900]) ).
tcf(c_42096,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2900]) ).
tcf(c_42097,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2900]) ).
tcf(c_42098,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2900]) ).
tcf(c_42099,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2900]) ).
tcf(c_42100,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2900]) ).
tcf(c_42101,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2900]) ).
tcf(c_42102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2900]) ).
tcf(c_42175,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X1),sK3(X3,X4,X1)),singleton(sK2(X3,X4,X1))) = sK1(X3,X4,X1) )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_42068]) ).
tcf(c_42176,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X1),X4)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_42068]) ).
tcf(c_42177,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X1),X3)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_42068]) ).
tcf(c_42178,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X1,X3,X4),X4)
| ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_42068]) ).
tcf(c_42179,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X1,X4),X4)
| ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_42068]) ).
tcf(c_42180,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X1,unordered_pair(singleton(X3),unordered_pair(sK5(singleton(X4),X1,unordered_pair(unordered_pair(sK4(X1,X2,X0),X4),singleton(X4))),X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_42068]) ).
tcf(c_42181,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X2,unordered_pair(singleton(X3),unordered_pair(sK5(singleton(X4),X2,unordered_pair(unordered_pair(sK5(X1,X2,X0),X4),singleton(X4))),X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_42068]) ).
tcf(c_42182,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(sK5(singleton(X5),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5),singleton(X5))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_42068]) ).
tcf(c_42183,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(sK5(singleton(X5),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5),singleton(X5))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_42068]) ).
tcf(c_42184,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(sK5(singleton(X5),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5),singleton(X5))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_42068]) ).
tcf(c_42185,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(sK5(singleton(X5),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5),singleton(X5))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_42068]) ).
tcf(c_42186,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(sK5(singleton(X5),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5),singleton(X5))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_42068]) ).
tcf(c_42187,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(sK5(singleton(X5),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5),singleton(X5))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_42068]) ).
tcf(c_42189,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X1 )
| ( sK2(singleton(X3),X4,X1) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(singleton(X3),X4,X1),X2),singleton(X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_42068]) ).
tcf(c_42190,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X3) = singleton(X4) )
| ( sK1(X1,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK2(X1,X3,singleton(X4)),X2),singleton(X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_42068]) ).
tcf(c_42191,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X1 )
| ( sK3(X3,singleton(X4),X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,singleton(X4),X1),X2),singleton(X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_42068]) ).
tcf(c_42192,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X1) = singleton(X4) )
| ( sK1(X3,X1,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK3(X3,X1,singleton(X4)),X2),singleton(X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_42068]) ).
tcf(c_42193,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_42068]) ).
tcf(c_42194,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_42068]) ).
tcf(c_42195,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_42068]) ).
tcf(c_42196,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X1,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_42068]) ).
tcf(c_42197,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_42068]) ).
tcf(c_42198,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_42068]) ).
tcf(c_42199,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_42068]) ).
tcf(c_42200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X1,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_42068]) ).
tcf(c_42201,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_42068]) ).
tcf(c_42202,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_42068]) ).
tcf(c_42203,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_42068]) ).
tcf(c_42204,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_42068]) ).
tcf(c_42205,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_42068]) ).
tcf(c_42206,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_42068]) ).
tcf(c_42207,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_42068]) ).
tcf(c_42208,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_42068]) ).
tcf(c_42396,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(singleton(X3),X1,unordered_pair(singleton(X3),unordered_pair(X0,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2901]) ).
tcf(c_42397,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2901]) ).
tcf(c_42398,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2901]) ).
tcf(c_42399,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2901]) ).
tcf(c_42400,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2901]) ).
tcf(c_42401,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2901]) ).
tcf(c_42402,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK5(X1,X4,unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(X3,sK4(X1,X2,X0)))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2901]) ).
tcf(c_42403,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK5(X2,X4,unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(X3,sK5(X1,X2,X0)))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2901]) ).
tcf(c_42404,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK5(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2901]) ).
tcf(c_42405,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK5(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2901]) ).
tcf(c_42406,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK5(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2901]) ).
tcf(c_42407,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK5(cartesian_product2(X1,X3),X5,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2901]) ).
tcf(c_42408,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK5(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2901]) ).
tcf(c_42409,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK5(cartesian_product2(X3,X1),X5,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2901]) ).
tcf(c_42411,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(singleton(X4),X5,X3)),unordered_pair(X0,sK1(singleton(X4),X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2901]) ).
tcf(c_42412,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,singleton(X5))),unordered_pair(X0,sK2(X3,X4,singleton(X5))))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2901]) ).
tcf(c_42413,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,singleton(X5),X3)),unordered_pair(X0,sK1(X4,singleton(X5),X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2901]) ).
tcf(c_42414,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,singleton(X5))),unordered_pair(X0,sK3(X4,X3,singleton(X5))))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2901]) ).
tcf(c_42415,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2901]) ).
tcf(c_42416,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2901]) ).
tcf(c_42417,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2901]) ).
tcf(c_42418,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2901]) ).
tcf(c_42419,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2901]) ).
tcf(c_42420,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2901]) ).
tcf(c_42421,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2901]) ).
tcf(c_42422,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2901]) ).
tcf(c_42423,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2901]) ).
tcf(c_42424,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2901]) ).
tcf(c_42425,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2901]) ).
tcf(c_42426,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2901]) ).
tcf(c_42427,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2901]) ).
tcf(c_42428,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2901]) ).
tcf(c_42429,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2901]) ).
tcf(c_42430,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2901]) ).
tcf(c_42432,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X1),sK3(X3,X4,X1)),singleton(sK2(X3,X4,X1))) = sK1(X3,X4,X1) )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_42396]) ).
tcf(c_42433,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X1),X4)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_42396]) ).
tcf(c_42434,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X1),X3)
| ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_42396]) ).
tcf(c_42435,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X1,X3,X4),X4)
| ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK2(X1,X3,X4),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_42396]) ).
tcf(c_42436,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X1,X4),X4)
| ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK3(X3,X1,X4),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_42396]) ).
tcf(c_42437,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X1,unordered_pair(singleton(X3),unordered_pair(sK5(singleton(X4),X1,unordered_pair(singleton(X4),unordered_pair(sK4(X1,X2,X0),X4))),X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_42396]) ).
tcf(c_42438,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),X2,unordered_pair(singleton(X3),unordered_pair(sK5(singleton(X4),X2,unordered_pair(singleton(X4),unordered_pair(sK5(X1,X2,X0),X4))),X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_42396]) ).
tcf(c_42439,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(sK5(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_42396]) ).
tcf(c_42440,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(sK5(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_42396]) ).
tcf(c_42441,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(sK5(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_42396]) ).
tcf(c_42442,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(sK5(singleton(X5),cartesian_product2(X1,X3),unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_42396]) ).
tcf(c_42443,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(sK5(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_42396]) ).
tcf(c_42444,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(sK5(singleton(X5),cartesian_product2(X3,X1),unordered_pair(singleton(X5),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_42396]) ).
tcf(c_42446,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X1 )
| ( sK2(singleton(X3),X4,X1) = X3 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(singleton(X3),X4,X1),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_42396]) ).
tcf(c_42447,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X3) = singleton(X4) )
| ( sK1(X1,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK2(X1,X3,singleton(X4)),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_42396]) ).
tcf(c_42448,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X1 )
| ( sK3(X3,singleton(X4),X1) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,singleton(X4),X1),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_42396]) ).
tcf(c_42449,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X1) = singleton(X4) )
| ( sK1(X3,X1,singleton(X4)) = X4 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK3(X3,X1,singleton(X4)),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_42396]) ).
tcf(c_42450,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK3(X3,X1,X4),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_42396]) ).
tcf(c_42451,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK3(X3,X1,X4),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_42396]) ).
tcf(c_42452,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK3(X3,X1,X4),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_42396]) ).
tcf(c_42453,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X1,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK3(X3,X1,X4),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_42396]) ).
tcf(c_42454,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK2(X1,X3,X4),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_42396]) ).
tcf(c_42455,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK2(X1,X3,X4),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_42396]) ).
tcf(c_42456,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK2(X1,X3,X4),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_42396]) ).
tcf(c_42457,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X1,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK2(X1,X3,X4),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_42396]) ).
tcf(c_42458,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_42396]) ).
tcf(c_42459,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_42396]) ).
tcf(c_42460,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_42396]) ).
tcf(c_42461,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_42396]) ).
tcf(c_42462,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X1),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_42396]) ).
tcf(c_42463,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_42396]) ).
tcf(c_42464,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_42396]) ).
tcf(c_42465,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X1)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_42396]) ).
tcf(c_42542,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),singleton(X3),unordered_pair(singleton(X2),unordered_pair(sK5(X1,singleton(X3),unordered_pair(singleton(X0),unordered_pair(X3,X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2902]) ).
tcf(c_42543,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2902]) ).
tcf(c_42544,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2902]) ).
tcf(c_42545,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2902]) ).
tcf(c_42546,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2902]) ).
tcf(c_42547,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2902]) ).
tcf(c_42548,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(singleton(X5),unordered_pair(sK5(X4,X1,unordered_pair(singleton(X3),unordered_pair(sK4(X1,X2,X0),X3))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2902]) ).
tcf(c_42549,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(singleton(X5),unordered_pair(sK5(X4,X2,unordered_pair(singleton(X3),unordered_pair(sK5(X1,X2,X0),X3))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2902]) ).
tcf(c_42550,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(singleton(X6),unordered_pair(sK5(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X4))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2902]) ).
tcf(c_42551,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(singleton(X6),unordered_pair(sK5(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X4))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2902]) ).
tcf(c_42552,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(singleton(X6),unordered_pair(sK5(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X4))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2902]) ).
tcf(c_42553,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(singleton(X6),unordered_pair(sK5(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X4))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2902]) ).
tcf(c_42554,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(singleton(X6),unordered_pair(sK5(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X4))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2902]) ).
tcf(c_42555,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(singleton(X6),unordered_pair(sK5(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X4))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2902]) ).
tcf(c_42557,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(singleton(X4),X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2902]) ).
tcf(c_42558,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,singleton(X5)),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2902]) ).
tcf(c_42559,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,singleton(X5),X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2902]) ).
tcf(c_42560,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,singleton(X5)),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2902]) ).
tcf(c_42561,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2902]) ).
tcf(c_42562,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2902]) ).
tcf(c_42563,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2902]) ).
tcf(c_42564,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2902]) ).
tcf(c_42565,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2902]) ).
tcf(c_42566,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2902]) ).
tcf(c_42567,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2902]) ).
tcf(c_42568,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2902]) ).
tcf(c_42569,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2902]) ).
tcf(c_42570,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2902]) ).
tcf(c_42571,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2902]) ).
tcf(c_42572,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2902]) ).
tcf(c_42573,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2902]) ).
tcf(c_42574,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2902]) ).
tcf(c_42575,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2902]) ).
tcf(c_42576,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2902]) ).
tcf(c_42718,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X2),sK3(X3,X4,X2)),singleton(sK2(X3,X4,X2))) = sK1(X3,X4,X2) )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_42542]) ).
tcf(c_42719,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X2),X4)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_42542]) ).
tcf(c_42720,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X2),X3)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_42542]) ).
tcf(c_42721,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X2,X3,X4),X4)
| ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(X1,sK2(X2,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_42542]) ).
tcf(c_42722,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X2,X4),X4)
| ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(X1,sK3(X3,X2,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_42542]) ).
tcf(c_42723,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(singleton(X3),unordered_pair(sK5(X1,singleton(X4),unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(X4,sK4(X1,X2,X0)))),X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_42542]) ).
tcf(c_42724,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(singleton(X3),unordered_pair(sK5(X2,singleton(X4),unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(X4,sK5(X1,X2,X0)))),X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_42542]) ).
tcf(c_42725,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(sK5(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X2))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_42542]) ).
tcf(c_42726,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(sK5(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X0,X2))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_42542]) ).
tcf(c_42727,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(sK5(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(X5,unordered_pair(unordered_pair(X2,X0),singleton(X0))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_42542]) ).
tcf(c_42728,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(sK5(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(X5,unordered_pair(singleton(X0),unordered_pair(X2,X0))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_42542]) ).
tcf(c_42729,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(sK5(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X0,X2))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_42542]) ).
tcf(c_42730,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(sK5(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(X5,unordered_pair(singleton(X2),unordered_pair(X2,X0))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_42542]) ).
tcf(c_42732,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X2 )
| ( sK2(singleton(X3),X4,X2) = X3 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(singleton(X3),X4,X2)),unordered_pair(X1,sK1(singleton(X3),X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_42542]) ).
tcf(c_42733,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK1(X2,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,singleton(X4))),unordered_pair(X1,sK2(X2,X3,singleton(X4))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_42542]) ).
tcf(c_42734,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X2 )
| ( sK3(X3,singleton(X4),X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,singleton(X4),X2)),unordered_pair(X1,sK1(X3,singleton(X4),X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_42542]) ).
tcf(c_42735,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X2) = singleton(X4) )
| ( sK1(X3,X2,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,singleton(X4))),unordered_pair(X1,sK3(X3,X2,singleton(X4))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_42542]) ).
tcf(c_42736,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(X1,sK3(X3,X2,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_42542]) ).
tcf(c_42737,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(X1,sK3(X3,X2,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_42542]) ).
tcf(c_42738,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(X1,sK3(X3,X2,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_42542]) ).
tcf(c_42739,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X2,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(X1,sK3(X3,X2,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_42542]) ).
tcf(c_42740,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(X1,sK2(X2,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_42542]) ).
tcf(c_42741,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(X1,sK2(X2,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_42542]) ).
tcf(c_42742,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(X1,sK2(X2,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_42542]) ).
tcf(c_42743,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X2,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(X1,sK2(X2,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_42542]) ).
tcf(c_42744,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_42542]) ).
tcf(c_42745,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_42542]) ).
tcf(c_42746,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_42542]) ).
tcf(c_42747,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_42542]) ).
tcf(c_42748,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_42542]) ).
tcf(c_42749,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_42542]) ).
tcf(c_42750,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_42542]) ).
tcf(c_42751,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_42542]) ).
tcf(c_42941,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK4(singleton(X2),singleton(X3),unordered_pair(singleton(X2),unordered_pair(sK5(X1,singleton(X3),unordered_pair(singleton(X0),unordered_pair(X0,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_2903]) ).
tcf(c_42942,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( unordered_pair(unordered_pair(sK2(X4,X5,X3),sK3(X4,X5,X3)),singleton(sK2(X4,X5,X3))) = sK1(X4,X5,X3) )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2903]) ).
tcf(c_42943,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,X3),X5)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2903]) ).
tcf(c_42944,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X3),X4)
| ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2903]) ).
tcf(c_42945,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X3,X4,X5),X5)
| ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2903]) ).
tcf(c_42946,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,X3,X5),X5)
| ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2903]) ).
tcf(c_42947,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X1,unordered_pair(singleton(X5),unordered_pair(sK5(X4,X1,unordered_pair(singleton(X3),unordered_pair(X3,sK4(X1,X2,X0)))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_2903]) ).
tcf(c_42948,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X5),X2,unordered_pair(singleton(X5),unordered_pair(sK5(X4,X2,unordered_pair(singleton(X3),unordered_pair(X3,sK5(X1,X2,X0)))),X5))) = X5 )
| ~ in(X3,X4)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_2903]) ).
tcf(c_42949,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(singleton(X6),unordered_pair(sK5(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_2903]) ).
tcf(c_42950,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(singleton(X6),unordered_pair(sK5(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_2903]) ).
tcf(c_42951,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(singleton(X6),unordered_pair(sK5(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_2903]) ).
tcf(c_42952,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X1,X3),unordered_pair(singleton(X6),unordered_pair(sK5(X5,cartesian_product2(X1,X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_2903]) ).
tcf(c_42953,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(singleton(X6),unordered_pair(sK5(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_2903]) ).
tcf(c_42954,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( sK4(singleton(X6),cartesian_product2(X3,X1),unordered_pair(singleton(X6),unordered_pair(sK5(X5,cartesian_product2(X3,X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))))),X6))) = X6 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_2903]) ).
tcf(c_42956,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X3 )
| ( sK2(singleton(X4),X5,X3) = X4 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(singleton(X4),X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2903]) ).
tcf(c_42957,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X5) )
| ( sK1(X3,X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,singleton(X5))))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2903]) ).
tcf(c_42958,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X3 )
| ( sK3(X4,singleton(X5),X3) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,singleton(X5),X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2903]) ).
tcf(c_42959,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X3) = singleton(X5) )
| ( sK1(X4,X3,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,singleton(X5))))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2903]) ).
tcf(c_42960,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2903]) ).
tcf(c_42961,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2903]) ).
tcf(c_42962,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2903]) ).
tcf(c_42963,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,X3,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2903]) ).
tcf(c_42964,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2903]) ).
tcf(c_42965,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2903]) ).
tcf(c_42966,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2903]) ).
tcf(c_42967,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X3,X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2903]) ).
tcf(c_42968,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2903]) ).
tcf(c_42969,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2903]) ).
tcf(c_42970,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2903]) ).
tcf(c_42971,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2903]) ).
tcf(c_42972,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,X3),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2903]) ).
tcf(c_42973,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2903]) ).
tcf(c_42974,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2903]) ).
tcf(c_42975,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,X3)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2903]) ).
tcf(c_43358,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( unordered_pair(unordered_pair(sK2(X3,X4,X2),sK3(X3,X4,X2)),singleton(sK2(X3,X4,X2))) = sK1(X3,X4,X2) )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_42941]) ).
tcf(c_43359,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X3,X4,X2),X4)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_42941]) ).
tcf(c_43360,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X2),X3)
| ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_42941]) ).
tcf(c_43361,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X2,X3,X4),X4)
| ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(sK2(X2,X3,X4),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_42941]) ).
tcf(c_43362,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK1(X3,X2,X4),X4)
| ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(sK3(X3,X2,X4),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_42941]) ).
tcf(c_43363,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(singleton(X3),unordered_pair(sK5(X1,singleton(X4),unordered_pair(singleton(sK4(X1,X2,X0)),unordered_pair(sK4(X1,X2,X0),X4))),X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_60,c_42941]) ).
tcf(c_43364,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK4(singleton(X3),singleton(X4),unordered_pair(singleton(X3),unordered_pair(sK5(X2,singleton(X4),unordered_pair(singleton(sK5(X1,X2,X0)),unordered_pair(sK5(X1,X2,X0),X4))),X3))) = X3 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_42941]) ).
tcf(c_43365,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(sK5(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X5))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_42941]) ).
tcf(c_43366,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(sK5(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X5))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_42941]) ).
tcf(c_43367,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(sK5(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X5))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_42941]) ).
tcf(c_43368,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(sK5(cartesian_product2(X1,X3),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X5))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_42941]) ).
tcf(c_43369,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(sK5(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X5))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_42941]) ).
tcf(c_43370,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),singleton(X5),unordered_pair(singleton(X4),unordered_pair(sK5(cartesian_product2(X3,X1),singleton(X5),unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X5))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_42941]) ).
tcf(c_43372,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = X2 )
| ( sK2(singleton(X3),X4,X2) = X3 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(singleton(X3),X4,X2)),unordered_pair(sK1(singleton(X3),X4,X2),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_42941]) ).
tcf(c_43373,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = singleton(X4) )
| ( sK1(X2,X3,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,singleton(X4))),unordered_pair(sK2(X2,X3,singleton(X4)),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_42941]) ).
tcf(c_43374,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = X2 )
| ( sK3(X3,singleton(X4),X2) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,singleton(X4),X2)),unordered_pair(sK1(X3,singleton(X4),X2),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_42941]) ).
tcf(c_43375,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,X2) = singleton(X4) )
| ( sK1(X3,X2,singleton(X4)) = X4 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,singleton(X4))),unordered_pair(sK3(X3,X2,singleton(X4)),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_42941]) ).
tcf(c_43376,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(sK3(X3,X2,X4),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_42941]) ).
tcf(c_43377,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(sK3(X3,X2,X4),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_42941]) ).
tcf(c_43378,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(sK3(X3,X2,X4),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_42941]) ).
tcf(c_43379,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X3,X2,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(sK3(X3,X2,X4),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_42941]) ).
tcf(c_43380,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(sK2(X2,X3,X4),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_42941]) ).
tcf(c_43381,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(sK2(X2,X3,X4),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_42941]) ).
tcf(c_43382,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(sK2(X2,X3,X4),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_42941]) ).
tcf(c_43383,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK1(X2,X3,X4)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(sK2(X2,X3,X4),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_42941]) ).
tcf(c_43384,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK2(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_42941]) ).
tcf(c_43385,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_42941]) ).
tcf(c_43386,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_42941]) ).
tcf(c_43387,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK2(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_42941]) ).
tcf(c_43388,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK3(X3,X4,X2),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_42941]) ).
tcf(c_43389,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_42941]) ).
tcf(c_43390,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_42941]) ).
tcf(c_43391,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK3(X3,X4,X2)),singleton(X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_42941]) ).
tcf(c_43588,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),sK3(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(sK2(X4,X5,cartesian_product2(singleton(X2),X3)))) = sK1(X4,X5,cartesian_product2(singleton(X2),X3)) )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0),singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2956]) ).
tcf(c_43589,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X5)
| ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0),singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2956]) ).
tcf(c_43590,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X4)
| ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0),singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2956]) ).
tcf(c_43591,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(sK2(cartesian_product2(singleton(X2),X3),X4,X5),X0),singleton(sK2(cartesian_product2(singleton(X2),X3),X4,X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2956]) ).
tcf(c_43592,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(sK3(X4,cartesian_product2(singleton(X2),X3),X5),X0),singleton(sK3(X4,cartesian_product2(singleton(X2),X3),X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2956]) ).
tcf(c_43593,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X1),X2,sK4(cartesian_product2(singleton(X1),X2),X5,unordered_pair(unordered_pair(sK4(cartesian_product2(singleton(X1),X2),X3,X0),X4),singleton(sK4(cartesian_product2(singleton(X1),X2),X3,X0))))) = X1 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(cartesian_product2(singleton(X1),X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_2956]) ).
tcf(c_43594,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X5,unordered_pair(unordered_pair(sK5(X1,cartesian_product2(singleton(X2),X3),X0),X4),singleton(sK5(X1,cartesian_product2(singleton(X2),X3),X0))))) = X2 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(X1,cartesian_product2(singleton(X2),X3))) ),
inference(superposition,[status(thm)],[c_61,c_2956]) ).
tcf(c_43595,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X1),X3,sK4(cartesian_product2(singleton(X1),X3),X5,unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X2),singleton(X0)),X4),singleton(unordered_pair(unordered_pair(X0,X2),singleton(X0)))))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_64,c_2956]) ).
tcf(c_43597,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X1),X3,sK4(cartesian_product2(singleton(X1),X3),X5,unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X4),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0)))))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_809,c_2956]) ).
tcf(c_43598,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X1),X3,sK4(cartesian_product2(singleton(X1),X3),X5,unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X4),singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0)))))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_882,c_2956]) ).
tcf(c_43600,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X1),X3,sK4(cartesian_product2(singleton(X1),X3),X5,unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X4),singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2)))))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_900,c_2956]) ).
tcf(c_43601,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(singleton(X4),X5) )
| ( sK2(singleton(X4),X5,cartesian_product2(singleton(X2),X3)) = X4 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(sK1(singleton(X4),X5,cartesian_product2(singleton(X2),X3)),X0),singleton(sK1(singleton(X4),X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2956]) ).
tcf(c_43602,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = singleton(X5) )
| ( sK1(cartesian_product2(singleton(X2),X3),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(sK2(cartesian_product2(singleton(X2),X3),X4,singleton(X5)),X0),singleton(sK2(cartesian_product2(singleton(X2),X3),X4,singleton(X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2956]) ).
tcf(c_43603,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,singleton(X5)) )
| ( sK3(X4,singleton(X5),cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(sK1(X4,singleton(X5),cartesian_product2(singleton(X2),X3)),X0),singleton(sK1(X4,singleton(X5),cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2956]) ).
tcf(c_43604,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(singleton(X2),X3),singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(sK3(X4,cartesian_product2(singleton(X2),X3),singleton(X5)),X0),singleton(sK3(X4,cartesian_product2(singleton(X2),X3),singleton(X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2956]) ).
tcf(c_43605,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(sK3(X4,cartesian_product2(singleton(X2),X3),X5),X0),singleton(sK3(X4,cartesian_product2(singleton(X2),X3),X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2956]) ).
tcf(c_43606,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(sK3(X4,cartesian_product2(singleton(X2),X3),X5),X0),singleton(sK3(X4,cartesian_product2(singleton(X2),X3),X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2956]) ).
tcf(c_43607,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(singleton(X2),X3),X5)))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(sK3(X4,cartesian_product2(singleton(X2),X3),X5),X0),singleton(sK3(X4,cartesian_product2(singleton(X2),X3),X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2956]) ).
tcf(c_43608,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(singleton(X2),X3),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(sK3(X4,cartesian_product2(singleton(X2),X3),X5),X0),singleton(sK3(X4,cartesian_product2(singleton(X2),X3),X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2956]) ).
tcf(c_43609,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(sK2(cartesian_product2(singleton(X2),X3),X4,X5),X0),singleton(sK2(cartesian_product2(singleton(X2),X3),X4,X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2956]) ).
tcf(c_43610,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(sK2(cartesian_product2(singleton(X2),X3),X4,X5),X0),singleton(sK2(cartesian_product2(singleton(X2),X3),X4,X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2956]) ).
tcf(c_43611,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(singleton(X2),X3),X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(sK2(cartesian_product2(singleton(X2),X3),X4,X5),X0),singleton(sK2(cartesian_product2(singleton(X2),X3),X4,X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2956]) ).
tcf(c_43612,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(singleton(X2),X3),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(sK2(cartesian_product2(singleton(X2),X3),X4,X5),X0),singleton(sK2(cartesian_product2(singleton(X2),X3),X4,X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2956]) ).
tcf(c_43613,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0),singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2956]) ).
tcf(c_43614,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0),singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2956]) ).
tcf(c_43615,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(singleton(X2),X3))))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0),singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2956]) ).
tcf(c_43616,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0),singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2956]) ).
tcf(c_43617,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0),singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2956]) ).
tcf(c_43618,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0),singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2956]) ).
tcf(c_43619,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(singleton(X2),X3))))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0),singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2956]) ).
tcf(c_43620,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0),singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2956]) ).
tcf(c_43706,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X2,X3) )
| ( sK4(singleton(X4),X5,sK5(X1,cartesian_product2(singleton(X4),X5),unordered_pair(unordered_pair(X0,sK1(X2,X3,cartesian_product2(singleton(X4),X5))),singleton(X0)))) = X4 )
| ( unordered_pair(unordered_pair(sK2(X2,X3,cartesian_product2(singleton(X4),X5)),sK3(X2,X3,cartesian_product2(singleton(X4),X5))),singleton(sK2(X2,X3,cartesian_product2(singleton(X4),X5)))) = sK1(X2,X3,cartesian_product2(singleton(X4),X5)) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_3012]) ).
tcf(c_43707,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X5)
| ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_3012]) ).
tcf(c_43708,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X4)
| ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_3012]) ).
tcf(c_43709,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(X0,sK2(cartesian_product2(singleton(X2),X3),X4,X5)),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_3012]) ).
tcf(c_43710,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(X0,sK3(X4,cartesian_product2(singleton(X2),X3),X5)),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_3012]) ).
tcf(c_43711,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X1),X2,sK5(X5,cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X4,sK4(cartesian_product2(singleton(X1),X2),X3,X0)),singleton(X4)))) = X1 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(cartesian_product2(singleton(X1),X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_3012]) ).
tcf(c_43712,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X2),X3,sK5(X5,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(X4,sK5(X1,cartesian_product2(singleton(X2),X3),X0)),singleton(X4)))) = X2 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(X1,cartesian_product2(singleton(X2),X3))) ),
inference(superposition,[status(thm)],[c_61,c_3012]) ).
tcf(c_43713,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X1),X3,sK5(X5,cartesian_product2(singleton(X1),X3),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X0,X2),singleton(X0))),singleton(X4)))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_64,c_3012]) ).
tcf(c_43715,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X1),X3,sK5(X5,cartesian_product2(singleton(X1),X3),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))),singleton(X4)))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_809,c_3012]) ).
tcf(c_43716,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X1),X3,sK5(X5,cartesian_product2(singleton(X1),X3),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))),singleton(X4)))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_882,c_3012]) ).
tcf(c_43718,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X1),X3,sK5(X5,cartesian_product2(singleton(X1),X3),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))),singleton(X4)))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_900,c_3012]) ).
tcf(c_43719,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(singleton(X4),X5) )
| ( sK2(singleton(X4),X5,cartesian_product2(singleton(X2),X3)) = X4 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(X0,sK1(singleton(X4),X5,cartesian_product2(singleton(X2),X3))),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_3012]) ).
tcf(c_43720,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = singleton(X5) )
| ( sK1(cartesian_product2(singleton(X2),X3),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(X0,sK2(cartesian_product2(singleton(X2),X3),X4,singleton(X5))),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_3012]) ).
tcf(c_43721,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,singleton(X5)) )
| ( sK3(X4,singleton(X5),cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(X0,sK1(X4,singleton(X5),cartesian_product2(singleton(X2),X3))),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_3012]) ).
tcf(c_43722,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(singleton(X2),X3),singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(X0,sK3(X4,cartesian_product2(singleton(X2),X3),singleton(X5))),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_3012]) ).
tcf(c_43723,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(X0,sK3(X4,cartesian_product2(singleton(X2),X3),X5)),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_3012]) ).
tcf(c_43724,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(X0,sK3(X4,cartesian_product2(singleton(X2),X3),X5)),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_3012]) ).
tcf(c_43725,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(singleton(X2),X3),X5)))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(X0,sK3(X4,cartesian_product2(singleton(X2),X3),X5)),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_3012]) ).
tcf(c_43726,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(singleton(X2),X3),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(X0,sK3(X4,cartesian_product2(singleton(X2),X3),X5)),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_3012]) ).
tcf(c_43727,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(X0,sK2(cartesian_product2(singleton(X2),X3),X4,X5)),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_3012]) ).
tcf(c_43728,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(X0,sK2(cartesian_product2(singleton(X2),X3),X4,X5)),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_3012]) ).
tcf(c_43729,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(singleton(X2),X3),X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(X0,sK2(cartesian_product2(singleton(X2),X3),X4,X5)),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_3012]) ).
tcf(c_43730,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(singleton(X2),X3),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(X0,sK2(cartesian_product2(singleton(X2),X3),X4,X5)),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_3012]) ).
tcf(c_43731,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_3012]) ).
tcf(c_43732,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_3012]) ).
tcf(c_43733,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(singleton(X2),X3))))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_3012]) ).
tcf(c_43734,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_3012]) ).
tcf(c_43735,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_3012]) ).
tcf(c_43736,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_3012]) ).
tcf(c_43737,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(singleton(X2),X3))))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_3012]) ).
tcf(c_43738,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_3012]) ).
tcf(c_43828,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,singleton(X3))),sK3(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(sK2(X4,X5,cartesian_product2(X2,singleton(X3))))) = sK1(X4,X5,cartesian_product2(X2,singleton(X3))) )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0),singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_3058]) ).
tcf(c_43829,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X2,singleton(X3))),X5)
| ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0),singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_3058]) ).
tcf(c_43830,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X2,singleton(X3))),X4)
| ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0),singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_3058]) ).
tcf(c_43831,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X2,singleton(X3)),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(sK2(cartesian_product2(X2,singleton(X3)),X4,X5),X0),singleton(sK2(cartesian_product2(X2,singleton(X3)),X4,X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_3058]) ).
tcf(c_43832,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X2,singleton(X3)),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(sK3(X4,cartesian_product2(X2,singleton(X3)),X5),X0),singleton(sK3(X4,cartesian_product2(X2,singleton(X3)),X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_3058]) ).
tcf(c_43833,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X1,singleton(X2),sK4(cartesian_product2(X1,singleton(X2)),X5,unordered_pair(unordered_pair(sK4(cartesian_product2(X1,singleton(X2)),X3,X0),X4),singleton(sK4(cartesian_product2(X1,singleton(X2)),X3,X0))))) = X2 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(cartesian_product2(X1,singleton(X2)),X3)) ),
inference(superposition,[status(thm)],[c_60,c_3058]) ).
tcf(c_43834,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X5,unordered_pair(unordered_pair(sK5(X1,cartesian_product2(X2,singleton(X3)),X0),X4),singleton(sK5(X1,cartesian_product2(X2,singleton(X3)),X0))))) = X3 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,singleton(X3)))) ),
inference(superposition,[status(thm)],[c_61,c_3058]) ).
tcf(c_43835,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X3,singleton(X1),sK4(cartesian_product2(X3,singleton(X1)),X5,unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X4),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2)))))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_64,c_3058]) ).
tcf(c_43837,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X3,singleton(X1),sK4(cartesian_product2(X3,singleton(X1)),X5,unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X2),singleton(X2)),X4),singleton(unordered_pair(unordered_pair(X0,X2),singleton(X2)))))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_809,c_3058]) ).
tcf(c_43838,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X3,singleton(X1),sK4(cartesian_product2(X3,singleton(X1)),X5,unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X4),singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2)))))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_882,c_3058]) ).
tcf(c_43840,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X3,singleton(X1),sK4(cartesian_product2(X3,singleton(X1)),X5,unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X4),singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0)))))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_900,c_3058]) ).
tcf(c_43841,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X2,singleton(X3)) )
| ( sK2(singleton(X4),X5,cartesian_product2(X2,singleton(X3))) = X4 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(sK1(singleton(X4),X5,cartesian_product2(X2,singleton(X3))),X0),singleton(sK1(singleton(X4),X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_3058]) ).
tcf(c_43842,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X2,singleton(X3)),X4,singleton(X5)) = X5 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(sK2(cartesian_product2(X2,singleton(X3)),X4,singleton(X5)),X0),singleton(sK2(cartesian_product2(X2,singleton(X3)),X4,singleton(X5)))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_3058]) ).
tcf(c_43843,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,singleton(X5)) )
| ( sK3(X4,singleton(X5),cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(sK1(X4,singleton(X5),cartesian_product2(X2,singleton(X3))),X0),singleton(sK1(X4,singleton(X5),cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_3058]) ).
tcf(c_43844,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X2,singleton(X3)),singleton(X5)) = X5 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(sK3(X4,cartesian_product2(X2,singleton(X3)),singleton(X5)),X0),singleton(sK3(X4,cartesian_product2(X2,singleton(X3)),singleton(X5)))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_3058]) ).
tcf(c_43845,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X2,singleton(X3)),X5),X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(sK3(X4,cartesian_product2(X2,singleton(X3)),X5),X0),singleton(sK3(X4,cartesian_product2(X2,singleton(X3)),X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_3058]) ).
tcf(c_43846,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X2,singleton(X3)),X5),X6),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(sK3(X4,cartesian_product2(X2,singleton(X3)),X5),X0),singleton(sK3(X4,cartesian_product2(X2,singleton(X3)),X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_3058]) ).
tcf(c_43847,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X2,singleton(X3)),X5)))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(sK3(X4,cartesian_product2(X2,singleton(X3)),X5),X0),singleton(sK3(X4,cartesian_product2(X2,singleton(X3)),X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_3058]) ).
tcf(c_43848,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X2,singleton(X3)),X5)),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(sK3(X4,cartesian_product2(X2,singleton(X3)),X5),X0),singleton(sK3(X4,cartesian_product2(X2,singleton(X3)),X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_3058]) ).
tcf(c_43849,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X2,singleton(X3)),X4,X5),X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(sK2(cartesian_product2(X2,singleton(X3)),X4,X5),X0),singleton(sK2(cartesian_product2(X2,singleton(X3)),X4,X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_3058]) ).
tcf(c_43850,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X2,singleton(X3)),X4,X5),X6),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(sK2(cartesian_product2(X2,singleton(X3)),X4,X5),X0),singleton(sK2(cartesian_product2(X2,singleton(X3)),X4,X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_3058]) ).
tcf(c_43851,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X2,singleton(X3)),X4,X5)))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(sK2(cartesian_product2(X2,singleton(X3)),X4,X5),X0),singleton(sK2(cartesian_product2(X2,singleton(X3)),X4,X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_3058]) ).
tcf(c_43852,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X2,singleton(X3)),X4,X5)),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(sK2(cartesian_product2(X2,singleton(X3)),X4,X5),X0),singleton(sK2(cartesian_product2(X2,singleton(X3)),X4,X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_3058]) ).
tcf(c_43853,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X2,singleton(X3))),X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0),singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_3058]) ).
tcf(c_43854,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,singleton(X3))),X6),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0),singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_3058]) ).
tcf(c_43855,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X2,singleton(X3)))))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0),singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_3058]) ).
tcf(c_43856,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0),singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_3058]) ).
tcf(c_43857,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X2,singleton(X3))),X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0),singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_3058]) ).
tcf(c_43858,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X2,singleton(X3))),X6),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0),singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_3058]) ).
tcf(c_43859,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X2,singleton(X3)))))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0),singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_3058]) ).
tcf(c_43860,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0),singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_3058]) ).
tcf(c_44109,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = cartesian_product2(X2,X3) )
| ( sK5(X4,singleton(X5),sK5(X1,cartesian_product2(X4,singleton(X5)),unordered_pair(unordered_pair(X0,sK1(X2,X3,cartesian_product2(X4,singleton(X5)))),singleton(X0)))) = X5 )
| ( unordered_pair(unordered_pair(sK2(X2,X3,cartesian_product2(X4,singleton(X5))),sK3(X2,X3,cartesian_product2(X4,singleton(X5)))),singleton(sK2(X2,X3,cartesian_product2(X4,singleton(X5))))) = sK1(X2,X3,cartesian_product2(X4,singleton(X5))) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_3137]) ).
tcf(c_44110,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X2,singleton(X3))),X5)
| ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_3137]) ).
tcf(c_44111,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X2,singleton(X3))),X4)
| ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_3137]) ).
tcf(c_44112,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X2,singleton(X3)),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(X0,sK2(cartesian_product2(X2,singleton(X3)),X4,X5)),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_3137]) ).
tcf(c_44113,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X2,singleton(X3)),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(X0,sK3(X4,cartesian_product2(X2,singleton(X3)),X5)),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_3137]) ).
tcf(c_44114,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X1,singleton(X2),sK5(X5,cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X4,sK4(cartesian_product2(X1,singleton(X2)),X3,X0)),singleton(X4)))) = X2 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(cartesian_product2(X1,singleton(X2)),X3)) ),
inference(superposition,[status(thm)],[c_60,c_3137]) ).
tcf(c_44115,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X2,singleton(X3),sK5(X5,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(X4,sK5(X1,cartesian_product2(X2,singleton(X3)),X0)),singleton(X4)))) = X3 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,singleton(X3)))) ),
inference(superposition,[status(thm)],[c_61,c_3137]) ).
tcf(c_44116,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X3,singleton(X1),sK5(X5,cartesian_product2(X3,singleton(X1)),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))),singleton(X4)))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_64,c_3137]) ).
tcf(c_44118,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X3,singleton(X1),sK5(X5,cartesian_product2(X3,singleton(X1)),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X0,X2),singleton(X2))),singleton(X4)))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_809,c_3137]) ).
tcf(c_44119,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X3,singleton(X1),sK5(X5,cartesian_product2(X3,singleton(X1)),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))),singleton(X4)))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_882,c_3137]) ).
tcf(c_44121,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X3,singleton(X1),sK5(X5,cartesian_product2(X3,singleton(X1)),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))),singleton(X4)))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_900,c_3137]) ).
tcf(c_44122,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X2,singleton(X3)) )
| ( sK2(singleton(X4),X5,cartesian_product2(X2,singleton(X3))) = X4 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(X0,sK1(singleton(X4),X5,cartesian_product2(X2,singleton(X3)))),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_3137]) ).
tcf(c_44123,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X2,singleton(X3)),X4,singleton(X5)) = X5 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(X0,sK2(cartesian_product2(X2,singleton(X3)),X4,singleton(X5))),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_3137]) ).
tcf(c_44124,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,singleton(X5)) )
| ( sK3(X4,singleton(X5),cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(X0,sK1(X4,singleton(X5),cartesian_product2(X2,singleton(X3)))),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_3137]) ).
tcf(c_44125,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X2,singleton(X3)),singleton(X5)) = X5 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(X0,sK3(X4,cartesian_product2(X2,singleton(X3)),singleton(X5))),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_3137]) ).
tcf(c_44126,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X2,singleton(X3)),X5),X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(X0,sK3(X4,cartesian_product2(X2,singleton(X3)),X5)),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_3137]) ).
tcf(c_44127,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X2,singleton(X3)),X5),X6),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(X0,sK3(X4,cartesian_product2(X2,singleton(X3)),X5)),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_3137]) ).
tcf(c_44128,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X2,singleton(X3)),X5)))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(X0,sK3(X4,cartesian_product2(X2,singleton(X3)),X5)),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_3137]) ).
tcf(c_44129,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X2,singleton(X3)),X5)),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(X0,sK3(X4,cartesian_product2(X2,singleton(X3)),X5)),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_3137]) ).
tcf(c_44130,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X2,singleton(X3)),X4,X5),X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(X0,sK2(cartesian_product2(X2,singleton(X3)),X4,X5)),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_3137]) ).
tcf(c_44131,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X2,singleton(X3)),X4,X5),X6),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(X0,sK2(cartesian_product2(X2,singleton(X3)),X4,X5)),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_3137]) ).
tcf(c_44132,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X2,singleton(X3)),X4,X5)))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(X0,sK2(cartesian_product2(X2,singleton(X3)),X4,X5)),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_3137]) ).
tcf(c_44133,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X2,singleton(X3)),X4,X5)),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(X0,sK2(cartesian_product2(X2,singleton(X3)),X4,X5)),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_3137]) ).
tcf(c_44134,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X2,singleton(X3))),X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_3137]) ).
tcf(c_44135,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,singleton(X3))),X6),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_3137]) ).
tcf(c_44136,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X2,singleton(X3)))))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_3137]) ).
tcf(c_44137,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_3137]) ).
tcf(c_44138,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X2,singleton(X3))),X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_3137]) ).
tcf(c_44139,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X2,singleton(X3))),X6),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_3137]) ).
tcf(c_44140,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X2,singleton(X3)))))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_3137]) ).
tcf(c_44141,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_3137]) ).
tcf(c_44251,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),sK3(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(sK2(X4,X5,cartesian_product2(singleton(X2),X3)))) = sK1(X4,X5,cartesian_product2(singleton(X2),X3)) )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2958]) ).
tcf(c_44252,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X5)
| ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2958]) ).
tcf(c_44253,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X4)
| ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2958]) ).
tcf(c_44254,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(X0,sK2(cartesian_product2(singleton(X2),X3),X4,X5)),singleton(sK2(cartesian_product2(singleton(X2),X3),X4,X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2958]) ).
tcf(c_44255,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(X0,sK3(X4,cartesian_product2(singleton(X2),X3),X5)),singleton(sK3(X4,cartesian_product2(singleton(X2),X3),X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2958]) ).
tcf(c_44256,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X1),X2,sK4(cartesian_product2(singleton(X1),X2),X5,unordered_pair(unordered_pair(X4,sK4(cartesian_product2(singleton(X1),X2),X3,X0)),singleton(sK4(cartesian_product2(singleton(X1),X2),X3,X0))))) = X1 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(cartesian_product2(singleton(X1),X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_2958]) ).
tcf(c_44257,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X5,unordered_pair(unordered_pair(X4,sK5(X1,cartesian_product2(singleton(X2),X3),X0)),singleton(sK5(X1,cartesian_product2(singleton(X2),X3),X0))))) = X2 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(X1,cartesian_product2(singleton(X2),X3))) ),
inference(superposition,[status(thm)],[c_61,c_2958]) ).
tcf(c_44258,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X1),X3,sK4(cartesian_product2(singleton(X1),X3),X5,unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X0,X2),singleton(X0))),singleton(unordered_pair(unordered_pair(X0,X2),singleton(X0)))))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_64,c_2958]) ).
tcf(c_44260,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X1),X3,sK4(cartesian_product2(singleton(X1),X3),X5,unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0))),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0)))))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_809,c_2958]) ).
tcf(c_44261,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X1),X3,sK4(cartesian_product2(singleton(X1),X3),X5,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0))),singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0)))))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_882,c_2958]) ).
tcf(c_44263,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X1),X3,sK4(cartesian_product2(singleton(X1),X3),X5,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2))),singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2)))))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_900,c_2958]) ).
tcf(c_44264,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(singleton(X4),X5) )
| ( sK2(singleton(X4),X5,cartesian_product2(singleton(X2),X3)) = X4 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(X0,sK1(singleton(X4),X5,cartesian_product2(singleton(X2),X3))),singleton(sK1(singleton(X4),X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2958]) ).
tcf(c_44265,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = singleton(X5) )
| ( sK1(cartesian_product2(singleton(X2),X3),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(X0,sK2(cartesian_product2(singleton(X2),X3),X4,singleton(X5))),singleton(sK2(cartesian_product2(singleton(X2),X3),X4,singleton(X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2958]) ).
tcf(c_44266,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,singleton(X5)) )
| ( sK3(X4,singleton(X5),cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(X0,sK1(X4,singleton(X5),cartesian_product2(singleton(X2),X3))),singleton(sK1(X4,singleton(X5),cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2958]) ).
tcf(c_44267,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(singleton(X2),X3),singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(X0,sK3(X4,cartesian_product2(singleton(X2),X3),singleton(X5))),singleton(sK3(X4,cartesian_product2(singleton(X2),X3),singleton(X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2958]) ).
tcf(c_44268,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(X0,sK3(X4,cartesian_product2(singleton(X2),X3),X5)),singleton(sK3(X4,cartesian_product2(singleton(X2),X3),X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2958]) ).
tcf(c_44269,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(X0,sK3(X4,cartesian_product2(singleton(X2),X3),X5)),singleton(sK3(X4,cartesian_product2(singleton(X2),X3),X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2958]) ).
tcf(c_44270,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(singleton(X2),X3),X5)))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(X0,sK3(X4,cartesian_product2(singleton(X2),X3),X5)),singleton(sK3(X4,cartesian_product2(singleton(X2),X3),X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2958]) ).
tcf(c_44271,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(singleton(X2),X3),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(X0,sK3(X4,cartesian_product2(singleton(X2),X3),X5)),singleton(sK3(X4,cartesian_product2(singleton(X2),X3),X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2958]) ).
tcf(c_44272,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(X0,sK2(cartesian_product2(singleton(X2),X3),X4,X5)),singleton(sK2(cartesian_product2(singleton(X2),X3),X4,X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2958]) ).
tcf(c_44273,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(X0,sK2(cartesian_product2(singleton(X2),X3),X4,X5)),singleton(sK2(cartesian_product2(singleton(X2),X3),X4,X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2958]) ).
tcf(c_44274,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(singleton(X2),X3),X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(X0,sK2(cartesian_product2(singleton(X2),X3),X4,X5)),singleton(sK2(cartesian_product2(singleton(X2),X3),X4,X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2958]) ).
tcf(c_44275,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(singleton(X2),X3),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(X0,sK2(cartesian_product2(singleton(X2),X3),X4,X5)),singleton(sK2(cartesian_product2(singleton(X2),X3),X4,X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2958]) ).
tcf(c_44276,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2958]) ).
tcf(c_44277,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2958]) ).
tcf(c_44278,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(singleton(X2),X3))))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2958]) ).
tcf(c_44279,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2958]) ).
tcf(c_44280,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2958]) ).
tcf(c_44281,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2958]) ).
tcf(c_44282,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(singleton(X2),X3))))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2958]) ).
tcf(c_44283,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2958]) ).
tcf(c_44320,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),sK3(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(sK2(X4,X5,cartesian_product2(singleton(X2),X3)))) = sK1(X4,X5,cartesian_product2(singleton(X2),X3)) )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3))),unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2959]) ).
tcf(c_44321,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X5)
| ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3))),unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2959]) ).
tcf(c_44322,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X4)
| ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3))),unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2959]) ).
tcf(c_44323,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK2(cartesian_product2(singleton(X2),X3),X4,X5)),unordered_pair(X0,sK2(cartesian_product2(singleton(X2),X3),X4,X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2959]) ).
tcf(c_44324,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK3(X4,cartesian_product2(singleton(X2),X3),X5)),unordered_pair(X0,sK3(X4,cartesian_product2(singleton(X2),X3),X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2959]) ).
tcf(c_44325,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X1),X2,sK4(cartesian_product2(singleton(X1),X2),X5,unordered_pair(singleton(sK4(cartesian_product2(singleton(X1),X2),X3,X0)),unordered_pair(X4,sK4(cartesian_product2(singleton(X1),X2),X3,X0))))) = X1 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(cartesian_product2(singleton(X1),X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_2959]) ).
tcf(c_44326,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X5,unordered_pair(singleton(sK5(X1,cartesian_product2(singleton(X2),X3),X0)),unordered_pair(X4,sK5(X1,cartesian_product2(singleton(X2),X3),X0))))) = X2 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(X1,cartesian_product2(singleton(X2),X3))) ),
inference(superposition,[status(thm)],[c_61,c_2959]) ).
tcf(c_44327,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X1),X3,sK4(cartesian_product2(singleton(X1),X3),X5,unordered_pair(singleton(unordered_pair(unordered_pair(X0,X2),singleton(X0))),unordered_pair(X4,unordered_pair(unordered_pair(X0,X2),singleton(X0)))))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_64,c_2959]) ).
tcf(c_44329,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X1),X3,sK4(cartesian_product2(singleton(X1),X3),X5,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0)))))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_809,c_2959]) ).
tcf(c_44330,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X1),X3,sK4(cartesian_product2(singleton(X1),X3),X5,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0)))))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_882,c_2959]) ).
tcf(c_44332,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X1),X3,sK4(cartesian_product2(singleton(X1),X3),X5,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2)))))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_900,c_2959]) ).
tcf(c_44333,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(singleton(X4),X5) )
| ( sK2(singleton(X4),X5,cartesian_product2(singleton(X2),X3)) = X4 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK1(singleton(X4),X5,cartesian_product2(singleton(X2),X3))),unordered_pair(X0,sK1(singleton(X4),X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2959]) ).
tcf(c_44334,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = singleton(X5) )
| ( sK1(cartesian_product2(singleton(X2),X3),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK2(cartesian_product2(singleton(X2),X3),X4,singleton(X5))),unordered_pair(X0,sK2(cartesian_product2(singleton(X2),X3),X4,singleton(X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2959]) ).
tcf(c_44335,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,singleton(X5)) )
| ( sK3(X4,singleton(X5),cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK1(X4,singleton(X5),cartesian_product2(singleton(X2),X3))),unordered_pair(X0,sK1(X4,singleton(X5),cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2959]) ).
tcf(c_44336,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(singleton(X2),X3),singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK3(X4,cartesian_product2(singleton(X2),X3),singleton(X5))),unordered_pair(X0,sK3(X4,cartesian_product2(singleton(X2),X3),singleton(X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2959]) ).
tcf(c_44337,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK3(X4,cartesian_product2(singleton(X2),X3),X5)),unordered_pair(X0,sK3(X4,cartesian_product2(singleton(X2),X3),X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2959]) ).
tcf(c_44338,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK3(X4,cartesian_product2(singleton(X2),X3),X5)),unordered_pair(X0,sK3(X4,cartesian_product2(singleton(X2),X3),X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2959]) ).
tcf(c_44339,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(singleton(X2),X3),X5)))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK3(X4,cartesian_product2(singleton(X2),X3),X5)),unordered_pair(X0,sK3(X4,cartesian_product2(singleton(X2),X3),X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2959]) ).
tcf(c_44340,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(singleton(X2),X3),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK3(X4,cartesian_product2(singleton(X2),X3),X5)),unordered_pair(X0,sK3(X4,cartesian_product2(singleton(X2),X3),X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2959]) ).
tcf(c_44341,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK2(cartesian_product2(singleton(X2),X3),X4,X5)),unordered_pair(X0,sK2(cartesian_product2(singleton(X2),X3),X4,X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2959]) ).
tcf(c_44342,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK2(cartesian_product2(singleton(X2),X3),X4,X5)),unordered_pair(X0,sK2(cartesian_product2(singleton(X2),X3),X4,X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2959]) ).
tcf(c_44343,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(singleton(X2),X3),X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK2(cartesian_product2(singleton(X2),X3),X4,X5)),unordered_pair(X0,sK2(cartesian_product2(singleton(X2),X3),X4,X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2959]) ).
tcf(c_44344,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(singleton(X2),X3),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK2(cartesian_product2(singleton(X2),X3),X4,X5)),unordered_pair(X0,sK2(cartesian_product2(singleton(X2),X3),X4,X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2959]) ).
tcf(c_44345,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3))),unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2959]) ).
tcf(c_44346,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3))),unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2959]) ).
tcf(c_44347,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(singleton(X2),X3))))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3))),unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2959]) ).
tcf(c_44348,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3))),unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2959]) ).
tcf(c_44349,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3))),unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2959]) ).
tcf(c_44350,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3))),unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2959]) ).
tcf(c_44351,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(singleton(X2),X3))))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3))),unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2959]) ).
tcf(c_44352,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3))),unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2959]) ).
tcf(c_44508,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),sK3(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(sK2(X4,X5,cartesian_product2(singleton(X2),X3)))) = sK1(X4,X5,cartesian_product2(singleton(X2),X3)) )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3))),unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_2961]) ).
tcf(c_44509,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X5)
| ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3))),unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2961]) ).
tcf(c_44510,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X4)
| ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3))),unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2961]) ).
tcf(c_44511,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK2(cartesian_product2(singleton(X2),X3),X4,X5)),unordered_pair(sK2(cartesian_product2(singleton(X2),X3),X4,X5),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_2961]) ).
tcf(c_44512,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK3(X4,cartesian_product2(singleton(X2),X3),X5)),unordered_pair(sK3(X4,cartesian_product2(singleton(X2),X3),X5),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_2961]) ).
tcf(c_44513,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X1),X2,sK4(cartesian_product2(singleton(X1),X2),X5,unordered_pair(singleton(sK4(cartesian_product2(singleton(X1),X2),X3,X0)),unordered_pair(sK4(cartesian_product2(singleton(X1),X2),X3,X0),X4)))) = X1 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(cartesian_product2(singleton(X1),X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_2961]) ).
tcf(c_44514,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X5,unordered_pair(singleton(sK5(X1,cartesian_product2(singleton(X2),X3),X0)),unordered_pair(sK5(X1,cartesian_product2(singleton(X2),X3),X0),X4)))) = X2 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(X1,cartesian_product2(singleton(X2),X3))) ),
inference(superposition,[status(thm)],[c_61,c_2961]) ).
tcf(c_44515,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X1),X3,sK4(cartesian_product2(singleton(X1),X3),X5,unordered_pair(singleton(unordered_pair(unordered_pair(X0,X2),singleton(X0))),unordered_pair(unordered_pair(unordered_pair(X0,X2),singleton(X0)),X4)))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_64,c_2961]) ).
tcf(c_44517,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X1),X3,sK4(cartesian_product2(singleton(X1),X3),X5,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X0))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X4)))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_809,c_2961]) ).
tcf(c_44518,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X1),X3,sK4(cartesian_product2(singleton(X1),X3),X5,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X4)))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_882,c_2961]) ).
tcf(c_44520,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X1),X3,sK4(cartesian_product2(singleton(X1),X3),X5,unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X4)))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_900,c_2961]) ).
tcf(c_44521,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(singleton(X4),X5) )
| ( sK2(singleton(X4),X5,cartesian_product2(singleton(X2),X3)) = X4 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK1(singleton(X4),X5,cartesian_product2(singleton(X2),X3))),unordered_pair(sK1(singleton(X4),X5,cartesian_product2(singleton(X2),X3)),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_2961]) ).
tcf(c_44522,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = singleton(X5) )
| ( sK1(cartesian_product2(singleton(X2),X3),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK2(cartesian_product2(singleton(X2),X3),X4,singleton(X5))),unordered_pair(sK2(cartesian_product2(singleton(X2),X3),X4,singleton(X5)),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_2961]) ).
tcf(c_44523,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,singleton(X5)) )
| ( sK3(X4,singleton(X5),cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK1(X4,singleton(X5),cartesian_product2(singleton(X2),X3))),unordered_pair(sK1(X4,singleton(X5),cartesian_product2(singleton(X2),X3)),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_2961]) ).
tcf(c_44524,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(singleton(X2),X3),singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK3(X4,cartesian_product2(singleton(X2),X3),singleton(X5))),unordered_pair(sK3(X4,cartesian_product2(singleton(X2),X3),singleton(X5)),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_2961]) ).
tcf(c_44525,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK3(X4,cartesian_product2(singleton(X2),X3),X5)),unordered_pair(sK3(X4,cartesian_product2(singleton(X2),X3),X5),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_2961]) ).
tcf(c_44526,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK3(X4,cartesian_product2(singleton(X2),X3),X5)),unordered_pair(sK3(X4,cartesian_product2(singleton(X2),X3),X5),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_2961]) ).
tcf(c_44527,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(singleton(X2),X3),X5)))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK3(X4,cartesian_product2(singleton(X2),X3),X5)),unordered_pair(sK3(X4,cartesian_product2(singleton(X2),X3),X5),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_2961]) ).
tcf(c_44528,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(singleton(X2),X3),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK3(X4,cartesian_product2(singleton(X2),X3),X5)),unordered_pair(sK3(X4,cartesian_product2(singleton(X2),X3),X5),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_2961]) ).
tcf(c_44529,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK2(cartesian_product2(singleton(X2),X3),X4,X5)),unordered_pair(sK2(cartesian_product2(singleton(X2),X3),X4,X5),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_2961]) ).
tcf(c_44530,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK2(cartesian_product2(singleton(X2),X3),X4,X5)),unordered_pair(sK2(cartesian_product2(singleton(X2),X3),X4,X5),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_2961]) ).
tcf(c_44531,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(singleton(X2),X3),X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK2(cartesian_product2(singleton(X2),X3),X4,X5)),unordered_pair(sK2(cartesian_product2(singleton(X2),X3),X4,X5),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_2961]) ).
tcf(c_44532,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(singleton(X2),X3),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK2(cartesian_product2(singleton(X2),X3),X4,X5)),unordered_pair(sK2(cartesian_product2(singleton(X2),X3),X4,X5),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_2961]) ).
tcf(c_44533,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3))),unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_2961]) ).
tcf(c_44534,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3))),unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_2961]) ).
tcf(c_44535,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(singleton(X2),X3))))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3))),unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_2961]) ).
tcf(c_44536,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3))),unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_2961]) ).
tcf(c_44537,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3))),unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_2961]) ).
tcf(c_44538,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3))),unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_2961]) ).
tcf(c_44539,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(singleton(X2),X3))))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3))),unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_2961]) ).
tcf(c_44540,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3))),unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_2961]) ).
tcf(c_44620,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X2,X3) )
| ( sK4(singleton(X4),X5,sK5(X1,cartesian_product2(singleton(X4),X5),unordered_pair(unordered_pair(sK1(X2,X3,cartesian_product2(singleton(X4),X5)),X0),singleton(X0)))) = X4 )
| ( unordered_pair(unordered_pair(sK2(X2,X3,cartesian_product2(singleton(X4),X5)),sK3(X2,X3,cartesian_product2(singleton(X4),X5))),singleton(sK2(X2,X3,cartesian_product2(singleton(X4),X5)))) = sK1(X2,X3,cartesian_product2(singleton(X4),X5)) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_3014]) ).
tcf(c_44621,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X5)
| ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_3014]) ).
tcf(c_44622,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X4)
| ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_3014]) ).
tcf(c_44623,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(sK2(cartesian_product2(singleton(X2),X3),X4,X5),X0),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_3014]) ).
tcf(c_44624,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(sK3(X4,cartesian_product2(singleton(X2),X3),X5),X0),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_3014]) ).
tcf(c_44625,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X1),X2,sK5(X5,cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(sK4(cartesian_product2(singleton(X1),X2),X3,X0),X4),singleton(X4)))) = X1 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(cartesian_product2(singleton(X1),X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_3014]) ).
tcf(c_44626,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X2),X3,sK5(X5,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(sK5(X1,cartesian_product2(singleton(X2),X3),X0),X4),singleton(X4)))) = X2 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(X1,cartesian_product2(singleton(X2),X3))) ),
inference(superposition,[status(thm)],[c_61,c_3014]) ).
tcf(c_44627,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X1),X3,sK5(X5,cartesian_product2(singleton(X1),X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X2),singleton(X0)),X4),singleton(X4)))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_64,c_3014]) ).
tcf(c_44629,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X1),X3,sK5(X5,cartesian_product2(singleton(X1),X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X4),singleton(X4)))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_809,c_3014]) ).
tcf(c_44630,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X1),X3,sK5(X5,cartesian_product2(singleton(X1),X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X4),singleton(X4)))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_882,c_3014]) ).
tcf(c_44632,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X1),X3,sK5(X5,cartesian_product2(singleton(X1),X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X4),singleton(X4)))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_900,c_3014]) ).
tcf(c_44633,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(singleton(X4),X5) )
| ( sK2(singleton(X4),X5,cartesian_product2(singleton(X2),X3)) = X4 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(sK1(singleton(X4),X5,cartesian_product2(singleton(X2),X3)),X0),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_3014]) ).
tcf(c_44634,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = singleton(X5) )
| ( sK1(cartesian_product2(singleton(X2),X3),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(sK2(cartesian_product2(singleton(X2),X3),X4,singleton(X5)),X0),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_3014]) ).
tcf(c_44635,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,singleton(X5)) )
| ( sK3(X4,singleton(X5),cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(sK1(X4,singleton(X5),cartesian_product2(singleton(X2),X3)),X0),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_3014]) ).
tcf(c_44636,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(singleton(X2),X3),singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(sK3(X4,cartesian_product2(singleton(X2),X3),singleton(X5)),X0),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_3014]) ).
tcf(c_44637,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(sK3(X4,cartesian_product2(singleton(X2),X3),X5),X0),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_3014]) ).
tcf(c_44638,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(sK3(X4,cartesian_product2(singleton(X2),X3),X5),X0),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_3014]) ).
tcf(c_44639,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(singleton(X2),X3),X5)))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(sK3(X4,cartesian_product2(singleton(X2),X3),X5),X0),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_3014]) ).
tcf(c_44640,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(singleton(X2),X3),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(sK3(X4,cartesian_product2(singleton(X2),X3),X5),X0),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_3014]) ).
tcf(c_44641,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(sK2(cartesian_product2(singleton(X2),X3),X4,X5),X0),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_3014]) ).
tcf(c_44642,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(sK2(cartesian_product2(singleton(X2),X3),X4,X5),X0),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_3014]) ).
tcf(c_44643,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(singleton(X2),X3),X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(sK2(cartesian_product2(singleton(X2),X3),X4,X5),X0),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_3014]) ).
tcf(c_44644,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(singleton(X2),X3),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(sK2(cartesian_product2(singleton(X2),X3),X4,X5),X0),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_3014]) ).
tcf(c_44645,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_3014]) ).
tcf(c_44646,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_3014]) ).
tcf(c_44647,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(singleton(X2),X3))))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_3014]) ).
tcf(c_44648,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_3014]) ).
tcf(c_44649,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_3014]) ).
tcf(c_44650,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_3014]) ).
tcf(c_44651,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(singleton(X2),X3))))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_3014]) ).
tcf(c_44652,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_3014]) ).
tcf(c_44735,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X2,X3) )
| ( sK4(singleton(X4),X5,sK5(X1,cartesian_product2(singleton(X4),X5),unordered_pair(singleton(X0),unordered_pair(sK1(X2,X3,cartesian_product2(singleton(X4),X5)),X0)))) = X4 )
| ( unordered_pair(unordered_pair(sK2(X2,X3,cartesian_product2(singleton(X4),X5)),sK3(X2,X3,cartesian_product2(singleton(X4),X5))),singleton(sK2(X2,X3,cartesian_product2(singleton(X4),X5)))) = sK1(X2,X3,cartesian_product2(singleton(X4),X5)) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_3015]) ).
tcf(c_44736,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X5)
| ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_3015]) ).
tcf(c_44737,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X4)
| ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_3015]) ).
tcf(c_44738,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(sK2(cartesian_product2(singleton(X2),X3),X4,X5),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_3015]) ).
tcf(c_44739,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(sK3(X4,cartesian_product2(singleton(X2),X3),X5),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_3015]) ).
tcf(c_44740,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X1),X2,sK5(X5,cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X4),unordered_pair(sK4(cartesian_product2(singleton(X1),X2),X3,X0),X4)))) = X1 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(cartesian_product2(singleton(X1),X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_3015]) ).
tcf(c_44741,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X2),X3,sK5(X5,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X4),unordered_pair(sK5(X1,cartesian_product2(singleton(X2),X3),X0),X4)))) = X2 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(X1,cartesian_product2(singleton(X2),X3))) ),
inference(superposition,[status(thm)],[c_61,c_3015]) ).
tcf(c_44742,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X1),X3,sK5(X5,cartesian_product2(singleton(X1),X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(X0,X2),singleton(X0)),X4)))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_64,c_3015]) ).
tcf(c_44744,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X1),X3,sK5(X5,cartesian_product2(singleton(X1),X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X0)),X4)))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_809,c_3015]) ).
tcf(c_44745,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X1),X3,sK5(X5,cartesian_product2(singleton(X1),X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X2,X0)),X4)))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_882,c_3015]) ).
tcf(c_44747,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X1),X3,sK5(X5,cartesian_product2(singleton(X1),X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X4)))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_900,c_3015]) ).
tcf(c_44748,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(singleton(X4),X5) )
| ( sK2(singleton(X4),X5,cartesian_product2(singleton(X2),X3)) = X4 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(sK1(singleton(X4),X5,cartesian_product2(singleton(X2),X3)),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_3015]) ).
tcf(c_44749,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = singleton(X5) )
| ( sK1(cartesian_product2(singleton(X2),X3),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(sK2(cartesian_product2(singleton(X2),X3),X4,singleton(X5)),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_3015]) ).
tcf(c_44750,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,singleton(X5)) )
| ( sK3(X4,singleton(X5),cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(sK1(X4,singleton(X5),cartesian_product2(singleton(X2),X3)),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_3015]) ).
tcf(c_44751,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(singleton(X2),X3),singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(sK3(X4,cartesian_product2(singleton(X2),X3),singleton(X5)),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_3015]) ).
tcf(c_44752,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(sK3(X4,cartesian_product2(singleton(X2),X3),X5),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_3015]) ).
tcf(c_44753,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(sK3(X4,cartesian_product2(singleton(X2),X3),X5),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_3015]) ).
tcf(c_44754,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(singleton(X2),X3),X5)))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(sK3(X4,cartesian_product2(singleton(X2),X3),X5),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_3015]) ).
tcf(c_44755,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(singleton(X2),X3),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(sK3(X4,cartesian_product2(singleton(X2),X3),X5),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_3015]) ).
tcf(c_44756,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(sK2(cartesian_product2(singleton(X2),X3),X4,X5),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_3015]) ).
tcf(c_44757,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(sK2(cartesian_product2(singleton(X2),X3),X4,X5),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_3015]) ).
tcf(c_44758,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(singleton(X2),X3),X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(sK2(cartesian_product2(singleton(X2),X3),X4,X5),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_3015]) ).
tcf(c_44759,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(singleton(X2),X3),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(sK2(cartesian_product2(singleton(X2),X3),X4,X5),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_3015]) ).
tcf(c_44760,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_3015]) ).
tcf(c_44761,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_3015]) ).
tcf(c_44762,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(singleton(X2),X3))))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_3015]) ).
tcf(c_44763,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_3015]) ).
tcf(c_44764,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_3015]) ).
tcf(c_44765,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_3015]) ).
tcf(c_44766,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(singleton(X2),X3))))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_3015]) ).
tcf(c_44767,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_3015]) ).
tcf(c_44844,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X2,X3) )
| ( sK4(singleton(X4),X5,sK5(X1,cartesian_product2(singleton(X4),X5),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X2,X3,cartesian_product2(singleton(X4),X5)))))) = X4 )
| ( unordered_pair(unordered_pair(sK2(X2,X3,cartesian_product2(singleton(X4),X5)),sK3(X2,X3,cartesian_product2(singleton(X4),X5))),singleton(sK2(X2,X3,cartesian_product2(singleton(X4),X5)))) = sK1(X2,X3,cartesian_product2(singleton(X4),X5)) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_3017]) ).
tcf(c_44845,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X5)
| ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_3017]) ).
tcf(c_44846,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X4)
| ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_3017]) ).
tcf(c_44847,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(X0,sK2(cartesian_product2(singleton(X2),X3),X4,X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_3017]) ).
tcf(c_44848,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,cartesian_product2(singleton(X2),X3),X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_3017]) ).
tcf(c_44849,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X1),X2,sK5(X5,cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X4),unordered_pair(X4,sK4(cartesian_product2(singleton(X1),X2),X3,X0))))) = X1 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(cartesian_product2(singleton(X1),X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_3017]) ).
tcf(c_44850,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X2),X3,sK5(X5,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X4),unordered_pair(X4,sK5(X1,cartesian_product2(singleton(X2),X3),X0))))) = X2 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(X1,cartesian_product2(singleton(X2),X3))) ),
inference(superposition,[status(thm)],[c_61,c_3017]) ).
tcf(c_44851,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X1),X3,sK5(X5,cartesian_product2(singleton(X1),X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(X0,X2),singleton(X0)))))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_64,c_3017]) ).
tcf(c_44853,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X1),X3,sK5(X5,cartesian_product2(singleton(X1),X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X0)))))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_809,c_3017]) ).
tcf(c_44854,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X1),X3,sK5(X5,cartesian_product2(singleton(X1),X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X2,X0)))))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_882,c_3017]) ).
tcf(c_44856,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X1),X3,sK5(X5,cartesian_product2(singleton(X1),X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X0),unordered_pair(X0,X2)))))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_900,c_3017]) ).
tcf(c_44857,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(singleton(X4),X5) )
| ( sK2(singleton(X4),X5,cartesian_product2(singleton(X2),X3)) = X4 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(X0,sK1(singleton(X4),X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_3017]) ).
tcf(c_44858,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = singleton(X5) )
| ( sK1(cartesian_product2(singleton(X2),X3),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(X0,sK2(cartesian_product2(singleton(X2),X3),X4,singleton(X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_3017]) ).
tcf(c_44859,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,singleton(X5)) )
| ( sK3(X4,singleton(X5),cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,singleton(X5),cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_3017]) ).
tcf(c_44860,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(singleton(X2),X3),singleton(X5)) = X5 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,cartesian_product2(singleton(X2),X3),singleton(X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_3017]) ).
tcf(c_44861,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,cartesian_product2(singleton(X2),X3),X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_3017]) ).
tcf(c_44862,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,cartesian_product2(singleton(X2),X3),X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_3017]) ).
tcf(c_44863,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(singleton(X2),X3),X5)))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,cartesian_product2(singleton(X2),X3),X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_3017]) ).
tcf(c_44864,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(singleton(X2),X3),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,cartesian_product2(singleton(X2),X3),X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_3017]) ).
tcf(c_44865,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(X0,sK2(cartesian_product2(singleton(X2),X3),X4,X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_3017]) ).
tcf(c_44866,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(X0,sK2(cartesian_product2(singleton(X2),X3),X4,X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_3017]) ).
tcf(c_44867,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(singleton(X2),X3),X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(X0,sK2(cartesian_product2(singleton(X2),X3),X4,X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_3017]) ).
tcf(c_44868,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(singleton(X2),X3),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(X0,sK2(cartesian_product2(singleton(X2),X3),X4,X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_3017]) ).
tcf(c_44869,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_3017]) ).
tcf(c_44870,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_3017]) ).
tcf(c_44871,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(singleton(X2),X3))))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_3017]) ).
tcf(c_44872,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_3017]) ).
tcf(c_44873,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_3017]) ).
tcf(c_44874,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_3017]) ).
tcf(c_44875,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(singleton(X2),X3))))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_3017]) ).
tcf(c_44876,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_3017]) ).
tcf(c_45121,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,singleton(X3))),sK3(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(sK2(X4,X5,cartesian_product2(X2,singleton(X3))))) = sK1(X4,X5,cartesian_product2(X2,singleton(X3))) )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_3060]) ).
tcf(c_45122,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X2,singleton(X3))),X5)
| ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_3060]) ).
tcf(c_45123,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X2,singleton(X3))),X4)
| ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_3060]) ).
tcf(c_45124,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X2,singleton(X3)),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(X0,sK2(cartesian_product2(X2,singleton(X3)),X4,X5)),singleton(sK2(cartesian_product2(X2,singleton(X3)),X4,X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_3060]) ).
tcf(c_45125,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X2,singleton(X3)),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(X0,sK3(X4,cartesian_product2(X2,singleton(X3)),X5)),singleton(sK3(X4,cartesian_product2(X2,singleton(X3)),X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_3060]) ).
tcf(c_45126,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X1,singleton(X2),sK4(cartesian_product2(X1,singleton(X2)),X5,unordered_pair(unordered_pair(X4,sK4(cartesian_product2(X1,singleton(X2)),X3,X0)),singleton(sK4(cartesian_product2(X1,singleton(X2)),X3,X0))))) = X2 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(cartesian_product2(X1,singleton(X2)),X3)) ),
inference(superposition,[status(thm)],[c_60,c_3060]) ).
tcf(c_45127,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X5,unordered_pair(unordered_pair(X4,sK5(X1,cartesian_product2(X2,singleton(X3)),X0)),singleton(sK5(X1,cartesian_product2(X2,singleton(X3)),X0))))) = X3 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,singleton(X3)))) ),
inference(superposition,[status(thm)],[c_61,c_3060]) ).
tcf(c_45128,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X3,singleton(X1),sK4(cartesian_product2(X3,singleton(X1)),X5,unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2))),singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2)))))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_64,c_3060]) ).
tcf(c_45130,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X3,singleton(X1),sK4(cartesian_product2(X3,singleton(X1)),X5,unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(X0,X2),singleton(X2))),singleton(unordered_pair(unordered_pair(X0,X2),singleton(X2)))))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_809,c_3060]) ).
tcf(c_45131,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X3,singleton(X1),sK4(cartesian_product2(X3,singleton(X1)),X5,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2))),singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2)))))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_882,c_3060]) ).
tcf(c_45133,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X3,singleton(X1),sK4(cartesian_product2(X3,singleton(X1)),X5,unordered_pair(unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0))),singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0)))))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_900,c_3060]) ).
tcf(c_45134,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X2,singleton(X3)) )
| ( sK2(singleton(X4),X5,cartesian_product2(X2,singleton(X3))) = X4 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(X0,sK1(singleton(X4),X5,cartesian_product2(X2,singleton(X3)))),singleton(sK1(singleton(X4),X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_3060]) ).
tcf(c_45135,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X2,singleton(X3)),X4,singleton(X5)) = X5 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(X0,sK2(cartesian_product2(X2,singleton(X3)),X4,singleton(X5))),singleton(sK2(cartesian_product2(X2,singleton(X3)),X4,singleton(X5)))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_3060]) ).
tcf(c_45136,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,singleton(X5)) )
| ( sK3(X4,singleton(X5),cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(X0,sK1(X4,singleton(X5),cartesian_product2(X2,singleton(X3)))),singleton(sK1(X4,singleton(X5),cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_3060]) ).
tcf(c_45137,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X2,singleton(X3)),singleton(X5)) = X5 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(X0,sK3(X4,cartesian_product2(X2,singleton(X3)),singleton(X5))),singleton(sK3(X4,cartesian_product2(X2,singleton(X3)),singleton(X5)))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_3060]) ).
tcf(c_45138,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X2,singleton(X3)),X5),X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(X0,sK3(X4,cartesian_product2(X2,singleton(X3)),X5)),singleton(sK3(X4,cartesian_product2(X2,singleton(X3)),X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_3060]) ).
tcf(c_45139,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X2,singleton(X3)),X5),X6),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(X0,sK3(X4,cartesian_product2(X2,singleton(X3)),X5)),singleton(sK3(X4,cartesian_product2(X2,singleton(X3)),X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_3060]) ).
tcf(c_45140,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X2,singleton(X3)),X5)))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(X0,sK3(X4,cartesian_product2(X2,singleton(X3)),X5)),singleton(sK3(X4,cartesian_product2(X2,singleton(X3)),X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_3060]) ).
tcf(c_45141,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X2,singleton(X3)),X5)),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(X0,sK3(X4,cartesian_product2(X2,singleton(X3)),X5)),singleton(sK3(X4,cartesian_product2(X2,singleton(X3)),X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_3060]) ).
tcf(c_45142,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X2,singleton(X3)),X4,X5),X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(X0,sK2(cartesian_product2(X2,singleton(X3)),X4,X5)),singleton(sK2(cartesian_product2(X2,singleton(X3)),X4,X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_3060]) ).
tcf(c_45143,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X2,singleton(X3)),X4,X5),X6),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(X0,sK2(cartesian_product2(X2,singleton(X3)),X4,X5)),singleton(sK2(cartesian_product2(X2,singleton(X3)),X4,X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_3060]) ).
tcf(c_45144,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X2,singleton(X3)),X4,X5)))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(X0,sK2(cartesian_product2(X2,singleton(X3)),X4,X5)),singleton(sK2(cartesian_product2(X2,singleton(X3)),X4,X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_3060]) ).
tcf(c_45145,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X2,singleton(X3)),X4,X5)),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(X0,sK2(cartesian_product2(X2,singleton(X3)),X4,X5)),singleton(sK2(cartesian_product2(X2,singleton(X3)),X4,X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_3060]) ).
tcf(c_45146,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X2,singleton(X3))),X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_3060]) ).
tcf(c_45147,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,singleton(X3))),X6),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_3060]) ).
tcf(c_45148,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X2,singleton(X3)))))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_3060]) ).
tcf(c_45149,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_3060]) ).
tcf(c_45150,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X2,singleton(X3))),X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_3060]) ).
tcf(c_45151,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X2,singleton(X3))),X6),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_3060]) ).
tcf(c_45152,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X2,singleton(X3)))))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_3060]) ).
tcf(c_45153,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_3060]) ).
tcf(c_45188,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,singleton(X3))),sK3(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(sK2(X4,X5,cartesian_product2(X2,singleton(X3))))) = sK1(X4,X5,cartesian_product2(X2,singleton(X3))) )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_3061]) ).
tcf(c_45189,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X2,singleton(X3))),X5)
| ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_3061]) ).
tcf(c_45190,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X2,singleton(X3))),X4)
| ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_3061]) ).
tcf(c_45191,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X2,singleton(X3)),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK2(cartesian_product2(X2,singleton(X3)),X4,X5)),unordered_pair(X0,sK2(cartesian_product2(X2,singleton(X3)),X4,X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_3061]) ).
tcf(c_45192,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X2,singleton(X3)),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK3(X4,cartesian_product2(X2,singleton(X3)),X5)),unordered_pair(X0,sK3(X4,cartesian_product2(X2,singleton(X3)),X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_3061]) ).
tcf(c_45193,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X1,singleton(X2),sK4(cartesian_product2(X1,singleton(X2)),X5,unordered_pair(singleton(sK4(cartesian_product2(X1,singleton(X2)),X3,X0)),unordered_pair(X4,sK4(cartesian_product2(X1,singleton(X2)),X3,X0))))) = X2 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(cartesian_product2(X1,singleton(X2)),X3)) ),
inference(superposition,[status(thm)],[c_60,c_3061]) ).
tcf(c_45194,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X5,unordered_pair(singleton(sK5(X1,cartesian_product2(X2,singleton(X3)),X0)),unordered_pair(X4,sK5(X1,cartesian_product2(X2,singleton(X3)),X0))))) = X3 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,singleton(X3)))) ),
inference(superposition,[status(thm)],[c_61,c_3061]) ).
tcf(c_45195,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X3,singleton(X1),sK4(cartesian_product2(X3,singleton(X1)),X5,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2)))))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_64,c_3061]) ).
tcf(c_45197,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X3,singleton(X1),sK4(cartesian_product2(X3,singleton(X1)),X5,unordered_pair(singleton(unordered_pair(unordered_pair(X0,X2),singleton(X2))),unordered_pair(X4,unordered_pair(unordered_pair(X0,X2),singleton(X2)))))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_809,c_3061]) ).
tcf(c_45198,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X3,singleton(X1),sK4(cartesian_product2(X3,singleton(X1)),X5,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2)))))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_882,c_3061]) ).
tcf(c_45200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X3,singleton(X1),sK4(cartesian_product2(X3,singleton(X1)),X5,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0)))))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_900,c_3061]) ).
tcf(c_45201,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X2,singleton(X3)) )
| ( sK2(singleton(X4),X5,cartesian_product2(X2,singleton(X3))) = X4 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK1(singleton(X4),X5,cartesian_product2(X2,singleton(X3)))),unordered_pair(X0,sK1(singleton(X4),X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_3061]) ).
tcf(c_45202,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X2,singleton(X3)),X4,singleton(X5)) = X5 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK2(cartesian_product2(X2,singleton(X3)),X4,singleton(X5))),unordered_pair(X0,sK2(cartesian_product2(X2,singleton(X3)),X4,singleton(X5)))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_3061]) ).
tcf(c_45203,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,singleton(X5)) )
| ( sK3(X4,singleton(X5),cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK1(X4,singleton(X5),cartesian_product2(X2,singleton(X3)))),unordered_pair(X0,sK1(X4,singleton(X5),cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_3061]) ).
tcf(c_45204,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X2,singleton(X3)),singleton(X5)) = X5 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK3(X4,cartesian_product2(X2,singleton(X3)),singleton(X5))),unordered_pair(X0,sK3(X4,cartesian_product2(X2,singleton(X3)),singleton(X5)))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_3061]) ).
tcf(c_45205,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X2,singleton(X3)),X5),X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK3(X4,cartesian_product2(X2,singleton(X3)),X5)),unordered_pair(X0,sK3(X4,cartesian_product2(X2,singleton(X3)),X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_3061]) ).
tcf(c_45206,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X2,singleton(X3)),X5),X6),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK3(X4,cartesian_product2(X2,singleton(X3)),X5)),unordered_pair(X0,sK3(X4,cartesian_product2(X2,singleton(X3)),X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_3061]) ).
tcf(c_45207,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X2,singleton(X3)),X5)))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK3(X4,cartesian_product2(X2,singleton(X3)),X5)),unordered_pair(X0,sK3(X4,cartesian_product2(X2,singleton(X3)),X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_3061]) ).
tcf(c_45208,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X2,singleton(X3)),X5)),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK3(X4,cartesian_product2(X2,singleton(X3)),X5)),unordered_pair(X0,sK3(X4,cartesian_product2(X2,singleton(X3)),X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_3061]) ).
tcf(c_45209,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X2,singleton(X3)),X4,X5),X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK2(cartesian_product2(X2,singleton(X3)),X4,X5)),unordered_pair(X0,sK2(cartesian_product2(X2,singleton(X3)),X4,X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_3061]) ).
tcf(c_45210,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X2,singleton(X3)),X4,X5),X6),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK2(cartesian_product2(X2,singleton(X3)),X4,X5)),unordered_pair(X0,sK2(cartesian_product2(X2,singleton(X3)),X4,X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_3061]) ).
tcf(c_45211,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X2,singleton(X3)),X4,X5)))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK2(cartesian_product2(X2,singleton(X3)),X4,X5)),unordered_pair(X0,sK2(cartesian_product2(X2,singleton(X3)),X4,X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_3061]) ).
tcf(c_45212,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X2,singleton(X3)),X4,X5)),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK2(cartesian_product2(X2,singleton(X3)),X4,X5)),unordered_pair(X0,sK2(cartesian_product2(X2,singleton(X3)),X4,X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_3061]) ).
tcf(c_45213,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X2,singleton(X3))),X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_3061]) ).
tcf(c_45214,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,singleton(X3))),X6),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_3061]) ).
tcf(c_45215,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X2,singleton(X3)))))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_3061]) ).
tcf(c_45216,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_3061]) ).
tcf(c_45217,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X2,singleton(X3))),X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_3061]) ).
tcf(c_45218,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X2,singleton(X3))),X6),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_3061]) ).
tcf(c_45219,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X2,singleton(X3)))))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_3061]) ).
tcf(c_45220,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_3061]) ).
tcf(c_45368,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,singleton(X3))),sK3(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(sK2(X4,X5,cartesian_product2(X2,singleton(X3))))) = sK1(X4,X5,cartesian_product2(X2,singleton(X3))) )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_3063]) ).
tcf(c_45369,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X2,singleton(X3))),X5)
| ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_3063]) ).
tcf(c_45370,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X2,singleton(X3))),X4)
| ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_3063]) ).
tcf(c_45371,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X2,singleton(X3)),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK2(cartesian_product2(X2,singleton(X3)),X4,X5)),unordered_pair(sK2(cartesian_product2(X2,singleton(X3)),X4,X5),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_3063]) ).
tcf(c_45372,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X2,singleton(X3)),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK3(X4,cartesian_product2(X2,singleton(X3)),X5)),unordered_pair(sK3(X4,cartesian_product2(X2,singleton(X3)),X5),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_3063]) ).
tcf(c_45373,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X1,singleton(X2),sK4(cartesian_product2(X1,singleton(X2)),X5,unordered_pair(singleton(sK4(cartesian_product2(X1,singleton(X2)),X3,X0)),unordered_pair(sK4(cartesian_product2(X1,singleton(X2)),X3,X0),X4)))) = X2 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(cartesian_product2(X1,singleton(X2)),X3)) ),
inference(superposition,[status(thm)],[c_60,c_3063]) ).
tcf(c_45374,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X5,unordered_pair(singleton(sK5(X1,cartesian_product2(X2,singleton(X3)),X0)),unordered_pair(sK5(X1,cartesian_product2(X2,singleton(X3)),X0),X4)))) = X3 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,singleton(X3)))) ),
inference(superposition,[status(thm)],[c_61,c_3063]) ).
tcf(c_45375,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X3,singleton(X1),sK4(cartesian_product2(X3,singleton(X1)),X5,unordered_pair(singleton(unordered_pair(unordered_pair(X2,X0),singleton(X2))),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X4)))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_64,c_3063]) ).
tcf(c_45377,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X3,singleton(X1),sK4(cartesian_product2(X3,singleton(X1)),X5,unordered_pair(singleton(unordered_pair(unordered_pair(X0,X2),singleton(X2))),unordered_pair(unordered_pair(unordered_pair(X0,X2),singleton(X2)),X4)))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_809,c_3063]) ).
tcf(c_45378,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X3,singleton(X1),sK4(cartesian_product2(X3,singleton(X1)),X5,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X0,X2))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X4)))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_882,c_3063]) ).
tcf(c_45380,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X3,singleton(X1),sK4(cartesian_product2(X3,singleton(X1)),X5,unordered_pair(singleton(unordered_pair(singleton(X2),unordered_pair(X2,X0))),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X4)))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_900,c_3063]) ).
tcf(c_45381,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X2,singleton(X3)) )
| ( sK2(singleton(X4),X5,cartesian_product2(X2,singleton(X3))) = X4 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK1(singleton(X4),X5,cartesian_product2(X2,singleton(X3)))),unordered_pair(sK1(singleton(X4),X5,cartesian_product2(X2,singleton(X3))),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_3063]) ).
tcf(c_45382,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X2,singleton(X3)),X4,singleton(X5)) = X5 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK2(cartesian_product2(X2,singleton(X3)),X4,singleton(X5))),unordered_pair(sK2(cartesian_product2(X2,singleton(X3)),X4,singleton(X5)),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_3063]) ).
tcf(c_45383,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,singleton(X5)) )
| ( sK3(X4,singleton(X5),cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK1(X4,singleton(X5),cartesian_product2(X2,singleton(X3)))),unordered_pair(sK1(X4,singleton(X5),cartesian_product2(X2,singleton(X3))),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_3063]) ).
tcf(c_45384,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X2,singleton(X3)),singleton(X5)) = X5 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK3(X4,cartesian_product2(X2,singleton(X3)),singleton(X5))),unordered_pair(sK3(X4,cartesian_product2(X2,singleton(X3)),singleton(X5)),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_3063]) ).
tcf(c_45385,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X2,singleton(X3)),X5),X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK3(X4,cartesian_product2(X2,singleton(X3)),X5)),unordered_pair(sK3(X4,cartesian_product2(X2,singleton(X3)),X5),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_3063]) ).
tcf(c_45386,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X2,singleton(X3)),X5),X6),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK3(X4,cartesian_product2(X2,singleton(X3)),X5)),unordered_pair(sK3(X4,cartesian_product2(X2,singleton(X3)),X5),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_3063]) ).
tcf(c_45387,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X2,singleton(X3)),X5)))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK3(X4,cartesian_product2(X2,singleton(X3)),X5)),unordered_pair(sK3(X4,cartesian_product2(X2,singleton(X3)),X5),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_3063]) ).
tcf(c_45388,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X2,singleton(X3)),X5)),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK3(X4,cartesian_product2(X2,singleton(X3)),X5)),unordered_pair(sK3(X4,cartesian_product2(X2,singleton(X3)),X5),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_3063]) ).
tcf(c_45389,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X2,singleton(X3)),X4,X5),X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK2(cartesian_product2(X2,singleton(X3)),X4,X5)),unordered_pair(sK2(cartesian_product2(X2,singleton(X3)),X4,X5),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_3063]) ).
tcf(c_45390,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X2,singleton(X3)),X4,X5),X6),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK2(cartesian_product2(X2,singleton(X3)),X4,X5)),unordered_pair(sK2(cartesian_product2(X2,singleton(X3)),X4,X5),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_3063]) ).
tcf(c_45391,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X2,singleton(X3)),X4,X5)))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK2(cartesian_product2(X2,singleton(X3)),X4,X5)),unordered_pair(sK2(cartesian_product2(X2,singleton(X3)),X4,X5),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_3063]) ).
tcf(c_45392,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X2,singleton(X3)),X4,X5)),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK2(cartesian_product2(X2,singleton(X3)),X4,X5)),unordered_pair(sK2(cartesian_product2(X2,singleton(X3)),X4,X5),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_3063]) ).
tcf(c_45393,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X2,singleton(X3))),X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_3063]) ).
tcf(c_45394,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,singleton(X3))),X6),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_3063]) ).
tcf(c_45395,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X2,singleton(X3)))))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_3063]) ).
tcf(c_45396,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_3063]) ).
tcf(c_45397,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X2,singleton(X3))),X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_3063]) ).
tcf(c_45398,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X2,singleton(X3))),X6),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_3063]) ).
tcf(c_45399,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X2,singleton(X3)))))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_3063]) ).
tcf(c_45400,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_3063]) ).
tcf(c_45596,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = cartesian_product2(X2,X3) )
| ( sK5(X4,singleton(X5),sK5(X1,cartesian_product2(X4,singleton(X5)),unordered_pair(unordered_pair(sK1(X2,X3,cartesian_product2(X4,singleton(X5))),X0),singleton(X0)))) = X5 )
| ( unordered_pair(unordered_pair(sK2(X2,X3,cartesian_product2(X4,singleton(X5))),sK3(X2,X3,cartesian_product2(X4,singleton(X5)))),singleton(sK2(X2,X3,cartesian_product2(X4,singleton(X5))))) = sK1(X2,X3,cartesian_product2(X4,singleton(X5))) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_3139]) ).
tcf(c_45597,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X2,singleton(X3))),X5)
| ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_3139]) ).
tcf(c_45598,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X2,singleton(X3))),X4)
| ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_3139]) ).
tcf(c_45599,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X2,singleton(X3)),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(sK2(cartesian_product2(X2,singleton(X3)),X4,X5),X0),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_3139]) ).
tcf(c_45600,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X2,singleton(X3)),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(sK3(X4,cartesian_product2(X2,singleton(X3)),X5),X0),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_3139]) ).
tcf(c_45601,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X1,singleton(X2),sK5(X5,cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(sK4(cartesian_product2(X1,singleton(X2)),X3,X0),X4),singleton(X4)))) = X2 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(cartesian_product2(X1,singleton(X2)),X3)) ),
inference(superposition,[status(thm)],[c_60,c_3139]) ).
tcf(c_45602,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X2,singleton(X3),sK5(X5,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(sK5(X1,cartesian_product2(X2,singleton(X3)),X0),X4),singleton(X4)))) = X3 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,singleton(X3)))) ),
inference(superposition,[status(thm)],[c_61,c_3139]) ).
tcf(c_45603,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X3,singleton(X1),sK5(X5,cartesian_product2(X3,singleton(X1)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X4),singleton(X4)))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_64,c_3139]) ).
tcf(c_45605,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X3,singleton(X1),sK5(X5,cartesian_product2(X3,singleton(X1)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X2),singleton(X2)),X4),singleton(X4)))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_809,c_3139]) ).
tcf(c_45606,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X3,singleton(X1),sK5(X5,cartesian_product2(X3,singleton(X1)),unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X4),singleton(X4)))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_882,c_3139]) ).
tcf(c_45608,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X3,singleton(X1),sK5(X5,cartesian_product2(X3,singleton(X1)),unordered_pair(unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X4),singleton(X4)))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_900,c_3139]) ).
tcf(c_45609,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X2,singleton(X3)) )
| ( sK2(singleton(X4),X5,cartesian_product2(X2,singleton(X3))) = X4 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(sK1(singleton(X4),X5,cartesian_product2(X2,singleton(X3))),X0),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_3139]) ).
tcf(c_45610,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X2,singleton(X3)),X4,singleton(X5)) = X5 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(sK2(cartesian_product2(X2,singleton(X3)),X4,singleton(X5)),X0),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_3139]) ).
tcf(c_45611,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,singleton(X5)) )
| ( sK3(X4,singleton(X5),cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(sK1(X4,singleton(X5),cartesian_product2(X2,singleton(X3))),X0),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_3139]) ).
tcf(c_45612,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X2,singleton(X3)),singleton(X5)) = X5 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(sK3(X4,cartesian_product2(X2,singleton(X3)),singleton(X5)),X0),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_3139]) ).
tcf(c_45613,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X2,singleton(X3)),X5),X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(sK3(X4,cartesian_product2(X2,singleton(X3)),X5),X0),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_3139]) ).
tcf(c_45614,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X2,singleton(X3)),X5),X6),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(sK3(X4,cartesian_product2(X2,singleton(X3)),X5),X0),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_3139]) ).
tcf(c_45615,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X2,singleton(X3)),X5)))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(sK3(X4,cartesian_product2(X2,singleton(X3)),X5),X0),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_3139]) ).
tcf(c_45616,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X2,singleton(X3)),X5)),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(sK3(X4,cartesian_product2(X2,singleton(X3)),X5),X0),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_3139]) ).
tcf(c_45617,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X2,singleton(X3)),X4,X5),X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(sK2(cartesian_product2(X2,singleton(X3)),X4,X5),X0),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_3139]) ).
tcf(c_45618,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X2,singleton(X3)),X4,X5),X6),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(sK2(cartesian_product2(X2,singleton(X3)),X4,X5),X0),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_3139]) ).
tcf(c_45619,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X2,singleton(X3)),X4,X5)))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(sK2(cartesian_product2(X2,singleton(X3)),X4,X5),X0),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_3139]) ).
tcf(c_45620,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X2,singleton(X3)),X4,X5)),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(sK2(cartesian_product2(X2,singleton(X3)),X4,X5),X0),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_3139]) ).
tcf(c_45621,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X2,singleton(X3))),X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_3139]) ).
tcf(c_45622,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,singleton(X3))),X6),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_3139]) ).
tcf(c_45623,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X2,singleton(X3)))))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_3139]) ).
tcf(c_45624,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_3139]) ).
tcf(c_45625,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X2,singleton(X3))),X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_3139]) ).
tcf(c_45626,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X2,singleton(X3))),X6),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_3139]) ).
tcf(c_45627,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X2,singleton(X3)))))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_3139]) ).
tcf(c_45628,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0),singleton(X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_3139]) ).
tcf(c_45718,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = cartesian_product2(X2,X3) )
| ( sK5(X4,singleton(X5),sK5(X1,cartesian_product2(X4,singleton(X5)),unordered_pair(singleton(X0),unordered_pair(sK1(X2,X3,cartesian_product2(X4,singleton(X5))),X0)))) = X5 )
| ( unordered_pair(unordered_pair(sK2(X2,X3,cartesian_product2(X4,singleton(X5))),sK3(X2,X3,cartesian_product2(X4,singleton(X5)))),singleton(sK2(X2,X3,cartesian_product2(X4,singleton(X5))))) = sK1(X2,X3,cartesian_product2(X4,singleton(X5))) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_3140]) ).
tcf(c_45719,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X2,singleton(X3))),X5)
| ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_3140]) ).
tcf(c_45720,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X2,singleton(X3))),X4)
| ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_3140]) ).
tcf(c_45721,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X2,singleton(X3)),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(sK2(cartesian_product2(X2,singleton(X3)),X4,X5),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_3140]) ).
tcf(c_45722,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X2,singleton(X3)),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(sK3(X4,cartesian_product2(X2,singleton(X3)),X5),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_3140]) ).
tcf(c_45723,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X1,singleton(X2),sK5(X5,cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X4),unordered_pair(sK4(cartesian_product2(X1,singleton(X2)),X3,X0),X4)))) = X2 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(cartesian_product2(X1,singleton(X2)),X3)) ),
inference(superposition,[status(thm)],[c_60,c_3140]) ).
tcf(c_45724,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X2,singleton(X3),sK5(X5,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X4),unordered_pair(sK5(X1,cartesian_product2(X2,singleton(X3)),X0),X4)))) = X3 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,singleton(X3)))) ),
inference(superposition,[status(thm)],[c_61,c_3140]) ).
tcf(c_45725,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X3,singleton(X1),sK5(X5,cartesian_product2(X3,singleton(X1)),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X4)))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_64,c_3140]) ).
tcf(c_45727,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X3,singleton(X1),sK5(X5,cartesian_product2(X3,singleton(X1)),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(X0,X2),singleton(X2)),X4)))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_809,c_3140]) ).
tcf(c_45728,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X3,singleton(X1),sK5(X5,cartesian_product2(X3,singleton(X1)),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X4)))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_882,c_3140]) ).
tcf(c_45730,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X3,singleton(X1),sK5(X5,cartesian_product2(X3,singleton(X1)),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X4)))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_900,c_3140]) ).
tcf(c_45731,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X2,singleton(X3)) )
| ( sK2(singleton(X4),X5,cartesian_product2(X2,singleton(X3))) = X4 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(sK1(singleton(X4),X5,cartesian_product2(X2,singleton(X3))),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_3140]) ).
tcf(c_45732,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X2,singleton(X3)),X4,singleton(X5)) = X5 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(sK2(cartesian_product2(X2,singleton(X3)),X4,singleton(X5)),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_3140]) ).
tcf(c_45733,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,singleton(X5)) )
| ( sK3(X4,singleton(X5),cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(sK1(X4,singleton(X5),cartesian_product2(X2,singleton(X3))),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_3140]) ).
tcf(c_45734,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X2,singleton(X3)),singleton(X5)) = X5 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(sK3(X4,cartesian_product2(X2,singleton(X3)),singleton(X5)),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_3140]) ).
tcf(c_45735,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X2,singleton(X3)),X5),X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(sK3(X4,cartesian_product2(X2,singleton(X3)),X5),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_3140]) ).
tcf(c_45736,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X2,singleton(X3)),X5),X6),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(sK3(X4,cartesian_product2(X2,singleton(X3)),X5),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_3140]) ).
tcf(c_45737,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X2,singleton(X3)),X5)))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(sK3(X4,cartesian_product2(X2,singleton(X3)),X5),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_3140]) ).
tcf(c_45738,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X2,singleton(X3)),X5)),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(sK3(X4,cartesian_product2(X2,singleton(X3)),X5),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_3140]) ).
tcf(c_45739,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X2,singleton(X3)),X4,X5),X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(sK2(cartesian_product2(X2,singleton(X3)),X4,X5),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_3140]) ).
tcf(c_45740,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X2,singleton(X3)),X4,X5),X6),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(sK2(cartesian_product2(X2,singleton(X3)),X4,X5),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_3140]) ).
tcf(c_45741,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X2,singleton(X3)),X4,X5)))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(sK2(cartesian_product2(X2,singleton(X3)),X4,X5),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_3140]) ).
tcf(c_45742,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X2,singleton(X3)),X4,X5)),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(sK2(cartesian_product2(X2,singleton(X3)),X4,X5),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_3140]) ).
tcf(c_45743,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X2,singleton(X3))),X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_3140]) ).
tcf(c_45744,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,singleton(X3))),X6),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_3140]) ).
tcf(c_45745,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X2,singleton(X3)))))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_3140]) ).
tcf(c_45746,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_3140]) ).
tcf(c_45747,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X2,singleton(X3))),X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_3140]) ).
tcf(c_45748,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X2,singleton(X3))),X6),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_3140]) ).
tcf(c_45749,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X2,singleton(X3)))))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_3140]) ).
tcf(c_45750,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_3140]) ).
tcf(c_45937,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = cartesian_product2(X2,X3) )
| ( sK5(X4,singleton(X5),sK5(X1,cartesian_product2(X4,singleton(X5)),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X2,X3,cartesian_product2(X4,singleton(X5))))))) = X5 )
| ( unordered_pair(unordered_pair(sK2(X2,X3,cartesian_product2(X4,singleton(X5))),sK3(X2,X3,cartesian_product2(X4,singleton(X5)))),singleton(sK2(X2,X3,cartesian_product2(X4,singleton(X5))))) = sK1(X2,X3,cartesian_product2(X4,singleton(X5))) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_3142]) ).
tcf(c_45938,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X2,singleton(X3))),X5)
| ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_3142]) ).
tcf(c_45939,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X2,singleton(X3))),X4)
| ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_3142]) ).
tcf(c_45940,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X2,singleton(X3)),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(X0,sK2(cartesian_product2(X2,singleton(X3)),X4,X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_3142]) ).
tcf(c_45941,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X2,singleton(X3)),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,cartesian_product2(X2,singleton(X3)),X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_3142]) ).
tcf(c_45942,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X1,singleton(X2),sK5(X5,cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X4),unordered_pair(X4,sK4(cartesian_product2(X1,singleton(X2)),X3,X0))))) = X2 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(cartesian_product2(X1,singleton(X2)),X3)) ),
inference(superposition,[status(thm)],[c_60,c_3142]) ).
tcf(c_45943,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X2,singleton(X3),sK5(X5,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X4),unordered_pair(X4,sK5(X1,cartesian_product2(X2,singleton(X3)),X0))))) = X3 )
| ~ in(X4,X5)
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,singleton(X3)))) ),
inference(superposition,[status(thm)],[c_61,c_3142]) ).
tcf(c_45944,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X3,singleton(X1),sK5(X5,cartesian_product2(X3,singleton(X1)),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(X2,X0),singleton(X2)))))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_64,c_3142]) ).
tcf(c_45946,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X3,singleton(X1),sK5(X5,cartesian_product2(X3,singleton(X1)),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(X0,X2),singleton(X2)))))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_809,c_3142]) ).
tcf(c_45947,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X3,singleton(X1),sK5(X5,cartesian_product2(X3,singleton(X1)),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X0,X2)))))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_882,c_3142]) ).
tcf(c_45949,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK5(X3,singleton(X1),sK5(X5,cartesian_product2(X3,singleton(X1)),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X2),unordered_pair(X2,X0)))))) = X1 )
| ~ in(X4,X5)
| ~ in(X2,X3)
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_900,c_3142]) ).
tcf(c_45950,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X2,singleton(X3)) )
| ( sK2(singleton(X4),X5,cartesian_product2(X2,singleton(X3))) = X4 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(X0,sK1(singleton(X4),X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_799,c_3142]) ).
tcf(c_45951,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X2,singleton(X3)),X4,singleton(X5)) = X5 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(X0,sK2(cartesian_product2(X2,singleton(X3)),X4,singleton(X5)))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_800,c_3142]) ).
tcf(c_45952,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,singleton(X5)) )
| ( sK3(X4,singleton(X5),cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,singleton(X5),cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_803,c_3142]) ).
tcf(c_45953,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X2,singleton(X3)),singleton(X5)) = X5 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,cartesian_product2(X2,singleton(X3)),singleton(X5)))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_804,c_3142]) ).
tcf(c_45954,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X2,singleton(X3)),X5),X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,cartesian_product2(X2,singleton(X3)),X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2454,c_3142]) ).
tcf(c_45955,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X2,singleton(X3)),X5),X6),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,cartesian_product2(X2,singleton(X3)),X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1852,c_3142]) ).
tcf(c_45956,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X2,singleton(X3)),X5)))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,cartesian_product2(X2,singleton(X3)),X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1564,c_3142]) ).
tcf(c_45957,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X2,singleton(X3)),X5)),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,cartesian_product2(X2,singleton(X3)),X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1145,c_3142]) ).
tcf(c_45958,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X2,singleton(X3)),X4,X5),X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(X0,sK2(cartesian_product2(X2,singleton(X3)),X4,X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2455,c_3142]) ).
tcf(c_45959,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X2,singleton(X3)),X4,X5),X6),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(X0,sK2(cartesian_product2(X2,singleton(X3)),X4,X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1853,c_3142]) ).
tcf(c_45960,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X2,singleton(X3)),X4,X5)))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(X0,sK2(cartesian_product2(X2,singleton(X3)),X4,X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1565,c_3142]) ).
tcf(c_45961,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X2,singleton(X3)),X4,X5)),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(X0,sK2(cartesian_product2(X2,singleton(X3)),X4,X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1146,c_3142]) ).
tcf(c_45962,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X2,singleton(X3))),X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2456,c_3142]) ).
tcf(c_45963,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,singleton(X3))),X6),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1854,c_3142]) ).
tcf(c_45964,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X2,singleton(X3)))))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1566,c_3142]) ).
tcf(c_45965,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_3142]) ).
tcf(c_45966,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X2,singleton(X3))),X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2457,c_3142]) ).
tcf(c_45967,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X2,singleton(X3))),X6),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1855,c_3142]) ).
tcf(c_45968,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X2,singleton(X3)))))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1567,c_3142]) ).
tcf(c_45969,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(X6))) = X6 )
| ( sK5(X2,singleton(X3),sK5(X1,cartesian_product2(X2,singleton(X3)),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1148,c_3142]) ).
tcf(c_46196,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),sK3(X4,X5,cartesian_product2(X2,X3))),singleton(sK2(X4,X5,cartesian_product2(X2,X3)))) = sK1(X4,X5,cartesian_product2(X2,X3)) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_5395]) ).
tcf(c_46197,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X2,X3)),X5)
| ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_5395]) ).
tcf(c_46198,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X2,X3)),X4)
| ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_5395]) ).
tcf(c_46199,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X2,X3),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_5395]) ).
tcf(c_46200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X2,X3),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_5395]) ).
tcf(c_46201,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0))))),singleton(X4))) = X4 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_5395]) ).
tcf(c_46202,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X2),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0))))),singleton(X4))) = X4 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_61,c_5395]) ).
tcf(c_46203,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_5395]) ).
tcf(c_46204,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_5395]) ).
tcf(c_46205,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_5395]) ).
tcf(c_46206,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_5395]) ).
tcf(c_46207,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_5395]) ).
tcf(c_46208,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_5395]) ).
tcf(c_46209,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X2,X3) )
| ( sK2(singleton(X4),X5,cartesian_product2(X2,X3)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(singleton(X4),X5,cartesian_product2(X2,X3)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_5395]) ).
tcf(c_46210,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X2,X3),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,singleton(X5)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_5395]) ).
tcf(c_46211,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = cartesian_product2(X2,X3) )
| ( sK3(X4,singleton(X5),cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,singleton(X5),cartesian_product2(X2,X3)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_5395]) ).
tcf(c_46212,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X2,X3),singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),singleton(X5)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_5395]) ).
tcf(c_46213,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_5395]) ).
tcf(c_46214,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_5395]) ).
tcf(c_46215,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X2,X3),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_5395]) ).
tcf(c_46216,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X2,X3),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_5395]) ).
tcf(c_46217,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_5395]) ).
tcf(c_46218,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_5395]) ).
tcf(c_46219,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X2,X3),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_5395]) ).
tcf(c_46220,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X2,X3),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_5395]) ).
tcf(c_46221,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_5395]) ).
tcf(c_46222,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_5395]) ).
tcf(c_46223,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_5395]) ).
tcf(c_46224,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X2,X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_5395]) ).
tcf(c_46225,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X2,X3)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_5395]) ).
tcf(c_46226,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X2,X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_5395]) ).
tcf(c_46227,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_5395]) ).
tcf(c_46228,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X2,X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_5395]) ).
tcf(c_46562,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),sK3(X4,X5,cartesian_product2(X3,X2))),singleton(sK2(X4,X5,cartesian_product2(X3,X2)))) = sK1(X4,X5,cartesian_product2(X3,X2)) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_5396]) ).
tcf(c_46563,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X3,X2)),X5)
| ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_5396]) ).
tcf(c_46564,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X3,X2)),X4)
| ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_5396]) ).
tcf(c_46565,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X3,X2),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_5396]) ).
tcf(c_46566,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X3,X2),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_5396]) ).
tcf(c_46567,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X2),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0))))),singleton(X4))) = X4 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_5396]) ).
tcf(c_46568,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0))))),singleton(X4))) = X4 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_61,c_5396]) ).
tcf(c_46569,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_5396]) ).
tcf(c_46570,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_5396]) ).
tcf(c_46571,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_5396]) ).
tcf(c_46572,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_5396]) ).
tcf(c_46573,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_5396]) ).
tcf(c_46574,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0)))))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_5396]) ).
tcf(c_46575,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X3,X2) )
| ( sK2(singleton(X4),X5,cartesian_product2(X3,X2)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(singleton(X4),X5,cartesian_product2(X3,X2)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_5396]) ).
tcf(c_46576,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X3,X2),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,singleton(X5)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_5396]) ).
tcf(c_46577,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = cartesian_product2(X3,X2) )
| ( sK3(X4,singleton(X5),cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,singleton(X5),cartesian_product2(X3,X2)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_5396]) ).
tcf(c_46578,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X3,X2),singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),singleton(X5)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_5396]) ).
tcf(c_46579,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_5396]) ).
tcf(c_46580,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_5396]) ).
tcf(c_46581,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X3,X2),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_5396]) ).
tcf(c_46582,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X3,X2),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_5396]) ).
tcf(c_46583,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_5396]) ).
tcf(c_46584,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_5396]) ).
tcf(c_46585,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X3,X2),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_5396]) ).
tcf(c_46586,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X3,X2),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_5396]) ).
tcf(c_46587,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_5396]) ).
tcf(c_46588,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_5396]) ).
tcf(c_46589,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_5396]) ).
tcf(c_46590,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,X2))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_5396]) ).
tcf(c_46591,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X3,X2)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_5396]) ).
tcf(c_46592,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,X2)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_5396]) ).
tcf(c_46593,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_5396]) ).
tcf(c_46594,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,X2))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_5396]) ).
tcf(c_46979,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),sK3(X4,X5,cartesian_product2(X2,X3))),singleton(sK2(X4,X5,cartesian_product2(X2,X3)))) = sK1(X4,X5,cartesian_product2(X2,X3)) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_5641]) ).
tcf(c_46980,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X2,X3)),X5)
| ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_5641]) ).
tcf(c_46981,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X2,X3)),X4)
| ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_5641]) ).
tcf(c_46982,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X2,X3),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_5641]) ).
tcf(c_46983,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X2,X3),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_5641]) ).
tcf(c_46984,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0)),X5),singleton(X5))),singleton(X4))) = X4 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_5641]) ).
tcf(c_46985,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X2),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(sK4(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0)),X5),singleton(X5))),singleton(X4))) = X4 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_61,c_5641]) ).
tcf(c_46986,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2))),X5),singleton(X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_5641]) ).
tcf(c_46987,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2))),X5),singleton(X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_5641]) ).
tcf(c_46988,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0))),X5),singleton(X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_5641]) ).
tcf(c_46989,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0))),X5),singleton(X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_5641]) ).
tcf(c_46990,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2))),X5),singleton(X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_5641]) ).
tcf(c_46991,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0))),X5),singleton(X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_5641]) ).
tcf(c_46992,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X2,X3) )
| ( sK2(singleton(X4),X5,cartesian_product2(X2,X3)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK1(singleton(X4),X5,cartesian_product2(X2,X3))),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_5641]) ).
tcf(c_46993,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X2,X3),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,singleton(X5))),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_5641]) ).
tcf(c_46994,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = cartesian_product2(X2,X3) )
| ( sK3(X4,singleton(X5),cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,singleton(X5),cartesian_product2(X2,X3))),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_5641]) ).
tcf(c_46995,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X2,X3),singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),singleton(X5))),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_5641]) ).
tcf(c_46996,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_5641]) ).
tcf(c_46997,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_5641]) ).
tcf(c_46998,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X2,X3),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_5641]) ).
tcf(c_46999,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X2,X3),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_5641]) ).
tcf(c_47000,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_5641]) ).
tcf(c_47001,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_5641]) ).
tcf(c_47002,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X2,X3),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_5641]) ).
tcf(c_47003,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X2,X3),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_5641]) ).
tcf(c_47004,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_5641]) ).
tcf(c_47005,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_5641]) ).
tcf(c_47006,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_5641]) ).
tcf(c_47007,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X2,X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_5641]) ).
tcf(c_47008,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X2,X3)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_5641]) ).
tcf(c_47009,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X2,X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_5641]) ).
tcf(c_47010,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_5641]) ).
tcf(c_47011,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X2,X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_5641]) ).
tcf(c_47171,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),sK3(X4,X5,cartesian_product2(X3,X2))),singleton(sK2(X4,X5,cartesian_product2(X3,X2)))) = sK1(X4,X5,cartesian_product2(X3,X2)) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_5642]) ).
tcf(c_47172,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X3,X2)),X5)
| ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_5642]) ).
tcf(c_47173,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X3,X2)),X4)
| ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_5642]) ).
tcf(c_47174,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X3,X2),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_5642]) ).
tcf(c_47175,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X3,X2),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_5642]) ).
tcf(c_47176,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X2),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(sK5(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0)),X5),singleton(X5))),singleton(X4))) = X4 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_5642]) ).
tcf(c_47177,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(sK5(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0)),X5),singleton(X5))),singleton(X4))) = X4 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_61,c_5642]) ).
tcf(c_47178,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2))),X5),singleton(X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_5642]) ).
tcf(c_47179,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2))),X5),singleton(X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_5642]) ).
tcf(c_47180,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0))),X5),singleton(X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_5642]) ).
tcf(c_47181,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0))),X5),singleton(X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_5642]) ).
tcf(c_47182,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2))),X5),singleton(X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_5642]) ).
tcf(c_47183,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(X4,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0))),X5),singleton(X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_5642]) ).
tcf(c_47184,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X3,X2) )
| ( sK2(singleton(X4),X5,cartesian_product2(X3,X2)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK1(singleton(X4),X5,cartesian_product2(X3,X2))),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_5642]) ).
tcf(c_47185,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X3,X2),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,singleton(X5))),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_5642]) ).
tcf(c_47186,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = cartesian_product2(X3,X2) )
| ( sK3(X4,singleton(X5),cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,singleton(X5),cartesian_product2(X3,X2))),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_5642]) ).
tcf(c_47187,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X3,X2),singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),singleton(X5))),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_5642]) ).
tcf(c_47188,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_5642]) ).
tcf(c_47189,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_5642]) ).
tcf(c_47190,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X3,X2),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_5642]) ).
tcf(c_47191,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X3,X2),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_5642]) ).
tcf(c_47192,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_5642]) ).
tcf(c_47193,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_5642]) ).
tcf(c_47194,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X3,X2),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_5642]) ).
tcf(c_47195,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X3,X2),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_5642]) ).
tcf(c_47196,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_5642]) ).
tcf(c_47197,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_5642]) ).
tcf(c_47198,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_5642]) ).
tcf(c_47199,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,X2))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_5642]) ).
tcf(c_47200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X3,X2)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_5642]) ).
tcf(c_47201,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,X2)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_5642]) ).
tcf(c_47202,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_5642]) ).
tcf(c_47203,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,X2))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_5642]) ).
tcf(c_47306,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),sK3(X4,X5,cartesian_product2(X2,X3))),singleton(sK2(X4,X5,cartesian_product2(X2,X3)))) = sK1(X4,X5,cartesian_product2(X2,X3)) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_5824]) ).
tcf(c_47307,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X2,X3)),X5)
| ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_5824]) ).
tcf(c_47308,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X2,X3)),X4)
| ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_5824]) ).
tcf(c_47309,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X2,X3),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_5824]) ).
tcf(c_47310,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X2,X3),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_5824]) ).
tcf(c_47311,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0)),X5))),singleton(X4))) = X4 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_5824]) ).
tcf(c_47312,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X2),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(sK4(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0)),X5))),singleton(X4))) = X4 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_61,c_5824]) ).
tcf(c_47313,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2))),X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_5824]) ).
tcf(c_47314,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2))),X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_5824]) ).
tcf(c_47315,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0))),X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_5824]) ).
tcf(c_47316,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0))),X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_5824]) ).
tcf(c_47317,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2))),X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_5824]) ).
tcf(c_47318,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0))),X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_5824]) ).
tcf(c_47319,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X2,X3) )
| ( sK2(singleton(X4),X5,cartesian_product2(X2,X3)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(singleton(X4),X5,cartesian_product2(X2,X3))),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_5824]) ).
tcf(c_47320,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X2,X3),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,singleton(X5))),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_5824]) ).
tcf(c_47321,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = cartesian_product2(X2,X3) )
| ( sK3(X4,singleton(X5),cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,singleton(X5),cartesian_product2(X2,X3))),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_5824]) ).
tcf(c_47322,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X2,X3),singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),singleton(X5))),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_5824]) ).
tcf(c_47323,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_5824]) ).
tcf(c_47324,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_5824]) ).
tcf(c_47325,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X2,X3),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_5824]) ).
tcf(c_47326,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X2,X3),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_5824]) ).
tcf(c_47327,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_5824]) ).
tcf(c_47328,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_5824]) ).
tcf(c_47329,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X2,X3),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_5824]) ).
tcf(c_47330,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X2,X3),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_5824]) ).
tcf(c_47331,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_5824]) ).
tcf(c_47332,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_5824]) ).
tcf(c_47333,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_5824]) ).
tcf(c_47334,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X2,X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_5824]) ).
tcf(c_47335,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X2,X3)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_5824]) ).
tcf(c_47336,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X2,X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_5824]) ).
tcf(c_47337,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_5824]) ).
tcf(c_47338,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X2,X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_5824]) ).
tcf(c_47733,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),sK3(X4,X5,cartesian_product2(X3,X2))),singleton(sK2(X4,X5,cartesian_product2(X3,X2)))) = sK1(X4,X5,cartesian_product2(X3,X2)) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_5825]) ).
tcf(c_47734,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X3,X2)),X5)
| ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_5825]) ).
tcf(c_47735,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X3,X2)),X4)
| ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_5825]) ).
tcf(c_47736,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X3,X2),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_5825]) ).
tcf(c_47737,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X3,X2),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_5825]) ).
tcf(c_47738,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X2),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(sK5(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0)),X5))),singleton(X4))) = X4 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_5825]) ).
tcf(c_47739,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(sK5(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0)),X5))),singleton(X4))) = X4 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_61,c_5825]) ).
tcf(c_47740,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2))),X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_5825]) ).
tcf(c_47741,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2))),X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_5825]) ).
tcf(c_47742,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0))),X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_5825]) ).
tcf(c_47743,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0))),X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_5825]) ).
tcf(c_47744,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2))),X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_5825]) ).
tcf(c_47745,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0))),X5))),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_5825]) ).
tcf(c_47746,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X3,X2) )
| ( sK2(singleton(X4),X5,cartesian_product2(X3,X2)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(singleton(X4),X5,cartesian_product2(X3,X2))),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_5825]) ).
tcf(c_47747,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X3,X2),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,singleton(X5))),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_5825]) ).
tcf(c_47748,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = cartesian_product2(X3,X2) )
| ( sK3(X4,singleton(X5),cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,singleton(X5),cartesian_product2(X3,X2))),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_5825]) ).
tcf(c_47749,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X3,X2),singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),singleton(X5))),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_5825]) ).
tcf(c_47750,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_5825]) ).
tcf(c_47751,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_5825]) ).
tcf(c_47752,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X3,X2),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_5825]) ).
tcf(c_47753,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X3,X2),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_5825]) ).
tcf(c_47754,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_5825]) ).
tcf(c_47755,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_5825]) ).
tcf(c_47756,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X3,X2),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_5825]) ).
tcf(c_47757,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X3,X2),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_5825]) ).
tcf(c_47758,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_5825]) ).
tcf(c_47759,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_5825]) ).
tcf(c_47760,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_5825]) ).
tcf(c_47761,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,X2))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_5825]) ).
tcf(c_47762,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X3,X2)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_5825]) ).
tcf(c_47763,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,X2)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_5825]) ).
tcf(c_47764,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_5825]) ).
tcf(c_47765,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,X2))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_5825]) ).
tcf(c_48073,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),sK3(X4,X5,cartesian_product2(X2,X3))),singleton(sK2(X4,X5,cartesian_product2(X2,X3)))) = sK1(X4,X5,cartesian_product2(X2,X3)) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_7853]) ).
tcf(c_48074,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X2,X3)),X5)
| ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_7853]) ).
tcf(c_48075,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X2,X3)),X4)
| ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_7853]) ).
tcf(c_48076,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X2,X3),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_7853]) ).
tcf(c_48077,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X2,X3),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_7853]) ).
tcf(c_48078,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0))))))) = X4 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_7853]) ).
tcf(c_48079,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X2),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0))))))) = X4 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_61,c_7853]) ).
tcf(c_48080,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_7853]) ).
tcf(c_48081,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_7853]) ).
tcf(c_48082,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_7853]) ).
tcf(c_48083,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_7853]) ).
tcf(c_48084,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_7853]) ).
tcf(c_48085,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_7853]) ).
tcf(c_48086,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X2,X3) )
| ( sK2(singleton(X4),X5,cartesian_product2(X2,X3)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(singleton(X4),X5,cartesian_product2(X2,X3)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_7853]) ).
tcf(c_48087,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X2,X3),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,singleton(X5)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_7853]) ).
tcf(c_48088,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = cartesian_product2(X2,X3) )
| ( sK3(X4,singleton(X5),cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,singleton(X5),cartesian_product2(X2,X3)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_7853]) ).
tcf(c_48089,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X2,X3),singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),singleton(X5)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_7853]) ).
tcf(c_48090,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_7853]) ).
tcf(c_48091,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_7853]) ).
tcf(c_48092,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X2,X3),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_7853]) ).
tcf(c_48093,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X2,X3),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_7853]) ).
tcf(c_48094,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_7853]) ).
tcf(c_48095,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_7853]) ).
tcf(c_48096,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X2,X3),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_7853]) ).
tcf(c_48097,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X2,X3),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_7853]) ).
tcf(c_48098,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_7853]) ).
tcf(c_48099,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_7853]) ).
tcf(c_48100,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_7853]) ).
tcf(c_48101,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X2,X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_7853]) ).
tcf(c_48102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X2,X3)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_7853]) ).
tcf(c_48103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X2,X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_7853]) ).
tcf(c_48104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_7853]) ).
tcf(c_48105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X2,X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_7853]) ).
tcf(c_48268,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),sK3(X4,X5,cartesian_product2(X3,X2))),singleton(sK2(X4,X5,cartesian_product2(X3,X2)))) = sK1(X4,X5,cartesian_product2(X3,X2)) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_7854]) ).
tcf(c_48269,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X3,X2)),X5)
| ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_7854]) ).
tcf(c_48270,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X3,X2)),X4)
| ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_7854]) ).
tcf(c_48271,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X3,X2),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_7854]) ).
tcf(c_48272,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X3,X2),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_7854]) ).
tcf(c_48273,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X2),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0))))))) = X4 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_7854]) ).
tcf(c_48274,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0))))))) = X4 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_61,c_7854]) ).
tcf(c_48275,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_7854]) ).
tcf(c_48276,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_7854]) ).
tcf(c_48277,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_7854]) ).
tcf(c_48278,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_7854]) ).
tcf(c_48279,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_7854]) ).
tcf(c_48280,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0)))))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_7854]) ).
tcf(c_48281,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X3,X2) )
| ( sK2(singleton(X4),X5,cartesian_product2(X3,X2)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(singleton(X4),X5,cartesian_product2(X3,X2)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_7854]) ).
tcf(c_48282,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X3,X2),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,singleton(X5)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_7854]) ).
tcf(c_48283,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = cartesian_product2(X3,X2) )
| ( sK3(X4,singleton(X5),cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,singleton(X5),cartesian_product2(X3,X2)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_7854]) ).
tcf(c_48284,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X3,X2),singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),singleton(X5)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_7854]) ).
tcf(c_48285,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_7854]) ).
tcf(c_48286,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_7854]) ).
tcf(c_48287,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X3,X2),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_7854]) ).
tcf(c_48288,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X3,X2),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_7854]) ).
tcf(c_48289,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_7854]) ).
tcf(c_48290,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_7854]) ).
tcf(c_48291,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X3,X2),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_7854]) ).
tcf(c_48292,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X3,X2),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_7854]) ).
tcf(c_48293,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_7854]) ).
tcf(c_48294,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_7854]) ).
tcf(c_48295,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_7854]) ).
tcf(c_48296,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,X2))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_7854]) ).
tcf(c_48297,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X3,X2)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_7854]) ).
tcf(c_48298,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,X2)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_7854]) ).
tcf(c_48299,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_7854]) ).
tcf(c_48300,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,X2))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_7854]) ).
tcf(c_48328,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),sK3(X4,X5,cartesian_product2(X2,X3))),singleton(sK2(X4,X5,cartesian_product2(X2,X3)))) = sK1(X4,X5,cartesian_product2(X2,X3)) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_8151]) ).
tcf(c_48329,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X2,X3)),X5)
| ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_8151]) ).
tcf(c_48330,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X2,X3)),X4)
| ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_8151]) ).
tcf(c_48331,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X2,X3),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_8151]) ).
tcf(c_48332,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X2,X3),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_8151]) ).
tcf(c_48333,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0)),X5),singleton(X5))))) = X4 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_8151]) ).
tcf(c_48334,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X2),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(sK4(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0)),X5),singleton(X5))))) = X4 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_61,c_8151]) ).
tcf(c_48335,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2))),X5),singleton(X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_8151]) ).
tcf(c_48336,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2))),X5),singleton(X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_8151]) ).
tcf(c_48337,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0))),X5),singleton(X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_8151]) ).
tcf(c_48338,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0))),X5),singleton(X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_8151]) ).
tcf(c_48339,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2))),X5),singleton(X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_8151]) ).
tcf(c_48340,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0))),X5),singleton(X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_8151]) ).
tcf(c_48341,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X2,X3) )
| ( sK2(singleton(X4),X5,cartesian_product2(X2,X3)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK1(singleton(X4),X5,cartesian_product2(X2,X3))),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_8151]) ).
tcf(c_48342,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X2,X3),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,singleton(X5))),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_8151]) ).
tcf(c_48343,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = cartesian_product2(X2,X3) )
| ( sK3(X4,singleton(X5),cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,singleton(X5),cartesian_product2(X2,X3))),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_8151]) ).
tcf(c_48344,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X2,X3),singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),singleton(X5))),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_8151]) ).
tcf(c_48345,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_8151]) ).
tcf(c_48346,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_8151]) ).
tcf(c_48347,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X2,X3),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_8151]) ).
tcf(c_48348,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X2,X3),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_8151]) ).
tcf(c_48349,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_8151]) ).
tcf(c_48350,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_8151]) ).
tcf(c_48351,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X2,X3),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_8151]) ).
tcf(c_48352,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X2,X3),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_8151]) ).
tcf(c_48353,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_8151]) ).
tcf(c_48354,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_8151]) ).
tcf(c_48355,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_8151]) ).
tcf(c_48356,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X2,X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_8151]) ).
tcf(c_48357,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X2,X3)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_8151]) ).
tcf(c_48358,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X2,X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_8151]) ).
tcf(c_48359,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_8151]) ).
tcf(c_48360,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X2,X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_8151]) ).
tcf(c_48485,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),sK3(X4,X5,cartesian_product2(X3,X2))),singleton(sK2(X4,X5,cartesian_product2(X3,X2)))) = sK1(X4,X5,cartesian_product2(X3,X2)) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_8152]) ).
tcf(c_48486,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X3,X2)),X5)
| ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_8152]) ).
tcf(c_48487,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X3,X2)),X4)
| ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_8152]) ).
tcf(c_48488,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X3,X2),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_8152]) ).
tcf(c_48489,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X3,X2),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_8152]) ).
tcf(c_48490,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X2),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(sK5(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0)),X5),singleton(X5))))) = X4 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_8152]) ).
tcf(c_48491,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(sK5(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0)),X5),singleton(X5))))) = X4 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_61,c_8152]) ).
tcf(c_48492,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2))),X5),singleton(X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_8152]) ).
tcf(c_48493,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2))),X5),singleton(X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_8152]) ).
tcf(c_48494,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0))),X5),singleton(X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_8152]) ).
tcf(c_48495,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0))),X5),singleton(X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_8152]) ).
tcf(c_48496,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2))),X5),singleton(X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_8152]) ).
tcf(c_48497,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0))),X5),singleton(X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_8152]) ).
tcf(c_48498,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X3,X2) )
| ( sK2(singleton(X4),X5,cartesian_product2(X3,X2)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK1(singleton(X4),X5,cartesian_product2(X3,X2))),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_8152]) ).
tcf(c_48499,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X3,X2),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,singleton(X5))),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_8152]) ).
tcf(c_48500,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = cartesian_product2(X3,X2) )
| ( sK3(X4,singleton(X5),cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,singleton(X5),cartesian_product2(X3,X2))),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_8152]) ).
tcf(c_48501,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X3,X2),singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),singleton(X5))),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_8152]) ).
tcf(c_48502,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_8152]) ).
tcf(c_48503,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_8152]) ).
tcf(c_48504,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X3,X2),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_8152]) ).
tcf(c_48505,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X3,X2),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_8152]) ).
tcf(c_48506,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_8152]) ).
tcf(c_48507,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_8152]) ).
tcf(c_48508,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X3,X2),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_8152]) ).
tcf(c_48509,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X3,X2),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_8152]) ).
tcf(c_48510,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_8152]) ).
tcf(c_48511,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_8152]) ).
tcf(c_48512,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_8152]) ).
tcf(c_48513,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,X2))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_8152]) ).
tcf(c_48514,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X3,X2)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_8152]) ).
tcf(c_48515,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,X2)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_8152]) ).
tcf(c_48516,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_8152]) ).
tcf(c_48517,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,X2))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_8152]) ).
tcf(c_48559,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),sK3(X4,X5,cartesian_product2(X2,X3))),singleton(sK2(X4,X5,cartesian_product2(X2,X3)))) = sK1(X4,X5,cartesian_product2(X2,X3)) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_8457]) ).
tcf(c_48560,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X2,X3)),X5)
| ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_8457]) ).
tcf(c_48561,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X2,X3)),X4)
| ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_8457]) ).
tcf(c_48562,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X2,X3),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_8457]) ).
tcf(c_48563,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X2,X3),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_8457]) ).
tcf(c_48564,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0)),X5))))) = X4 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_8457]) ).
tcf(c_48565,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X2),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(sK4(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0)),X5))))) = X4 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_61,c_8457]) ).
tcf(c_48566,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2))),X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_8457]) ).
tcf(c_48567,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2))),X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_8457]) ).
tcf(c_48568,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0))),X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_8457]) ).
tcf(c_48569,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0))),X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_8457]) ).
tcf(c_48570,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2))),X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_8457]) ).
tcf(c_48571,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0))),X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_8457]) ).
tcf(c_48572,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X2,X3) )
| ( sK2(singleton(X4),X5,cartesian_product2(X2,X3)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(singleton(X4),X5,cartesian_product2(X2,X3))),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_8457]) ).
tcf(c_48573,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X2,X3),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,singleton(X5))),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_8457]) ).
tcf(c_48574,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = cartesian_product2(X2,X3) )
| ( sK3(X4,singleton(X5),cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,singleton(X5),cartesian_product2(X2,X3))),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_8457]) ).
tcf(c_48575,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X2,X3),singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),singleton(X5))),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_8457]) ).
tcf(c_48576,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_8457]) ).
tcf(c_48577,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_8457]) ).
tcf(c_48578,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X2,X3),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_8457]) ).
tcf(c_48579,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X2,X3),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_8457]) ).
tcf(c_48580,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_8457]) ).
tcf(c_48581,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_8457]) ).
tcf(c_48582,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X2,X3),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_8457]) ).
tcf(c_48583,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X2,X3),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_8457]) ).
tcf(c_48584,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_8457]) ).
tcf(c_48585,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_8457]) ).
tcf(c_48586,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_8457]) ).
tcf(c_48587,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X2,X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_8457]) ).
tcf(c_48588,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X2,X3)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_8457]) ).
tcf(c_48589,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X2,X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_8457]) ).
tcf(c_48590,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_8457]) ).
tcf(c_48591,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X2,X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_8457]) ).
tcf(c_48751,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),sK3(X4,X5,cartesian_product2(X3,X2))),singleton(sK2(X4,X5,cartesian_product2(X3,X2)))) = sK1(X4,X5,cartesian_product2(X3,X2)) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_8458]) ).
tcf(c_48752,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X3,X2)),X5)
| ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_8458]) ).
tcf(c_48753,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X3,X2)),X4)
| ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_8458]) ).
tcf(c_48754,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X3,X2),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_8458]) ).
tcf(c_48755,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X3,X2),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_8458]) ).
tcf(c_48756,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X2),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(sK5(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0)),X5))))) = X4 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_8458]) ).
tcf(c_48757,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(sK5(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0)),X5))))) = X4 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_61,c_8458]) ).
tcf(c_48758,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2))),X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_8458]) ).
tcf(c_48759,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2))),X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_8458]) ).
tcf(c_48760,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0))),X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_8458]) ).
tcf(c_48761,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0))),X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_8458]) ).
tcf(c_48762,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2))),X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_8458]) ).
tcf(c_48763,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(X4,unordered_pair(singleton(X5),unordered_pair(sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0))),X5))))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_8458]) ).
tcf(c_48764,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X3,X2) )
| ( sK2(singleton(X4),X5,cartesian_product2(X3,X2)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(singleton(X4),X5,cartesian_product2(X3,X2))),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_8458]) ).
tcf(c_48765,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X3,X2),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,singleton(X5))),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_8458]) ).
tcf(c_48766,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = cartesian_product2(X3,X2) )
| ( sK3(X4,singleton(X5),cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,singleton(X5),cartesian_product2(X3,X2))),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_8458]) ).
tcf(c_48767,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X3,X2),singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),singleton(X5))),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_8458]) ).
tcf(c_48768,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_8458]) ).
tcf(c_48769,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_8458]) ).
tcf(c_48770,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X3,X2),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_8458]) ).
tcf(c_48771,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X3,X2),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_8458]) ).
tcf(c_48772,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_8458]) ).
tcf(c_48773,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_8458]) ).
tcf(c_48774,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X3,X2),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_8458]) ).
tcf(c_48775,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X3,X2),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_8458]) ).
tcf(c_48776,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_8458]) ).
tcf(c_48777,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_8458]) ).
tcf(c_48778,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_8458]) ).
tcf(c_48779,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,X2))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_8458]) ).
tcf(c_48780,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X3,X2)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_8458]) ).
tcf(c_48781,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,X2)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_8458]) ).
tcf(c_48782,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_8458]) ).
tcf(c_48783,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,X2))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_8458]) ).
tcf(c_49018,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),sK3(X4,X5,cartesian_product2(X2,X3))),singleton(sK2(X4,X5,cartesian_product2(X2,X3)))) = sK1(X4,X5,cartesian_product2(X2,X3)) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_11092]) ).
tcf(c_49019,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X2,X3)),X5)
| ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_11092]) ).
tcf(c_49020,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X2,X3)),X4)
| ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_11092]) ).
tcf(c_49021,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X2,X3),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_11092]) ).
tcf(c_49022,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X2,X3),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_11092]) ).
tcf(c_49023,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0)))),X4),singleton(X4))) = X4 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_11092]) ).
tcf(c_49024,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,sK4(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0)))),X4),singleton(X4))) = X4 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_61,c_11092]) ).
tcf(c_49025,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,sK4(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_11092]) ).
tcf(c_49026,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_11092]) ).
tcf(c_49027,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,sK4(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_11092]) ).
tcf(c_49028,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_11092]) ).
tcf(c_49029,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_11092]) ).
tcf(c_49030,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_11092]) ).
tcf(c_49031,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X2,X3) )
| ( sK2(singleton(X4),X5,cartesian_product2(X2,X3)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(singleton(X4),X5,cartesian_product2(X2,X3))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_11092]) ).
tcf(c_49032,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X2,X3),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,singleton(X5))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_11092]) ).
tcf(c_49033,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = cartesian_product2(X2,X3) )
| ( sK3(X4,singleton(X5),cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,singleton(X5),cartesian_product2(X2,X3))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_11092]) ).
tcf(c_49034,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X2,X3),singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),singleton(X5))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_11092]) ).
tcf(c_49035,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_11092]) ).
tcf(c_49036,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_11092]) ).
tcf(c_49037,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X2,X3),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_11092]) ).
tcf(c_49038,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X2,X3),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_11092]) ).
tcf(c_49039,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_11092]) ).
tcf(c_49040,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_11092]) ).
tcf(c_49041,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X2,X3),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_11092]) ).
tcf(c_49042,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X2,X3),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_11092]) ).
tcf(c_49043,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_11092]) ).
tcf(c_49044,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_11092]) ).
tcf(c_49045,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_11092]) ).
tcf(c_49046,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X2,X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_11092]) ).
tcf(c_49047,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X2,X3)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_11092]) ).
tcf(c_49048,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X2,X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_11092]) ).
tcf(c_49049,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_11092]) ).
tcf(c_49050,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X2,X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_11092]) ).
tcf(c_49456,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),sK3(X4,X5,cartesian_product2(X3,X2))),singleton(sK2(X4,X5,cartesian_product2(X3,X2)))) = sK1(X4,X5,cartesian_product2(X3,X2)) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_11093]) ).
tcf(c_49457,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X3,X2)),X5)
| ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_11093]) ).
tcf(c_49458,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X3,X2)),X4)
| ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_11093]) ).
tcf(c_49459,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X3,X2),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_11093]) ).
tcf(c_49460,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X3,X2),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_11093]) ).
tcf(c_49461,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,sK5(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0)))),X4),singleton(X4))) = X4 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_11093]) ).
tcf(c_49462,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,sK5(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0)))),X4),singleton(X4))) = X4 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_61,c_11093]) ).
tcf(c_49463,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,sK5(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_11093]) ).
tcf(c_49464,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_11093]) ).
tcf(c_49465,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,sK5(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_11093]) ).
tcf(c_49466,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_11093]) ).
tcf(c_49467,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_11093]) ).
tcf(c_49468,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0))))),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_11093]) ).
tcf(c_49469,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X3,X2) )
| ( sK2(singleton(X4),X5,cartesian_product2(X3,X2)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(singleton(X4),X5,cartesian_product2(X3,X2))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_11093]) ).
tcf(c_49470,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X3,X2),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,singleton(X5))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_11093]) ).
tcf(c_49471,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = cartesian_product2(X3,X2) )
| ( sK3(X4,singleton(X5),cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,singleton(X5),cartesian_product2(X3,X2))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_11093]) ).
tcf(c_49472,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X3,X2),singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),singleton(X5))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_11093]) ).
tcf(c_49473,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_11093]) ).
tcf(c_49474,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_11093]) ).
tcf(c_49475,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X3,X2),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_11093]) ).
tcf(c_49476,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X3,X2),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_11093]) ).
tcf(c_49477,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_11093]) ).
tcf(c_49478,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_11093]) ).
tcf(c_49479,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X3,X2),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_11093]) ).
tcf(c_49480,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X3,X2),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_11093]) ).
tcf(c_49481,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_11093]) ).
tcf(c_49482,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_11093]) ).
tcf(c_49483,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_11093]) ).
tcf(c_49484,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,X2))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_11093]) ).
tcf(c_49485,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X3,X2)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_11093]) ).
tcf(c_49486,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,X2)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_11093]) ).
tcf(c_49487,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_11093]) ).
tcf(c_49488,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,X2))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_11093]) ).
tcf(c_49864,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),sK3(X4,X5,cartesian_product2(X2,X3))),singleton(sK2(X4,X5,cartesian_product2(X2,X3)))) = sK1(X4,X5,cartesian_product2(X2,X3)) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_11517]) ).
tcf(c_49865,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X2,X3)),X5)
| ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_11517]) ).
tcf(c_49866,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X2,X3)),X4)
| ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_11517]) ).
tcf(c_49867,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X2,X3),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_11517]) ).
tcf(c_49868,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X2,X3),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_11517]) ).
tcf(c_49869,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0)),X5),singleton(X5)),X4),singleton(X4))) = X4 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_11517]) ).
tcf(c_49870,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0)),X5),singleton(X5)),X4),singleton(X4))) = X4 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_61,c_11517]) ).
tcf(c_49871,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2))),X5),singleton(X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_11517]) ).
tcf(c_49872,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2))),X5),singleton(X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_11517]) ).
tcf(c_49873,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0))),X5),singleton(X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_11517]) ).
tcf(c_49874,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0))),X5),singleton(X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_11517]) ).
tcf(c_49875,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2))),X5),singleton(X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_11517]) ).
tcf(c_49876,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0))),X5),singleton(X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_11517]) ).
tcf(c_49877,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X2,X3) )
| ( sK2(singleton(X4),X5,cartesian_product2(X2,X3)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK1(singleton(X4),X5,cartesian_product2(X2,X3))),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_11517]) ).
tcf(c_49878,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X2,X3),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,singleton(X5))),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_11517]) ).
tcf(c_49879,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = cartesian_product2(X2,X3) )
| ( sK3(X4,singleton(X5),cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,singleton(X5),cartesian_product2(X2,X3))),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_11517]) ).
tcf(c_49880,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X2,X3),singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),singleton(X5))),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_11517]) ).
tcf(c_49881,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_11517]) ).
tcf(c_49882,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_11517]) ).
tcf(c_49883,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X2,X3),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_11517]) ).
tcf(c_49884,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X2,X3),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_11517]) ).
tcf(c_49885,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_11517]) ).
tcf(c_49886,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_11517]) ).
tcf(c_49887,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X2,X3),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_11517]) ).
tcf(c_49888,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X2,X3),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_11517]) ).
tcf(c_49889,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_11517]) ).
tcf(c_49890,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_11517]) ).
tcf(c_49891,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_11517]) ).
tcf(c_49892,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X2,X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_11517]) ).
tcf(c_49893,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X2,X3)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_11517]) ).
tcf(c_49894,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X2,X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_11517]) ).
tcf(c_49895,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_11517]) ).
tcf(c_49896,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X2,X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_11517]) ).
tcf(c_49924,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),sK3(X4,X5,cartesian_product2(X3,X2))),singleton(sK2(X4,X5,cartesian_product2(X3,X2)))) = sK1(X4,X5,cartesian_product2(X3,X2)) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_11518]) ).
tcf(c_49925,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X3,X2)),X5)
| ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_11518]) ).
tcf(c_49926,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X3,X2)),X4)
| ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_11518]) ).
tcf(c_49927,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X3,X2),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_11518]) ).
tcf(c_49928,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X3,X2),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_11518]) ).
tcf(c_49929,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK5(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0)),X5),singleton(X5)),X4),singleton(X4))) = X4 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_11518]) ).
tcf(c_49930,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK5(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0)),X5),singleton(X5)),X4),singleton(X4))) = X4 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_61,c_11518]) ).
tcf(c_49931,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2))),X5),singleton(X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_11518]) ).
tcf(c_49932,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2))),X5),singleton(X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_11518]) ).
tcf(c_49933,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0))),X5),singleton(X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_11518]) ).
tcf(c_49934,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0))),X5),singleton(X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_11518]) ).
tcf(c_49935,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2))),X5),singleton(X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_11518]) ).
tcf(c_49936,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0))),X5),singleton(X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_11518]) ).
tcf(c_49937,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X3,X2) )
| ( sK2(singleton(X4),X5,cartesian_product2(X3,X2)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK1(singleton(X4),X5,cartesian_product2(X3,X2))),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_11518]) ).
tcf(c_49938,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X3,X2),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,singleton(X5))),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_11518]) ).
tcf(c_49939,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = cartesian_product2(X3,X2) )
| ( sK3(X4,singleton(X5),cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,singleton(X5),cartesian_product2(X3,X2))),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_11518]) ).
tcf(c_49940,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X3,X2),singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),singleton(X5))),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_11518]) ).
tcf(c_49941,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_11518]) ).
tcf(c_49942,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_11518]) ).
tcf(c_49943,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X3,X2),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_11518]) ).
tcf(c_49944,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X3,X2),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_11518]) ).
tcf(c_49945,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_11518]) ).
tcf(c_49946,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_11518]) ).
tcf(c_49947,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X3,X2),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_11518]) ).
tcf(c_49948,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X3,X2),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_11518]) ).
tcf(c_49949,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_11518]) ).
tcf(c_49950,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_11518]) ).
tcf(c_49951,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_11518]) ).
tcf(c_49952,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,X2))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_11518]) ).
tcf(c_49953,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X3,X2)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_11518]) ).
tcf(c_49954,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,X2)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_11518]) ).
tcf(c_49955,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_11518]) ).
tcf(c_49956,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,X2))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_11518]) ).
tcf(c_50283,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),sK3(X4,X5,cartesian_product2(X2,X3))),singleton(sK2(X4,X5,cartesian_product2(X2,X3)))) = sK1(X4,X5,cartesian_product2(X2,X3)) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_12048]) ).
tcf(c_50284,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X2,X3)),X5)
| ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_12048]) ).
tcf(c_50285,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X2,X3)),X4)
| ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_12048]) ).
tcf(c_50286,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X2,X3),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_12048]) ).
tcf(c_50287,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X2,X3),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_12048]) ).
tcf(c_50288,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0)),X5)),X4),singleton(X4))) = X4 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_12048]) ).
tcf(c_50289,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(sK4(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0)),X5)),X4),singleton(X4))) = X4 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_61,c_12048]) ).
tcf(c_50290,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2))),X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_12048]) ).
tcf(c_50291,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2))),X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_12048]) ).
tcf(c_50292,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0))),X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_12048]) ).
tcf(c_50293,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0))),X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_12048]) ).
tcf(c_50294,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2))),X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_12048]) ).
tcf(c_50295,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0))),X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_12048]) ).
tcf(c_50296,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X2,X3) )
| ( sK2(singleton(X4),X5,cartesian_product2(X2,X3)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(singleton(X4),X5,cartesian_product2(X2,X3))),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_12048]) ).
tcf(c_50297,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X2,X3),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,singleton(X5))),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_12048]) ).
tcf(c_50298,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = cartesian_product2(X2,X3) )
| ( sK3(X4,singleton(X5),cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,singleton(X5),cartesian_product2(X2,X3))),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_12048]) ).
tcf(c_50299,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X2,X3),singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),singleton(X5))),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_12048]) ).
tcf(c_50300,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_12048]) ).
tcf(c_50301,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_12048]) ).
tcf(c_50302,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X2,X3),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_12048]) ).
tcf(c_50303,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X2,X3),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_12048]) ).
tcf(c_50304,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_12048]) ).
tcf(c_50305,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_12048]) ).
tcf(c_50306,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X2,X3),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_12048]) ).
tcf(c_50307,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X2,X3),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_12048]) ).
tcf(c_50308,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_12048]) ).
tcf(c_50309,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_12048]) ).
tcf(c_50310,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_12048]) ).
tcf(c_50311,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X2,X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_12048]) ).
tcf(c_50312,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X2,X3)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_12048]) ).
tcf(c_50313,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X2,X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_12048]) ).
tcf(c_50314,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_12048]) ).
tcf(c_50315,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X2,X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_12048]) ).
tcf(c_50472,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),sK3(X4,X5,cartesian_product2(X3,X2))),singleton(sK2(X4,X5,cartesian_product2(X3,X2)))) = sK1(X4,X5,cartesian_product2(X3,X2)) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_12049]) ).
tcf(c_50473,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X3,X2)),X5)
| ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_12049]) ).
tcf(c_50474,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X3,X2)),X4)
| ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_12049]) ).
tcf(c_50475,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X3,X2),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_12049]) ).
tcf(c_50476,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X3,X2),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_12049]) ).
tcf(c_50477,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(sK5(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0)),X5)),X4),singleton(X4))) = X4 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_12049]) ).
tcf(c_50478,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(sK5(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0)),X5)),X4),singleton(X4))) = X4 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_61,c_12049]) ).
tcf(c_50479,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2))),X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_12049]) ).
tcf(c_50480,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2))),X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_12049]) ).
tcf(c_50481,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0))),X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_12049]) ).
tcf(c_50482,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0))),X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_12049]) ).
tcf(c_50483,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2))),X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_12049]) ).
tcf(c_50484,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(unordered_pair(unordered_pair(singleton(X5),unordered_pair(sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0))),X5)),X4),singleton(X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_12049]) ).
tcf(c_50485,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X3,X2) )
| ( sK2(singleton(X4),X5,cartesian_product2(X3,X2)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(singleton(X4),X5,cartesian_product2(X3,X2))),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_12049]) ).
tcf(c_50486,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X3,X2),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,singleton(X5))),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_12049]) ).
tcf(c_50487,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = cartesian_product2(X3,X2) )
| ( sK3(X4,singleton(X5),cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,singleton(X5),cartesian_product2(X3,X2))),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_12049]) ).
tcf(c_50488,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X3,X2),singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),singleton(X5))),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_12049]) ).
tcf(c_50489,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_12049]) ).
tcf(c_50490,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_12049]) ).
tcf(c_50491,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X3,X2),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_12049]) ).
tcf(c_50492,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X3,X2),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_12049]) ).
tcf(c_50493,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_12049]) ).
tcf(c_50494,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_12049]) ).
tcf(c_50495,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X3,X2),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_12049]) ).
tcf(c_50496,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X3,X2),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_12049]) ).
tcf(c_50497,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_12049]) ).
tcf(c_50498,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_12049]) ).
tcf(c_50499,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_12049]) ).
tcf(c_50500,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,X2))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_12049]) ).
tcf(c_50501,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X3,X2)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_12049]) ).
tcf(c_50502,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,X2)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_12049]) ).
tcf(c_50503,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_12049]) ).
tcf(c_50504,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,X2))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_12049]) ).
tcf(c_50754,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),sK3(X4,X5,cartesian_product2(X2,X3))),singleton(sK2(X4,X5,cartesian_product2(X2,X3)))) = sK1(X4,X5,cartesian_product2(X2,X3)) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_15376]) ).
tcf(c_50755,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X2,X3)),X5)
| ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_15376]) ).
tcf(c_50756,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X2,X3)),X4)
| ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_15376]) ).
tcf(c_50757,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X2,X3),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_15376]) ).
tcf(c_50758,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X2,X3),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_15376]) ).
tcf(c_50759,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0)))),X4))) = X4 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_15376]) ).
tcf(c_50760,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X2),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,sK4(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0)))),X4))) = X4 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_61,c_15376]) ).
tcf(c_50761,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,sK4(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_15376]) ).
tcf(c_50762,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_15376]) ).
tcf(c_50763,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,sK4(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_15376]) ).
tcf(c_50764,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_15376]) ).
tcf(c_50765,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_15376]) ).
tcf(c_50766,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_15376]) ).
tcf(c_50767,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X2,X3) )
| ( sK2(singleton(X4),X5,cartesian_product2(X2,X3)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(singleton(X4),X5,cartesian_product2(X2,X3))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_15376]) ).
tcf(c_50768,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X2,X3),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,singleton(X5))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_15376]) ).
tcf(c_50769,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = cartesian_product2(X2,X3) )
| ( sK3(X4,singleton(X5),cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,singleton(X5),cartesian_product2(X2,X3))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_15376]) ).
tcf(c_50770,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X2,X3),singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),singleton(X5))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_15376]) ).
tcf(c_50771,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_15376]) ).
tcf(c_50772,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_15376]) ).
tcf(c_50773,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X2,X3),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_15376]) ).
tcf(c_50774,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X2,X3),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_15376]) ).
tcf(c_50775,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_15376]) ).
tcf(c_50776,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_15376]) ).
tcf(c_50777,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X2,X3),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_15376]) ).
tcf(c_50778,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X2,X3),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_15376]) ).
tcf(c_50779,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_15376]) ).
tcf(c_50780,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_15376]) ).
tcf(c_50781,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_15376]) ).
tcf(c_50782,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X2,X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_15376]) ).
tcf(c_50783,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X2,X3)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_15376]) ).
tcf(c_50784,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X2,X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_15376]) ).
tcf(c_50785,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_15376]) ).
tcf(c_50786,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X2,X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_15376]) ).
tcf(c_51165,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),sK3(X4,X5,cartesian_product2(X3,X2))),singleton(sK2(X4,X5,cartesian_product2(X3,X2)))) = sK1(X4,X5,cartesian_product2(X3,X2)) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_15377]) ).
tcf(c_51166,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X3,X2)),X5)
| ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_15377]) ).
tcf(c_51167,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X3,X2)),X4)
| ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_15377]) ).
tcf(c_51168,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X3,X2),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_15377]) ).
tcf(c_51169,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X3,X2),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_15377]) ).
tcf(c_51170,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X2),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,sK5(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0)))),X4))) = X4 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_15377]) ).
tcf(c_51171,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,sK5(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0)))),X4))) = X4 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_61,c_15377]) ).
tcf(c_51172,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,sK5(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_15377]) ).
tcf(c_51173,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_15377]) ).
tcf(c_51174,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,sK5(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_15377]) ).
tcf(c_51175,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_15377]) ).
tcf(c_51176,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_15377]) ).
tcf(c_51177,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(X5,sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0))))),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_15377]) ).
tcf(c_51178,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X3,X2) )
| ( sK2(singleton(X4),X5,cartesian_product2(X3,X2)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(singleton(X4),X5,cartesian_product2(X3,X2))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_15377]) ).
tcf(c_51179,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X3,X2),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,singleton(X5))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_15377]) ).
tcf(c_51180,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = cartesian_product2(X3,X2) )
| ( sK3(X4,singleton(X5),cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,singleton(X5),cartesian_product2(X3,X2))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_15377]) ).
tcf(c_51181,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X3,X2),singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),singleton(X5))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_15377]) ).
tcf(c_51182,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_15377]) ).
tcf(c_51183,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_15377]) ).
tcf(c_51184,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X3,X2),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_15377]) ).
tcf(c_51185,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X3,X2),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_15377]) ).
tcf(c_51186,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_15377]) ).
tcf(c_51187,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_15377]) ).
tcf(c_51188,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X3,X2),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_15377]) ).
tcf(c_51189,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X3,X2),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_15377]) ).
tcf(c_51190,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_15377]) ).
tcf(c_51191,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_15377]) ).
tcf(c_51192,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_15377]) ).
tcf(c_51193,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,X2))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_15377]) ).
tcf(c_51194,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X3,X2)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_15377]) ).
tcf(c_51195,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,X2)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_15377]) ).
tcf(c_51196,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_15377]) ).
tcf(c_51197,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,X2))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_15377]) ).
tcf(c_51531,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),sK3(X4,X5,cartesian_product2(X2,X3))),singleton(sK2(X4,X5,cartesian_product2(X2,X3)))) = sK1(X4,X5,cartesian_product2(X2,X3)) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_15722]) ).
tcf(c_51532,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X2,X3)),X5)
| ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_15722]) ).
tcf(c_51533,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X2,X3)),X4)
| ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_15722]) ).
tcf(c_51534,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X2,X3),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_15722]) ).
tcf(c_51535,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X2,X3),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_15722]) ).
tcf(c_51536,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0)),X5),singleton(X5)),X4))) = X4 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_15722]) ).
tcf(c_51537,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X2),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0)),X5),singleton(X5)),X4))) = X4 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_61,c_15722]) ).
tcf(c_51538,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2))),X5),singleton(X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_15722]) ).
tcf(c_51539,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2))),X5),singleton(X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_15722]) ).
tcf(c_51540,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0))),X5),singleton(X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_15722]) ).
tcf(c_51541,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0))),X5),singleton(X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_15722]) ).
tcf(c_51542,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2))),X5),singleton(X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_15722]) ).
tcf(c_51543,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0))),X5),singleton(X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_15722]) ).
tcf(c_51544,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X2,X3) )
| ( sK2(singleton(X4),X5,cartesian_product2(X2,X3)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK1(singleton(X4),X5,cartesian_product2(X2,X3))),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_15722]) ).
tcf(c_51545,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X2,X3),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,singleton(X5))),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_15722]) ).
tcf(c_51546,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = cartesian_product2(X2,X3) )
| ( sK3(X4,singleton(X5),cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,singleton(X5),cartesian_product2(X2,X3))),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_15722]) ).
tcf(c_51547,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X2,X3),singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),singleton(X5))),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_15722]) ).
tcf(c_51548,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_15722]) ).
tcf(c_51549,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_15722]) ).
tcf(c_51550,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X2,X3),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_15722]) ).
tcf(c_51551,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X2,X3),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_15722]) ).
tcf(c_51552,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_15722]) ).
tcf(c_51553,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_15722]) ).
tcf(c_51554,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X2,X3),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_15722]) ).
tcf(c_51555,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X2,X3),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_15722]) ).
tcf(c_51556,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_15722]) ).
tcf(c_51557,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_15722]) ).
tcf(c_51558,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_15722]) ).
tcf(c_51559,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X2,X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_15722]) ).
tcf(c_51560,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X2,X3)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_15722]) ).
tcf(c_51561,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X2,X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_15722]) ).
tcf(c_51562,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_15722]) ).
tcf(c_51563,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X2,X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_15722]) ).
tcf(c_51820,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),sK3(X4,X5,cartesian_product2(X3,X2))),singleton(sK2(X4,X5,cartesian_product2(X3,X2)))) = sK1(X4,X5,cartesian_product2(X3,X2)) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_15723]) ).
tcf(c_51821,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X3,X2)),X5)
| ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_15723]) ).
tcf(c_51822,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X3,X2)),X4)
| ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_15723]) ).
tcf(c_51823,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X3,X2),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_15723]) ).
tcf(c_51824,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X3,X2),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_15723]) ).
tcf(c_51825,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X2),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(sK5(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0)),X5),singleton(X5)),X4))) = X4 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_15723]) ).
tcf(c_51826,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(sK5(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0)),X5),singleton(X5)),X4))) = X4 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_61,c_15723]) ).
tcf(c_51827,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2))),X5),singleton(X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_15723]) ).
tcf(c_51828,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2))),X5),singleton(X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_15723]) ).
tcf(c_51829,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0))),X5),singleton(X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_15723]) ).
tcf(c_51830,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0))),X5),singleton(X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_15723]) ).
tcf(c_51831,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2))),X5),singleton(X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_15723]) ).
tcf(c_51832,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0))),X5),singleton(X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_15723]) ).
tcf(c_51833,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X3,X2) )
| ( sK2(singleton(X4),X5,cartesian_product2(X3,X2)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK1(singleton(X4),X5,cartesian_product2(X3,X2))),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_15723]) ).
tcf(c_51834,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X3,X2),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,singleton(X5))),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_15723]) ).
tcf(c_51835,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = cartesian_product2(X3,X2) )
| ( sK3(X4,singleton(X5),cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,singleton(X5),cartesian_product2(X3,X2))),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_15723]) ).
tcf(c_51836,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X3,X2),singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),singleton(X5))),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_15723]) ).
tcf(c_51837,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_15723]) ).
tcf(c_51838,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_15723]) ).
tcf(c_51839,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X3,X2),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_15723]) ).
tcf(c_51840,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X3,X2),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_15723]) ).
tcf(c_51841,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_15723]) ).
tcf(c_51842,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_15723]) ).
tcf(c_51843,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X3,X2),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_15723]) ).
tcf(c_51844,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X3,X2),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_15723]) ).
tcf(c_51845,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_15723]) ).
tcf(c_51846,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_15723]) ).
tcf(c_51847,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_15723]) ).
tcf(c_51848,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,X2))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_15723]) ).
tcf(c_51849,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X3,X2)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_15723]) ).
tcf(c_51850,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,X2)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_15723]) ).
tcf(c_51851,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_15723]) ).
tcf(c_51852,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,X2))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_15723]) ).
tcf(c_52646,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),sK3(X4,X5,cartesian_product2(X2,X3))),singleton(sK2(X4,X5,cartesian_product2(X2,X3)))) = sK1(X4,X5,cartesian_product2(X2,X3)) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_16266]) ).
tcf(c_52647,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X2,X3)),X5)
| ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_16266]) ).
tcf(c_52648,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X2,X3)),X4)
| ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_16266]) ).
tcf(c_52649,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X2,X3),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_16266]) ).
tcf(c_52650,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X2,X3),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_16266]) ).
tcf(c_52651,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0)),X5)),X4))) = X4 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_16266]) ).
tcf(c_52652,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X2),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(sK4(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0)),X5)),X4))) = X4 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_61,c_16266]) ).
tcf(c_52653,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2))),X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_16266]) ).
tcf(c_52654,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2))),X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_16266]) ).
tcf(c_52655,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0))),X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_16266]) ).
tcf(c_52656,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0))),X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_16266]) ).
tcf(c_52657,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2))),X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_16266]) ).
tcf(c_52658,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(sK4(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0))),X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_16266]) ).
tcf(c_52659,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X2,X3) )
| ( sK2(singleton(X4),X5,cartesian_product2(X2,X3)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(singleton(X4),X5,cartesian_product2(X2,X3))),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_16266]) ).
tcf(c_52660,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X2,X3),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,singleton(X5))),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_16266]) ).
tcf(c_52661,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = cartesian_product2(X2,X3) )
| ( sK3(X4,singleton(X5),cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,singleton(X5),cartesian_product2(X2,X3))),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_16266]) ).
tcf(c_52662,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X2,X3),singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),singleton(X5))),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_16266]) ).
tcf(c_52663,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_16266]) ).
tcf(c_52664,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_16266]) ).
tcf(c_52665,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X2,X3),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_16266]) ).
tcf(c_52666,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X2,X3),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_16266]) ).
tcf(c_52667,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_16266]) ).
tcf(c_52668,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_16266]) ).
tcf(c_52669,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X2,X3),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_16266]) ).
tcf(c_52670,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X2,X3),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_16266]) ).
tcf(c_52671,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_16266]) ).
tcf(c_52672,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_16266]) ).
tcf(c_52673,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_16266]) ).
tcf(c_52674,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X2,X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_16266]) ).
tcf(c_52675,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X2,X3)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_16266]) ).
tcf(c_52676,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X2,X3)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_16266]) ).
tcf(c_52677,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_16266]) ).
tcf(c_52678,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X2,X3))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_16266]) ).
tcf(c_53049,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),sK3(X4,X5,cartesian_product2(X3,X2))),singleton(sK2(X4,X5,cartesian_product2(X3,X2)))) = sK1(X4,X5,cartesian_product2(X3,X2)) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_16267]) ).
tcf(c_53050,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK3(X4,X5,cartesian_product2(X3,X2)),X5)
| ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_16267]) ).
tcf(c_53051,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,cartesian_product2(X3,X2)),X4)
| ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_16267]) ).
tcf(c_53052,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(cartesian_product2(X3,X2),X4,X5),X5)
| ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_16267]) ).
tcf(c_53053,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK1(X4,cartesian_product2(X3,X2),X5),X5)
| ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_16267]) ).
tcf(c_53054,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X2),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(sK5(X1,X2,sK4(cartesian_product2(X1,X2),X3,X0)),X5)),X4))) = X4 )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_60,c_16267]) ).
tcf(c_53055,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(sK5(X2,X3,sK5(X1,cartesian_product2(X2,X3),X0)),X5)),X4))) = X4 )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_61,c_16267]) ).
tcf(c_53056,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X2,X0),singleton(X2))),X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_16267]) ).
tcf(c_53057,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,X2))),X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_807,c_16267]) ).
tcf(c_53058,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X2,X0),singleton(X0))),X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_809,c_16267]) ).
tcf(c_53059,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X3),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X2,X0))),X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_882,c_16267]) ).
tcf(c_53060,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X0,X2))),X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_16267]) ).
tcf(c_53061,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( sK4(singleton(X4),cartesian_product2(singleton(X5),X1),unordered_pair(singleton(X4),unordered_pair(unordered_pair(singleton(X5),unordered_pair(sK5(X3,X1,unordered_pair(singleton(X2),unordered_pair(X2,X0))),X5)),X4))) = X4 )
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_900,c_16267]) ).
tcf(c_53062,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = cartesian_product2(X3,X2) )
| ( sK2(singleton(X4),X5,cartesian_product2(X3,X2)) = X4 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(singleton(X4),X5,cartesian_product2(X3,X2))),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_799,c_16267]) ).
tcf(c_53063,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = singleton(X5) )
| ( sK1(cartesian_product2(X3,X2),X4,singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,singleton(X5))),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_800,c_16267]) ).
tcf(c_53064,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = cartesian_product2(X3,X2) )
| ( sK3(X4,singleton(X5),cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,singleton(X5),cartesian_product2(X3,X2))),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_803,c_16267]) ).
tcf(c_53065,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = singleton(X5) )
| ( sK1(X4,cartesian_product2(X3,X2),singleton(X5)) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),singleton(X5))),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_804,c_16267]) ).
tcf(c_53066,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2454,c_16267]) ).
tcf(c_53067,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1852,c_16267]) ).
tcf(c_53068,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(X4,cartesian_product2(X3,X2),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1564,c_16267]) ).
tcf(c_53069,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(X4,cartesian_product2(X3,X2),X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1145,c_16267]) ).
tcf(c_53070,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2455,c_16267]) ).
tcf(c_53071,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1853,c_16267]) ).
tcf(c_53072,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK1(cartesian_product2(X3,X2),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1565,c_16267]) ).
tcf(c_53073,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK1(cartesian_product2(X3,X2),X4,X5)),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1146,c_16267]) ).
tcf(c_53074,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2456,c_16267]) ).
tcf(c_53075,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1854,c_16267]) ).
tcf(c_53076,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(singleton(X6),unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1566,c_16267]) ).
tcf(c_53077,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X4,unordered_pair(unordered_pair(X6,sK2(X4,X5,cartesian_product2(X3,X2))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1147,c_16267]) ).
tcf(c_53078,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(sK3(X4,X5,cartesian_product2(X3,X2)),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_2457,c_16267]) ).
tcf(c_53079,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,X2)),X6),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1855,c_16267]) ).
tcf(c_53080,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(singleton(X6),unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1567,c_16267]) ).
tcf(c_53081,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK4(singleton(X6),X5,unordered_pair(unordered_pair(X6,sK3(X4,X5,cartesian_product2(X3,X2))),singleton(X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1148,c_16267]) ).
tcf(c_53242,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,singleton(X3))
| ( cartesian_product2(X2,singleton(X3)) = singleton(X0) )
| ( sK1(X2,singleton(X3),singleton(X0)) = X0 )
| ( sK5(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK1(X2,singleton(X3),singleton(X0)),X1),singleton(sK1(X2,singleton(X3),singleton(X0))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1032,c_1384]) ).
tcf(c_53243,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(sK3(X3,X2,X4),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_42941]) ).
tcf(c_53244,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2903]) ).
tcf(c_53245,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(X1,sK3(X3,X2,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_42542]) ).
tcf(c_53246,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2902]) ).
tcf(c_53247,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK3(X3,X1,X4),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_42396]) ).
tcf(c_53248,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2901]) ).
tcf(c_53249,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_42068]) ).
tcf(c_53250,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2900]) ).
tcf(c_53251,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK3(X3,X1,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_41683]) ).
tcf(c_53252,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2899]) ).
tcf(c_53253,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(sK3(X3,X2,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_40876]) ).
tcf(c_53254,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2898]) ).
tcf(c_53255,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_40020]) ).
tcf(c_53256,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2827]) ).
tcf(c_53257,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_39078]) ).
tcf(c_53258,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2826]) ).
tcf(c_53259,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_38387]) ).
tcf(c_53260,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2825]) ).
tcf(c_53261,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_37946]) ).
tcf(c_53262,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2824]) ).
tcf(c_53263,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_37625]) ).
tcf(c_53264,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2823]) ).
tcf(c_53265,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(sK3(X3,X2,X4),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_36554]) ).
tcf(c_53266,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2736]) ).
tcf(c_53267,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_35937]) ).
tcf(c_53268,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2822]) ).
tcf(c_53269,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(X1,sK3(X3,X2,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_35157]) ).
tcf(c_53270,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2735]) ).
tcf(c_53271,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK3(X3,X1,X4),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_34740]) ).
tcf(c_53272,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2734]) ).
tcf(c_53273,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_34537]) ).
tcf(c_53274,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2733]) ).
tcf(c_53275,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK3(X3,X1,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_34285]) ).
tcf(c_53276,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2732]) ).
tcf(c_53277,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_33912]) ).
tcf(c_53278,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2679]) ).
tcf(c_53279,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_33513]) ).
tcf(c_53280,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2678]) ).
tcf(c_53281,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(sK3(X3,X2,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_32955]) ).
tcf(c_53282,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2731]) ).
tcf(c_53283,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_31618]) ).
tcf(c_53284,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2677]) ).
tcf(c_53285,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_30471]) ).
tcf(c_53286,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2676]) ).
tcf(c_53287,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_30093]) ).
tcf(c_53288,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2675]) ).
tcf(c_53289,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(sK3(X3,X2,X4),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_29608]) ).
tcf(c_53290,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2347]) ).
tcf(c_53291,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(X1,sK3(X3,X2,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_29355]) ).
tcf(c_53292,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2346]) ).
tcf(c_53293,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK3(X3,X1,X4),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_28822]) ).
tcf(c_53294,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2345]) ).
tcf(c_53295,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_28296]) ).
tcf(c_53296,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2674]) ).
tcf(c_53297,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_27575]) ).
tcf(c_53298,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2344]) ).
tcf(c_53299,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK3(X3,X1,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_27245]) ).
tcf(c_53300,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2343]) ).
tcf(c_53301,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_26883]) ).
tcf(c_53302,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2289]) ).
tcf(c_53303,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_26385]) ).
tcf(c_53304,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2288]) ).
tcf(c_53305,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_26012]) ).
tcf(c_53306,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2287]) ).
tcf(c_53307,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_25743]) ).
tcf(c_53308,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2286]) ).
tcf(c_53309,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(sK3(X3,X2,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_25328]) ).
tcf(c_53310,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2342]) ).
tcf(c_53311,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_24337]) ).
tcf(c_53312,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2285]) ).
tcf(c_53313,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(sK3(X3,X2,X4),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_23980]) ).
tcf(c_53314,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2185]) ).
tcf(c_53315,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(X1,sK3(X3,X2,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_23739]) ).
tcf(c_53316,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2184]) ).
tcf(c_53317,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK3(X3,X1,X4),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_23253]) ).
tcf(c_53318,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2183]) ).
tcf(c_53319,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_22960]) ).
tcf(c_53320,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2182]) ).
tcf(c_53321,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK3(X3,X1,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_22721]) ).
tcf(c_53322,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2181]) ).
tcf(c_53323,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_22587]) ).
tcf(c_53324,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2284]) ).
tcf(c_53325,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_21575]) ).
tcf(c_53326,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2109]) ).
tcf(c_53327,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_21200]) ).
tcf(c_53328,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2108]) ).
tcf(c_53329,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_20765]) ).
tcf(c_53330,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2107]) ).
tcf(c_53331,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_20286]) ).
tcf(c_53332,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2106]) ).
tcf(c_53333,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(sK3(X3,X2,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_19855]) ).
tcf(c_53334,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2180]) ).
tcf(c_53335,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_18803]) ).
tcf(c_53336,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2105]) ).
tcf(c_53337,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_18127]) ).
tcf(c_53338,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2104]) ).
tcf(c_53339,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_17483]) ).
tcf(c_53340,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2465]) ).
tcf(c_53341,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_16787]) ).
tcf(c_53342,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2464]) ).
tcf(c_53343,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_16125]) ).
tcf(c_53344,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2463]) ).
tcf(c_53345,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_15658]) ).
tcf(c_53346,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2462]) ).
tcf(c_53347,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_15187]) ).
tcf(c_53348,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2461]) ).
tcf(c_53349,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_14882]) ).
tcf(c_53350,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2460]) ).
tcf(c_53351,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_13234]) ).
tcf(c_53352,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_1863]) ).
tcf(c_53353,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_12125]) ).
tcf(c_53354,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_1862]) ).
tcf(c_53355,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_11834]) ).
tcf(c_53356,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_1861]) ).
tcf(c_53357,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_11410]) ).
tcf(c_53358,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_1860]) ).
tcf(c_53359,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_10829]) ).
tcf(c_53360,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_1859]) ).
tcf(c_53361,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_10535]) ).
tcf(c_53362,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_1858]) ).
tcf(c_53363,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_8720]) ).
tcf(c_53364,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_1575]) ).
tcf(c_53365,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_8554]) ).
tcf(c_53366,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_1574]) ).
tcf(c_53367,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_8285]) ).
tcf(c_53368,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_1573]) ).
tcf(c_53369,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_8027]) ).
tcf(c_53370,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_1572]) ).
tcf(c_53371,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_7766]) ).
tcf(c_53372,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_1571]) ).
tcf(c_53373,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_7495]) ).
tcf(c_53374,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_1570]) ).
tcf(c_53375,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_6164]) ).
tcf(c_53376,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_1156]) ).
tcf(c_53377,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_5987]) ).
tcf(c_53378,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_1155]) ).
tcf(c_53379,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_5758]) ).
tcf(c_53380,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_1154]) ).
tcf(c_53381,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_5518]) ).
tcf(c_53382,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_1153]) ).
tcf(c_53383,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X2,X4),X5),singleton(sK1(X3,X2,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_5291]) ).
tcf(c_53384,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_1152]) ).
tcf(c_53385,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,X1,X4),X5),singleton(sK1(X3,X1,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_4798]) ).
tcf(c_53386,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,X3,X5),X6),singleton(sK1(X4,X3,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_1151]) ).
tcf(c_53387,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK5(X3,singleton(X4),unordered_pair(singleton(sK3(X2,X3,X0)),unordered_pair(X4,sK3(X2,X3,X0)))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(X2,X3,X0),X1),singleton(sK1(X2,X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1384,c_2539]) ).
tcf(c_53389,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK5(X3,singleton(X4),unordered_pair(unordered_pair(X4,sK3(X2,X3,X0)),singleton(sK3(X2,X3,X0)))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(X2,X3,X0),X1),singleton(sK1(X2,X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1384,c_1929]) ).
tcf(c_53391,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK5(X3,singleton(X4),unordered_pair(singleton(sK3(X2,X3,X0)),unordered_pair(sK3(X2,X3,X0),X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(X2,X3,X0),X1),singleton(sK1(X2,X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1384,c_1643]) ).
tcf(c_53393,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK5(X3,singleton(X4),unordered_pair(unordered_pair(sK3(X2,X3,X0),X4),singleton(sK3(X2,X3,X0)))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(X2,X3,X0),X1),singleton(sK1(X2,X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1384,c_1306]) ).
tcf(c_53395,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X2 )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(sK3(X4,singleton(X5),X2),X0))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK1(X4,singleton(X5),X2),X3),singleton(sK1(X4,singleton(X5),X2)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_907]) ).
tcf(c_53396,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,singleton(X2)) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,singleton(X2),X4),X5),singleton(sK1(X3,singleton(X2),X4)))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK3(X3,singleton(X2),X4)),unordered_pair(X0,sK3(X3,singleton(X2),X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_906]) ).
tcf(c_53397,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X2 )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(sK3(X4,singleton(X5),X2),X0),singleton(X0))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK1(X4,singleton(X5),X2),X3),singleton(sK1(X4,singleton(X5),X2)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_899]) ).
tcf(c_53398,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,singleton(X2)) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,singleton(X2),X4),X5),singleton(sK1(X3,singleton(X2),X4)))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X0,sK3(X3,singleton(X2),X4)),singleton(sK3(X3,singleton(X2),X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_898]) ).
tcf(c_53399,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X2 )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,singleton(X5),X2)))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK1(X4,singleton(X5),X2),X3),singleton(sK1(X4,singleton(X5),X2)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_889]) ).
tcf(c_53400,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,singleton(X2)) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,singleton(X2),X4),X5),singleton(sK1(X3,singleton(X2),X4)))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK3(X3,singleton(X2),X4)),unordered_pair(sK3(X3,singleton(X2),X4),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_888]) ).
tcf(c_53401,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X2 )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(X0,sK3(X4,singleton(X5),X2)),singleton(X0))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK1(X4,singleton(X5),X2),X3),singleton(sK1(X4,singleton(X5),X2)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_863]) ).
tcf(c_53402,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,singleton(X2)) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,singleton(X2),X4),X5),singleton(sK1(X3,singleton(X2),X4)))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK3(X3,singleton(X2),X4),X0),singleton(sK3(X3,singleton(X2),X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_837]) ).
tcf(c_53404,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6),singleton(sK1(X4,cartesian_product2(X3,X2),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_16267]) ).
tcf(c_53405,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6),singleton(sK1(X4,cartesian_product2(X2,X3),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_16266]) ).
tcf(c_53406,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6),singleton(sK1(X4,cartesian_product2(X3,X2),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_15723]) ).
tcf(c_53407,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6),singleton(sK1(X4,cartesian_product2(X2,X3),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_15722]) ).
tcf(c_53408,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6),singleton(sK1(X4,cartesian_product2(X3,X2),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_15377]) ).
tcf(c_53409,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6),singleton(sK1(X4,cartesian_product2(X2,X3),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_15376]) ).
tcf(c_53410,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6),singleton(sK1(X4,cartesian_product2(X3,X2),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_12049]) ).
tcf(c_53411,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6),singleton(sK1(X4,cartesian_product2(X2,X3),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_12048]) ).
tcf(c_53412,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6),singleton(sK1(X4,cartesian_product2(X3,X2),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_11518]) ).
tcf(c_53413,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6),singleton(sK1(X4,cartesian_product2(X2,X3),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_11517]) ).
tcf(c_53414,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6),singleton(sK1(X4,cartesian_product2(X3,X2),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_11093]) ).
tcf(c_53415,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6),singleton(sK1(X4,cartesian_product2(X2,X3),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_11092]) ).
tcf(c_53416,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6),singleton(sK1(X4,cartesian_product2(X3,X2),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_8458]) ).
tcf(c_53417,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6),singleton(sK1(X4,cartesian_product2(X2,X3),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_8457]) ).
tcf(c_53418,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6),singleton(sK1(X4,cartesian_product2(X3,X2),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_8152]) ).
tcf(c_53419,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6),singleton(sK1(X4,cartesian_product2(X2,X3),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_8151]) ).
tcf(c_53420,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6),singleton(sK1(X4,cartesian_product2(X3,X2),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_7854]) ).
tcf(c_53421,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6),singleton(sK1(X4,cartesian_product2(X2,X3),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_7853]) ).
tcf(c_53422,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6),singleton(sK1(X4,cartesian_product2(X3,X2),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_5825]) ).
tcf(c_53423,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6),singleton(sK1(X4,cartesian_product2(X2,X3),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_5824]) ).
tcf(c_53424,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6),singleton(sK1(X4,cartesian_product2(X3,X2),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_5642]) ).
tcf(c_53425,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6),singleton(sK1(X4,cartesian_product2(X2,X3),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_5641]) ).
tcf(c_53426,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6),singleton(sK1(X4,cartesian_product2(X3,X2),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_5396]) ).
tcf(c_53427,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6),singleton(sK1(X4,cartesian_product2(X2,X3),X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_5395]) ).
tcf(c_53428,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X0)) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,cartesian_product2(X2,X0),X4),X5),singleton(sK1(X3,cartesian_product2(X2,X0),X4)))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))),unordered_pair(X1,sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1384,c_2611]) ).
tcf(c_53429,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X0,X2)) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,cartesian_product2(X0,X2),X4),X5),singleton(sK1(X3,cartesian_product2(X0,X2),X4)))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))),unordered_pair(X1,sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1384,c_2610]) ).
tcf(c_53430,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X0)) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,cartesian_product2(X2,X0),X4),X5),singleton(sK1(X3,cartesian_product2(X2,X0),X4)))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))),singleton(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1384,c_2036]) ).
tcf(c_53431,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X0,X2)) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,cartesian_product2(X0,X2),X4),X5),singleton(sK1(X3,cartesian_product2(X0,X2),X4)))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))),singleton(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1384,c_2035]) ).
tcf(c_53432,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X0)) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,cartesian_product2(X2,X0),X4),X5),singleton(sK1(X3,cartesian_product2(X2,X0),X4)))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))),unordered_pair(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4)),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1384,c_1703]) ).
tcf(c_53433,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X0,X2)) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,cartesian_product2(X0,X2),X4),X5),singleton(sK1(X3,cartesian_product2(X0,X2),X4)))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))),unordered_pair(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4)),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1384,c_1702]) ).
tcf(c_53434,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X0)) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,cartesian_product2(X2,X0),X4),X5),singleton(sK1(X3,cartesian_product2(X2,X0),X4)))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4)),X1),singleton(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1384,c_1389]) ).
tcf(c_53435,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X0,X2)) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X3,cartesian_product2(X0,X2),X4),X5),singleton(sK1(X3,cartesian_product2(X0,X2),X4)))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4)),X1),singleton(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1384,c_1388]) ).
tcf(c_53436,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(X3,X4)) = X0 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK5(X3,X4,sK3(X2,cartesian_product2(X3,X4),X0)),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(X2,cartesian_product2(X3,X4),X0),X1),singleton(sK1(X2,cartesian_product2(X3,X4),X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1384,c_2459]) ).
tcf(c_53437,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(X3,X4)) = X0 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK4(X3,X4,sK3(X2,cartesian_product2(X3,X4),X0)),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(X2,cartesian_product2(X3,X4),X0),X1),singleton(sK1(X2,cartesian_product2(X3,X4),X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1384,c_2458]) ).
tcf(c_53438,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(X3,X4)) = X0 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK5(X3,X4,sK3(X2,cartesian_product2(X3,X4),X0)),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(X2,cartesian_product2(X3,X4),X0),X1),singleton(sK1(X2,cartesian_product2(X3,X4),X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1384,c_1857]) ).
tcf(c_53439,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(X3,X4)) = X0 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK4(X3,X4,sK3(X2,cartesian_product2(X3,X4),X0)),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(X2,cartesian_product2(X3,X4),X0),X1),singleton(sK1(X2,cartesian_product2(X3,X4),X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1384,c_1856]) ).
tcf(c_53440,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(X3,X4)) = X0 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X3,X4,sK3(X2,cartesian_product2(X3,X4),X0))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(X2,cartesian_product2(X3,X4),X0),X1),singleton(sK1(X2,cartesian_product2(X3,X4),X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1384,c_1569]) ).
tcf(c_53441,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(X3,X4)) = X0 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X3,X4,sK3(X2,cartesian_product2(X3,X4),X0))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(X2,cartesian_product2(X3,X4),X0),X1),singleton(sK1(X2,cartesian_product2(X3,X4),X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1384,c_1568]) ).
tcf(c_53442,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(X3,X4)) = X0 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK5(X3,X4,sK3(X2,cartesian_product2(X3,X4),X0))),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(X2,cartesian_product2(X3,X4),X0),X1),singleton(sK1(X2,cartesian_product2(X3,X4),X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1384,c_1150]) ).
tcf(c_53443,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(X3,X4)) = X0 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK4(X3,X4,sK3(X2,cartesian_product2(X3,X4),X0))),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(X2,cartesian_product2(X3,X4),X0),X1),singleton(sK1(X2,cartesian_product2(X3,X4),X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1384,c_1149]) ).
tcf(c_53444,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,cartesian_product2(X0,X1)) = X3 )
| ( sK5(X3,singleton(X4),unordered_pair(unordered_pair(sK1(X2,cartesian_product2(X0,X1),X3),X4),singleton(sK1(X2,cartesian_product2(X0,X1),X3)))) = X4 )
| ( unordered_pair(unordered_pair(sK4(X0,X1,sK3(X2,cartesian_product2(X0,X1),X3)),sK5(X0,X1,sK3(X2,cartesian_product2(X0,X1),X3))),singleton(sK4(X0,X1,sK3(X2,cartesian_product2(X0,X1),X3)))) = sK3(X2,cartesian_product2(X0,X1),X3) ) ),
inference(superposition,[status(thm)],[c_1384,c_62]) ).
tcf(c_53445,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X6),singleton(sK1(X4,cartesian_product2(singleton(X2),X3),X5)))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,cartesian_product2(singleton(X2),X3),X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_3017]) ).
tcf(c_53446,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X6),singleton(sK1(X4,cartesian_product2(singleton(X2),X3),X5)))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(sK3(X4,cartesian_product2(singleton(X2),X3),X5),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_3015]) ).
tcf(c_53447,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X6),singleton(sK1(X4,cartesian_product2(singleton(X2),X3),X5)))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(sK3(X4,cartesian_product2(singleton(X2),X3),X5),X0),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_3014]) ).
tcf(c_53448,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X6),singleton(sK1(X4,cartesian_product2(singleton(X2),X3),X5)))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK3(X4,cartesian_product2(singleton(X2),X3),X5)),unordered_pair(sK3(X4,cartesian_product2(singleton(X2),X3),X5),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2961]) ).
tcf(c_53449,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X6),singleton(sK1(X4,cartesian_product2(singleton(X2),X3),X5)))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK3(X4,cartesian_product2(singleton(X2),X3),X5)),unordered_pair(X0,sK3(X4,cartesian_product2(singleton(X2),X3),X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2959]) ).
tcf(c_53450,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X6),singleton(sK1(X4,cartesian_product2(singleton(X2),X3),X5)))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(X0,sK3(X4,cartesian_product2(singleton(X2),X3),X5)),singleton(sK3(X4,cartesian_product2(singleton(X2),X3),X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2958]) ).
tcf(c_53451,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X6),singleton(sK1(X4,cartesian_product2(singleton(X2),X3),X5)))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(X0,sK3(X4,cartesian_product2(singleton(X2),X3),X5)),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_3012]) ).
tcf(c_53452,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X6),singleton(sK1(X4,cartesian_product2(singleton(X2),X3),X5)))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(sK3(X4,cartesian_product2(singleton(X2),X3),X5),X0),singleton(sK3(X4,cartesian_product2(singleton(X2),X3),X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2956]) ).
tcf(c_53453,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X5),X6)) = X2 )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X5),X6,sK3(X4,cartesian_product2(singleton(X5),X6),X2)),X0))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(singleton(X5),X6),X2),X3),singleton(sK1(X4,cartesian_product2(singleton(X5),X6),X2)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2545]) ).
tcf(c_53454,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X5),X6)) = X2 )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(sK4(singleton(X5),X6,sK3(X4,cartesian_product2(singleton(X5),X6),X2)),X0),singleton(X0))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(singleton(X5),X6),X2),X3),singleton(sK1(X4,cartesian_product2(singleton(X5),X6),X2)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_1935]) ).
tcf(c_53455,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X5),X6)) = X2 )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X5),X6,sK3(X4,cartesian_product2(singleton(X5),X6),X2))))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(singleton(X5),X6),X2),X3),singleton(sK1(X4,cartesian_product2(singleton(X5),X6),X2)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_1649]) ).
tcf(c_53456,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X5),X6)) = X2 )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(X0,sK4(singleton(X5),X6,sK3(X4,cartesian_product2(singleton(X5),X6),X2))),singleton(X0))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(singleton(X5),X6),X2),X3),singleton(sK1(X4,cartesian_product2(singleton(X5),X6),X2)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_1312]) ).
tcf(c_53457,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,cartesian_product2(singleton(X3),X4)) = X0 )
| ( sK4(singleton(X3),X4,sK3(X2,cartesian_product2(singleton(X3),X4),X0)) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(X2,cartesian_product2(singleton(X3),X4),X0),X1),singleton(sK1(X2,cartesian_product2(singleton(X3),X4),X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1384,c_787]) ).
tcf(c_53458,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X5,singleton(X6))) = X2 )
| ( sK5(X5,singleton(X6),sK5(X1,cartesian_product2(X5,singleton(X6)),unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,cartesian_product2(X5,singleton(X6)),X2))))) = X6 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X5,singleton(X6)),X2),X3),singleton(sK1(X4,cartesian_product2(X5,singleton(X6)),X2)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_3142]) ).
tcf(c_53459,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X5,singleton(X6))) = X2 )
| ( sK5(X5,singleton(X6),sK5(X1,cartesian_product2(X5,singleton(X6)),unordered_pair(singleton(X0),unordered_pair(sK3(X4,cartesian_product2(X5,singleton(X6)),X2),X0)))) = X6 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X5,singleton(X6)),X2),X3),singleton(sK1(X4,cartesian_product2(X5,singleton(X6)),X2)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_3140]) ).
tcf(c_53460,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X5,singleton(X6))) = X2 )
| ( sK5(X5,singleton(X6),sK5(X1,cartesian_product2(X5,singleton(X6)),unordered_pair(unordered_pair(sK3(X4,cartesian_product2(X5,singleton(X6)),X2),X0),singleton(X0)))) = X6 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X5,singleton(X6)),X2),X3),singleton(sK1(X4,cartesian_product2(X5,singleton(X6)),X2)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_3139]) ).
tcf(c_53461,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X2,singleton(X3)),X5),X6),singleton(sK1(X4,cartesian_product2(X2,singleton(X3)),X5)))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK3(X4,cartesian_product2(X2,singleton(X3)),X5)),unordered_pair(sK3(X4,cartesian_product2(X2,singleton(X3)),X5),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_3063]) ).
tcf(c_53462,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X2,singleton(X3)),X5),X6),singleton(sK1(X4,cartesian_product2(X2,singleton(X3)),X5)))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK3(X4,cartesian_product2(X2,singleton(X3)),X5)),unordered_pair(X0,sK3(X4,cartesian_product2(X2,singleton(X3)),X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_3061]) ).
tcf(c_53463,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X2,singleton(X3)),X5),X6),singleton(sK1(X4,cartesian_product2(X2,singleton(X3)),X5)))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(X0,sK3(X4,cartesian_product2(X2,singleton(X3)),X5)),singleton(sK3(X4,cartesian_product2(X2,singleton(X3)),X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_3060]) ).
tcf(c_53464,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X5,singleton(X6))) = X2 )
| ( sK5(X5,singleton(X6),sK5(X1,cartesian_product2(X5,singleton(X6)),unordered_pair(unordered_pair(X0,sK3(X4,cartesian_product2(X5,singleton(X6)),X2)),singleton(X0)))) = X6 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X5,singleton(X6)),X2),X3),singleton(sK1(X4,cartesian_product2(X5,singleton(X6)),X2)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_3137]) ).
tcf(c_53465,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X2,singleton(X3)),X5),X6),singleton(sK1(X4,cartesian_product2(X2,singleton(X3)),X5)))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(sK3(X4,cartesian_product2(X2,singleton(X3)),X5),X0),singleton(sK3(X4,cartesian_product2(X2,singleton(X3)),X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_3058]) ).
tcf(c_53466,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X5,singleton(X6))) = X2 )
| ( sK5(X1,singleton(X6),unordered_pair(singleton(X0),unordered_pair(sK5(X5,singleton(X6),sK3(X4,cartesian_product2(X5,singleton(X6)),X2)),X0))) = X6 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X5,singleton(X6)),X2),X3),singleton(sK1(X4,cartesian_product2(X5,singleton(X6)),X2)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_2546]) ).
tcf(c_53467,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X5,singleton(X6))) = X2 )
| ( sK5(X1,singleton(X6),unordered_pair(unordered_pair(sK5(X5,singleton(X6),sK3(X4,cartesian_product2(X5,singleton(X6)),X2)),X0),singleton(X0))) = X6 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X5,singleton(X6)),X2),X3),singleton(sK1(X4,cartesian_product2(X5,singleton(X6)),X2)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_1936]) ).
tcf(c_53468,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X5,singleton(X6))) = X2 )
| ( sK5(X1,singleton(X6),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X5,singleton(X6),sK3(X4,cartesian_product2(X5,singleton(X6)),X2))))) = X6 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X5,singleton(X6)),X2),X3),singleton(sK1(X4,cartesian_product2(X5,singleton(X6)),X2)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_1650]) ).
tcf(c_53469,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X5,singleton(X6))) = X2 )
| ( sK5(X1,singleton(X6),unordered_pair(unordered_pair(X0,sK5(X5,singleton(X6),sK3(X4,cartesian_product2(X5,singleton(X6)),X2))),singleton(X0))) = X6 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X5,singleton(X6)),X2),X3),singleton(sK1(X4,cartesian_product2(X5,singleton(X6)),X2)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1384,c_1313]) ).
tcf(c_53470,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,cartesian_product2(X3,singleton(X4))) = X0 )
| ( sK5(X3,singleton(X4),sK3(X2,cartesian_product2(X3,singleton(X4)),X0)) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(X2,cartesian_product2(X3,singleton(X4)),X0),X1),singleton(sK1(X2,cartesian_product2(X3,singleton(X4)),X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1384,c_789]) ).
tcf(c_53471,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(cartesian_product2(singleton(X3),X4),X5)) = X0 )
| ( sK4(singleton(X3),X4,sK4(cartesian_product2(singleton(X3),X4),X5,sK3(X2,cartesian_product2(cartesian_product2(singleton(X3),X4),X5),X0))) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(X2,cartesian_product2(cartesian_product2(singleton(X3),X4),X5),X0),X1),singleton(sK1(X2,cartesian_product2(cartesian_product2(singleton(X3),X4),X5),X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1384,c_835]) ).
tcf(c_53472,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(X3,cartesian_product2(singleton(X4),X5))) = X0 )
| ( sK4(singleton(X4),X5,sK5(X3,cartesian_product2(singleton(X4),X5),sK3(X2,cartesian_product2(X3,cartesian_product2(singleton(X4),X5)),X0))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(X2,cartesian_product2(X3,cartesian_product2(singleton(X4),X5)),X0),X1),singleton(sK1(X2,cartesian_product2(X3,cartesian_product2(singleton(X4),X5)),X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1384,c_836]) ).
tcf(c_53473,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(cartesian_product2(X3,singleton(X4)),X5)) = X0 )
| ( sK5(X3,singleton(X4),sK4(cartesian_product2(X3,singleton(X4)),X5,sK3(X2,cartesian_product2(cartesian_product2(X3,singleton(X4)),X5),X0))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(X2,cartesian_product2(cartesian_product2(X3,singleton(X4)),X5),X0),X1),singleton(sK1(X2,cartesian_product2(cartesian_product2(X3,singleton(X4)),X5),X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1384,c_861]) ).
tcf(c_53474,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(X3,cartesian_product2(X4,singleton(X5)))) = X0 )
| ( sK5(X4,singleton(X5),sK5(X3,cartesian_product2(X4,singleton(X5)),sK3(X2,cartesian_product2(X3,cartesian_product2(X4,singleton(X5))),X0))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(X2,cartesian_product2(X3,cartesian_product2(X4,singleton(X5))),X0),X1),singleton(sK1(X2,cartesian_product2(X3,cartesian_product2(X4,singleton(X5))),X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1384,c_862]) ).
tcf(c_53475,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X2,X1),X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5),X6),singleton(sK1(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK3(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_2896]) ).
tcf(c_53476,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X1,X2),X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5),X6),singleton(sK1(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK3(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_2820]) ).
tcf(c_53477,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X2,X1),X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5),X6),singleton(sK1(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK3(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_2729]) ).
tcf(c_53478,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X1,X2),X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5),X6),singleton(sK1(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK3(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_2672]) ).
tcf(c_53479,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X2,X1),X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5),X6),singleton(sK1(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK3(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_2340]) ).
tcf(c_53480,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X1,X2),X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5),X6),singleton(sK1(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK3(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_2282]) ).
tcf(c_53481,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X2,X1),X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5),X6),singleton(sK1(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK3(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_2178]) ).
tcf(c_53482,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X1,X2),X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5),X6),singleton(sK1(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK3(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_2102]) ).
tcf(c_53483,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X2,X1))) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5),X6),singleton(sK1(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK3(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_2897]) ).
tcf(c_53484,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X1,X2))) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5),X6),singleton(sK1(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK3(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_2821]) ).
tcf(c_53485,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X2,X1))) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5),X6),singleton(sK1(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK3(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_2730]) ).
tcf(c_53486,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X1,X2))) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5),X6),singleton(sK1(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK3(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_2673]) ).
tcf(c_53487,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X2,X1))) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5),X6),singleton(sK1(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK3(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_2341]) ).
tcf(c_53488,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X1,X2))) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5),X6),singleton(sK1(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK3(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_2283]) ).
tcf(c_53489,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X2,X1))) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5),X6),singleton(sK1(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK3(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_2179]) ).
tcf(c_53490,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X1,X2))) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5),X6),singleton(sK1(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK3(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1384,c_2103]) ).
tcf(c_55414,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X2,singleton(X2))
| ( cartesian_product2(singleton(X2),X3) = singleton(X0) )
| ( sK1(singleton(X2),X3,singleton(X0)) = X0 )
| ( sK5(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK1(singleton(X2),X3,singleton(X0)),X1),singleton(sK1(singleton(X2),X3,singleton(X0))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1009,c_1385]) ).
tcf(c_55415,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(sK2(X2,X3,X4),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_42941]) ).
tcf(c_55416,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2903]) ).
tcf(c_55417,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(X1,sK2(X2,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_42542]) ).
tcf(c_55418,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2902]) ).
tcf(c_55419,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK2(X1,X3,X4),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_42396]) ).
tcf(c_55420,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2901]) ).
tcf(c_55421,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_42068]) ).
tcf(c_55422,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2900]) ).
tcf(c_55423,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK2(X1,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_41683]) ).
tcf(c_55424,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2899]) ).
tcf(c_55425,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(sK2(X2,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_40876]) ).
tcf(c_55426,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2898]) ).
tcf(c_55427,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_40020]) ).
tcf(c_55428,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2827]) ).
tcf(c_55429,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_39078]) ).
tcf(c_55430,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2826]) ).
tcf(c_55431,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_38387]) ).
tcf(c_55432,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2825]) ).
tcf(c_55433,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_37946]) ).
tcf(c_55434,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2824]) ).
tcf(c_55435,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_37625]) ).
tcf(c_55436,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2823]) ).
tcf(c_55437,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(sK2(X2,X3,X4),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_36554]) ).
tcf(c_55438,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2736]) ).
tcf(c_55439,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_35937]) ).
tcf(c_55440,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2822]) ).
tcf(c_55441,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(X1,sK2(X2,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_35157]) ).
tcf(c_55442,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2735]) ).
tcf(c_55443,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK2(X1,X3,X4),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_34740]) ).
tcf(c_55444,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2734]) ).
tcf(c_55445,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_34537]) ).
tcf(c_55446,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2733]) ).
tcf(c_55447,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK2(X1,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_34285]) ).
tcf(c_55448,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2732]) ).
tcf(c_55449,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_33912]) ).
tcf(c_55450,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2679]) ).
tcf(c_55451,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_33513]) ).
tcf(c_55452,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2678]) ).
tcf(c_55453,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(sK2(X2,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_32955]) ).
tcf(c_55454,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2731]) ).
tcf(c_55455,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_31618]) ).
tcf(c_55456,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2677]) ).
tcf(c_55457,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_30471]) ).
tcf(c_55458,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2676]) ).
tcf(c_55459,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_30093]) ).
tcf(c_55460,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2675]) ).
tcf(c_55461,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(sK2(X2,X3,X4),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_29608]) ).
tcf(c_55462,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2347]) ).
tcf(c_55463,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(X1,sK2(X2,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_29355]) ).
tcf(c_55464,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2346]) ).
tcf(c_55465,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK2(X1,X3,X4),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_28822]) ).
tcf(c_55466,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2345]) ).
tcf(c_55467,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_28296]) ).
tcf(c_55468,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2674]) ).
tcf(c_55469,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_27575]) ).
tcf(c_55470,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2344]) ).
tcf(c_55471,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK2(X1,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_27245]) ).
tcf(c_55472,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2343]) ).
tcf(c_55473,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_26883]) ).
tcf(c_55474,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2289]) ).
tcf(c_55475,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_26385]) ).
tcf(c_55476,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2288]) ).
tcf(c_55477,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_26012]) ).
tcf(c_55478,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2287]) ).
tcf(c_55479,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_25743]) ).
tcf(c_55480,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2286]) ).
tcf(c_55481,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(sK2(X2,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_25328]) ).
tcf(c_55482,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2342]) ).
tcf(c_55483,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_24337]) ).
tcf(c_55484,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2285]) ).
tcf(c_55485,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(sK2(X2,X3,X4),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_23980]) ).
tcf(c_55486,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2185]) ).
tcf(c_55487,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(X1,sK2(X2,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_23739]) ).
tcf(c_55488,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2184]) ).
tcf(c_55489,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK2(X1,X3,X4),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_23253]) ).
tcf(c_55490,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2183]) ).
tcf(c_55491,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_22960]) ).
tcf(c_55492,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2182]) ).
tcf(c_55493,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK2(X1,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_22721]) ).
tcf(c_55494,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2181]) ).
tcf(c_55495,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_22587]) ).
tcf(c_55496,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2284]) ).
tcf(c_55497,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_21575]) ).
tcf(c_55498,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2109]) ).
tcf(c_55499,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_21200]) ).
tcf(c_55500,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2108]) ).
tcf(c_55501,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_20765]) ).
tcf(c_55502,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2107]) ).
tcf(c_55503,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_20286]) ).
tcf(c_55504,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2106]) ).
tcf(c_55505,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(sK2(X2,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_19855]) ).
tcf(c_55506,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2180]) ).
tcf(c_55507,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_18803]) ).
tcf(c_55508,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2105]) ).
tcf(c_55509,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_18127]) ).
tcf(c_55510,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2104]) ).
tcf(c_55511,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_17483]) ).
tcf(c_55512,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2465]) ).
tcf(c_55513,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_16787]) ).
tcf(c_55514,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2464]) ).
tcf(c_55515,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_16125]) ).
tcf(c_55516,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2463]) ).
tcf(c_55517,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_15658]) ).
tcf(c_55518,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2462]) ).
tcf(c_55519,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_15187]) ).
tcf(c_55520,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2461]) ).
tcf(c_55521,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_14882]) ).
tcf(c_55522,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2460]) ).
tcf(c_55523,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_13234]) ).
tcf(c_55524,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_1863]) ).
tcf(c_55525,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_12125]) ).
tcf(c_55526,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_1862]) ).
tcf(c_55527,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_11834]) ).
tcf(c_55528,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_1861]) ).
tcf(c_55529,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_11410]) ).
tcf(c_55530,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_1860]) ).
tcf(c_55531,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_10829]) ).
tcf(c_55532,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_1859]) ).
tcf(c_55533,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_10535]) ).
tcf(c_55534,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_1858]) ).
tcf(c_55535,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_8720]) ).
tcf(c_55536,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_1575]) ).
tcf(c_55537,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_8554]) ).
tcf(c_55538,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_1574]) ).
tcf(c_55539,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_8285]) ).
tcf(c_55540,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_1573]) ).
tcf(c_55541,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_8027]) ).
tcf(c_55542,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_1572]) ).
tcf(c_55543,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_7766]) ).
tcf(c_55544,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_1571]) ).
tcf(c_55545,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_7495]) ).
tcf(c_55546,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_1570]) ).
tcf(c_55547,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_6164]) ).
tcf(c_55548,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_1156]) ).
tcf(c_55549,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_5987]) ).
tcf(c_55550,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_1155]) ).
tcf(c_55551,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_5758]) ).
tcf(c_55552,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_1154]) ).
tcf(c_55553,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_5518]) ).
tcf(c_55554,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_1153]) ).
tcf(c_55555,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X2,X3,X4),X5),singleton(sK1(X2,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_5291]) ).
tcf(c_55556,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_1152]) ).
tcf(c_55557,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(X1,X3,X4),X5),singleton(sK1(X1,X3,X4)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_4798]) ).
tcf(c_55558,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(X3,X4,X5),X6),singleton(sK1(X3,X4,X5)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_1151]) ).
tcf(c_55559,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK5(X2,singleton(X4),unordered_pair(singleton(sK2(X2,X3,X0)),unordered_pair(X4,sK2(X2,X3,X0)))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(X2,X3,X0),X1),singleton(sK1(X2,X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1385,c_2539]) ).
tcf(c_55561,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK5(X2,singleton(X4),unordered_pair(unordered_pair(X4,sK2(X2,X3,X0)),singleton(sK2(X2,X3,X0)))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(X2,X3,X0),X1),singleton(sK1(X2,X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1385,c_1929]) ).
tcf(c_55563,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK5(X2,singleton(X4),unordered_pair(singleton(sK2(X2,X3,X0)),unordered_pair(sK2(X2,X3,X0),X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(X2,X3,X0),X1),singleton(sK1(X2,X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1385,c_1643]) ).
tcf(c_55565,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK5(X2,singleton(X4),unordered_pair(unordered_pair(sK2(X2,X3,X0),X4),singleton(sK2(X2,X3,X0)))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(X2,X3,X0),X1),singleton(sK1(X2,X3,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1385,c_1306]) ).
tcf(c_55567,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X2 )
| ( sK5(X1,singleton(X4),unordered_pair(singleton(X0),unordered_pair(sK2(singleton(X4),X5,X2),X0))) = X4 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK1(singleton(X4),X5,X2),X3),singleton(sK1(singleton(X4),X5,X2)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_907]) ).
tcf(c_55568,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(singleton(X2),X3,X4),X5),singleton(sK1(singleton(X2),X3,X4)))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK2(singleton(X2),X3,X4)),unordered_pair(X0,sK2(singleton(X2),X3,X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_906]) ).
tcf(c_55569,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X2 )
| ( sK5(X1,singleton(X4),unordered_pair(unordered_pair(sK2(singleton(X4),X5,X2),X0),singleton(X0))) = X4 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK1(singleton(X4),X5,X2),X3),singleton(sK1(singleton(X4),X5,X2)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_899]) ).
tcf(c_55570,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(singleton(X2),X3,X4),X5),singleton(sK1(singleton(X2),X3,X4)))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X0,sK2(singleton(X2),X3,X4)),singleton(sK2(singleton(X2),X3,X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_898]) ).
tcf(c_55571,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X2 )
| ( sK5(X1,singleton(X4),unordered_pair(singleton(X0),unordered_pair(X0,sK2(singleton(X4),X5,X2)))) = X4 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK1(singleton(X4),X5,X2),X3),singleton(sK1(singleton(X4),X5,X2)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_889]) ).
tcf(c_55572,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(singleton(X2),X3,X4),X5),singleton(sK1(singleton(X2),X3,X4)))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK2(singleton(X2),X3,X4)),unordered_pair(sK2(singleton(X2),X3,X4),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_888]) ).
tcf(c_55573,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X2 )
| ( sK5(X1,singleton(X4),unordered_pair(unordered_pair(X0,sK2(singleton(X4),X5,X2)),singleton(X0))) = X4 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK1(singleton(X4),X5,X2),X3),singleton(sK1(singleton(X4),X5,X2)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_863]) ).
tcf(c_55574,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(singleton(X2),X3,X4),X5),singleton(sK1(singleton(X2),X3,X4)))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK2(singleton(X2),X3,X4),X0),singleton(sK2(singleton(X2),X3,X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_837]) ).
tcf(c_55576,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6),singleton(sK1(cartesian_product2(X3,X2),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_16267]) ).
tcf(c_55577,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6),singleton(sK1(cartesian_product2(X2,X3),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_16266]) ).
tcf(c_55578,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6),singleton(sK1(cartesian_product2(X3,X2),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_15723]) ).
tcf(c_55579,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6),singleton(sK1(cartesian_product2(X2,X3),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_15722]) ).
tcf(c_55580,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6),singleton(sK1(cartesian_product2(X3,X2),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_15377]) ).
tcf(c_55581,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6),singleton(sK1(cartesian_product2(X2,X3),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_15376]) ).
tcf(c_55582,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6),singleton(sK1(cartesian_product2(X3,X2),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_12049]) ).
tcf(c_55583,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6),singleton(sK1(cartesian_product2(X2,X3),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_12048]) ).
tcf(c_55584,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6),singleton(sK1(cartesian_product2(X3,X2),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_11518]) ).
tcf(c_55585,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6),singleton(sK1(cartesian_product2(X2,X3),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_11517]) ).
tcf(c_55586,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6),singleton(sK1(cartesian_product2(X3,X2),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_11093]) ).
tcf(c_55587,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6),singleton(sK1(cartesian_product2(X2,X3),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_11092]) ).
tcf(c_55588,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6),singleton(sK1(cartesian_product2(X3,X2),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_8458]) ).
tcf(c_55589,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6),singleton(sK1(cartesian_product2(X2,X3),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_8457]) ).
tcf(c_55590,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6),singleton(sK1(cartesian_product2(X3,X2),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_8152]) ).
tcf(c_55591,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6),singleton(sK1(cartesian_product2(X2,X3),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_8151]) ).
tcf(c_55592,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6),singleton(sK1(cartesian_product2(X3,X2),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_7854]) ).
tcf(c_55593,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6),singleton(sK1(cartesian_product2(X2,X3),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_7853]) ).
tcf(c_55594,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6),singleton(sK1(cartesian_product2(X3,X2),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_5825]) ).
tcf(c_55595,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6),singleton(sK1(cartesian_product2(X2,X3),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_5824]) ).
tcf(c_55596,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6),singleton(sK1(cartesian_product2(X3,X2),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_5642]) ).
tcf(c_55597,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6),singleton(sK1(cartesian_product2(X2,X3),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_5641]) ).
tcf(c_55598,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6),singleton(sK1(cartesian_product2(X3,X2),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_5396]) ).
tcf(c_55599,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6),singleton(sK1(cartesian_product2(X2,X3),X4,X5)))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_5395]) ).
tcf(c_55600,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X0),X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X0),X3,X4),X5),singleton(sK1(cartesian_product2(X2,X0),X3,X4)))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))),unordered_pair(X1,sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1385,c_2611]) ).
tcf(c_55601,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X0,X2),X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(cartesian_product2(X0,X2),X3,X4),X5),singleton(sK1(cartesian_product2(X0,X2),X3,X4)))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))),unordered_pair(X1,sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1385,c_2610]) ).
tcf(c_55602,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X0),X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X0),X3,X4),X5),singleton(sK1(cartesian_product2(X2,X0),X3,X4)))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))),singleton(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1385,c_2036]) ).
tcf(c_55603,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X0,X2),X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(cartesian_product2(X0,X2),X3,X4),X5),singleton(sK1(cartesian_product2(X0,X2),X3,X4)))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))),singleton(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1385,c_2035]) ).
tcf(c_55604,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X0),X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X0),X3,X4),X5),singleton(sK1(cartesian_product2(X2,X0),X3,X4)))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))),unordered_pair(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4)),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1385,c_1703]) ).
tcf(c_55605,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X0,X2),X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(cartesian_product2(X0,X2),X3,X4),X5),singleton(sK1(cartesian_product2(X0,X2),X3,X4)))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))),unordered_pair(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4)),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1385,c_1702]) ).
tcf(c_55606,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X0),X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X0),X3,X4),X5),singleton(sK1(cartesian_product2(X2,X0),X3,X4)))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4)),X1),singleton(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1385,c_1389]) ).
tcf(c_55607,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X0,X2),X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK1(cartesian_product2(X0,X2),X3,X4),X5),singleton(sK1(cartesian_product2(X0,X2),X3,X4)))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4)),X1),singleton(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1385,c_1388]) ).
tcf(c_55608,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X0 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK5(X2,X3,sK2(cartesian_product2(X2,X3),X4,X0)),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X3),X4,X0),X1),singleton(sK1(cartesian_product2(X2,X3),X4,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1385,c_2459]) ).
tcf(c_55609,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X0 )
| ( sK4(singleton(X5),X2,unordered_pair(singleton(X5),unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X0)),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X3),X4,X0),X1),singleton(sK1(cartesian_product2(X2,X3),X4,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1385,c_2458]) ).
tcf(c_55610,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X0 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK5(X2,X3,sK2(cartesian_product2(X2,X3),X4,X0)),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X3),X4,X0),X1),singleton(sK1(cartesian_product2(X2,X3),X4,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1385,c_1857]) ).
tcf(c_55611,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X0 )
| ( sK4(singleton(X5),X2,unordered_pair(unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X0)),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X3),X4,X0),X1),singleton(sK1(cartesian_product2(X2,X3),X4,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1385,c_1856]) ).
tcf(c_55612,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X0 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X2,X3,sK2(cartesian_product2(X2,X3),X4,X0))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X3),X4,X0),X1),singleton(sK1(cartesian_product2(X2,X3),X4,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1385,c_1569]) ).
tcf(c_55613,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X0 )
| ( sK4(singleton(X5),X2,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X0))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X3),X4,X0),X1),singleton(sK1(cartesian_product2(X2,X3),X4,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1385,c_1568]) ).
tcf(c_55614,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X0 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK5(X2,X3,sK2(cartesian_product2(X2,X3),X4,X0))),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X3),X4,X0),X1),singleton(sK1(cartesian_product2(X2,X3),X4,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1385,c_1150]) ).
tcf(c_55615,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X0 )
| ( sK4(singleton(X5),X2,unordered_pair(unordered_pair(X5,sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X0))),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(cartesian_product2(X2,X3),X4,X0),X1),singleton(sK1(cartesian_product2(X2,X3),X4,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1385,c_1149]) ).
tcf(c_55616,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(X0,X1),X2) = X3 )
| ( sK5(X3,singleton(X4),unordered_pair(unordered_pair(sK1(cartesian_product2(X0,X1),X2,X3),X4),singleton(sK1(cartesian_product2(X0,X1),X2,X3)))) = X4 )
| ( unordered_pair(unordered_pair(sK4(X0,X1,sK2(cartesian_product2(X0,X1),X2,X3)),sK5(X0,X1,sK2(cartesian_product2(X0,X1),X2,X3))),singleton(sK4(X0,X1,sK2(cartesian_product2(X0,X1),X2,X3)))) = sK2(cartesian_product2(X0,X1),X2,X3) ) ),
inference(superposition,[status(thm)],[c_1385,c_62]) ).
tcf(c_55617,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X6),singleton(sK1(cartesian_product2(singleton(X2),X3),X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(X0,sK2(cartesian_product2(singleton(X2),X3),X4,X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_3017]) ).
tcf(c_55618,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X6),singleton(sK1(cartesian_product2(singleton(X2),X3),X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(sK2(cartesian_product2(singleton(X2),X3),X4,X5),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_3015]) ).
tcf(c_55619,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X6),singleton(sK1(cartesian_product2(singleton(X2),X3),X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(sK2(cartesian_product2(singleton(X2),X3),X4,X5),X0),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_3014]) ).
tcf(c_55620,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X6),singleton(sK1(cartesian_product2(singleton(X2),X3),X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK2(cartesian_product2(singleton(X2),X3),X4,X5)),unordered_pair(sK2(cartesian_product2(singleton(X2),X3),X4,X5),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2961]) ).
tcf(c_55621,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X6),singleton(sK1(cartesian_product2(singleton(X2),X3),X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK2(cartesian_product2(singleton(X2),X3),X4,X5)),unordered_pair(X0,sK2(cartesian_product2(singleton(X2),X3),X4,X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2959]) ).
tcf(c_55622,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X6),singleton(sK1(cartesian_product2(singleton(X2),X3),X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(X0,sK2(cartesian_product2(singleton(X2),X3),X4,X5)),singleton(sK2(cartesian_product2(singleton(X2),X3),X4,X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2958]) ).
tcf(c_55623,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X6),singleton(sK1(cartesian_product2(singleton(X2),X3),X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(X0,sK2(cartesian_product2(singleton(X2),X3),X4,X5)),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_3012]) ).
tcf(c_55624,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X6),singleton(sK1(cartesian_product2(singleton(X2),X3),X4,X5)))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(sK2(cartesian_product2(singleton(X2),X3),X4,X5),X0),singleton(sK2(cartesian_product2(singleton(X2),X3),X4,X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2956]) ).
tcf(c_55625,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X4),X5),X6) = X2 )
| ( sK5(X1,singleton(X4),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X4),X5,sK2(cartesian_product2(singleton(X4),X5),X6,X2)),X0))) = X4 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK1(cartesian_product2(singleton(X4),X5),X6,X2),X3),singleton(sK1(cartesian_product2(singleton(X4),X5),X6,X2)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2545]) ).
tcf(c_55626,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X4),X5),X6) = X2 )
| ( sK5(X1,singleton(X4),unordered_pair(unordered_pair(sK4(singleton(X4),X5,sK2(cartesian_product2(singleton(X4),X5),X6,X2)),X0),singleton(X0))) = X4 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK1(cartesian_product2(singleton(X4),X5),X6,X2),X3),singleton(sK1(cartesian_product2(singleton(X4),X5),X6,X2)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_1935]) ).
tcf(c_55627,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X4),X5),X6) = X2 )
| ( sK5(X1,singleton(X4),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X4),X5,sK2(cartesian_product2(singleton(X4),X5),X6,X2))))) = X4 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK1(cartesian_product2(singleton(X4),X5),X6,X2),X3),singleton(sK1(cartesian_product2(singleton(X4),X5),X6,X2)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_1649]) ).
tcf(c_55628,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X4),X5),X6) = X2 )
| ( sK5(X1,singleton(X4),unordered_pair(unordered_pair(X0,sK4(singleton(X4),X5,sK2(cartesian_product2(singleton(X4),X5),X6,X2))),singleton(X0))) = X4 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK1(cartesian_product2(singleton(X4),X5),X6,X2),X3),singleton(sK1(cartesian_product2(singleton(X4),X5),X6,X2)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_1312]) ).
tcf(c_55629,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X0 )
| ( sK4(singleton(X2),X3,sK2(cartesian_product2(singleton(X2),X3),X4,X0)) = X2 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X0),X1),singleton(sK1(cartesian_product2(singleton(X2),X3),X4,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1385,c_787]) ).
tcf(c_55630,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X4,singleton(X5)),X6) = X2 )
| ( sK5(X4,singleton(X5),sK5(X1,cartesian_product2(X4,singleton(X5)),unordered_pair(singleton(X0),unordered_pair(X0,sK2(cartesian_product2(X4,singleton(X5)),X6,X2))))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK1(cartesian_product2(X4,singleton(X5)),X6,X2),X3),singleton(sK1(cartesian_product2(X4,singleton(X5)),X6,X2)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_3142]) ).
tcf(c_55631,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X4,singleton(X5)),X6) = X2 )
| ( sK5(X4,singleton(X5),sK5(X1,cartesian_product2(X4,singleton(X5)),unordered_pair(singleton(X0),unordered_pair(sK2(cartesian_product2(X4,singleton(X5)),X6,X2),X0)))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK1(cartesian_product2(X4,singleton(X5)),X6,X2),X3),singleton(sK1(cartesian_product2(X4,singleton(X5)),X6,X2)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_3140]) ).
tcf(c_55632,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X4,singleton(X5)),X6) = X2 )
| ( sK5(X4,singleton(X5),sK5(X1,cartesian_product2(X4,singleton(X5)),unordered_pair(unordered_pair(sK2(cartesian_product2(X4,singleton(X5)),X6,X2),X0),singleton(X0)))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK1(cartesian_product2(X4,singleton(X5)),X6,X2),X3),singleton(sK1(cartesian_product2(X4,singleton(X5)),X6,X2)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_3139]) ).
tcf(c_55633,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(X2,singleton(X3)),X4,X5),X6),singleton(sK1(cartesian_product2(X2,singleton(X3)),X4,X5)))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK2(cartesian_product2(X2,singleton(X3)),X4,X5)),unordered_pair(sK2(cartesian_product2(X2,singleton(X3)),X4,X5),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_3063]) ).
tcf(c_55634,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(X2,singleton(X3)),X4,X5),X6),singleton(sK1(cartesian_product2(X2,singleton(X3)),X4,X5)))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK2(cartesian_product2(X2,singleton(X3)),X4,X5)),unordered_pair(X0,sK2(cartesian_product2(X2,singleton(X3)),X4,X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_3061]) ).
tcf(c_55635,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(X2,singleton(X3)),X4,X5),X6),singleton(sK1(cartesian_product2(X2,singleton(X3)),X4,X5)))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(X0,sK2(cartesian_product2(X2,singleton(X3)),X4,X5)),singleton(sK2(cartesian_product2(X2,singleton(X3)),X4,X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_3060]) ).
tcf(c_55636,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X4,singleton(X5)),X6) = X2 )
| ( sK5(X4,singleton(X5),sK5(X1,cartesian_product2(X4,singleton(X5)),unordered_pair(unordered_pair(X0,sK2(cartesian_product2(X4,singleton(X5)),X6,X2)),singleton(X0)))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK1(cartesian_product2(X4,singleton(X5)),X6,X2),X3),singleton(sK1(cartesian_product2(X4,singleton(X5)),X6,X2)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_3137]) ).
tcf(c_55637,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(X2,singleton(X3)),X4,X5),X6),singleton(sK1(cartesian_product2(X2,singleton(X3)),X4,X5)))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(sK2(cartesian_product2(X2,singleton(X3)),X4,X5),X0),singleton(sK2(cartesian_product2(X2,singleton(X3)),X4,X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_3058]) ).
tcf(c_55638,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X4,singleton(X5)),X6) = X2 )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(sK5(X4,singleton(X5),sK2(cartesian_product2(X4,singleton(X5)),X6,X2)),X0))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK1(cartesian_product2(X4,singleton(X5)),X6,X2),X3),singleton(sK1(cartesian_product2(X4,singleton(X5)),X6,X2)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_2546]) ).
tcf(c_55639,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X4,singleton(X5)),X6) = X2 )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(sK5(X4,singleton(X5),sK2(cartesian_product2(X4,singleton(X5)),X6,X2)),X0),singleton(X0))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK1(cartesian_product2(X4,singleton(X5)),X6,X2),X3),singleton(sK1(cartesian_product2(X4,singleton(X5)),X6,X2)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_1936]) ).
tcf(c_55640,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X4,singleton(X5)),X6) = X2 )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X4,singleton(X5),sK2(cartesian_product2(X4,singleton(X5)),X6,X2))))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK1(cartesian_product2(X4,singleton(X5)),X6,X2),X3),singleton(sK1(cartesian_product2(X4,singleton(X5)),X6,X2)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_1650]) ).
tcf(c_55641,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X4,singleton(X5)),X6) = X2 )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(X0,sK5(X4,singleton(X5),sK2(cartesian_product2(X4,singleton(X5)),X6,X2))),singleton(X0))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK1(cartesian_product2(X4,singleton(X5)),X6,X2),X3),singleton(sK1(cartesian_product2(X4,singleton(X5)),X6,X2)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1385,c_1313]) ).
tcf(c_55642,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X0 )
| ( sK5(X2,singleton(X3),sK2(cartesian_product2(X2,singleton(X3)),X4,X0)) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(cartesian_product2(X2,singleton(X3)),X4,X0),X1),singleton(sK1(cartesian_product2(X2,singleton(X3)),X4,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1385,c_789]) ).
tcf(c_55643,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(singleton(X2),X3),X4),X5) = X0 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X4,sK2(cartesian_product2(cartesian_product2(singleton(X2),X3),X4),X5,X0))) = X2 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(cartesian_product2(cartesian_product2(singleton(X2),X3),X4),X5,X0),X1),singleton(sK1(cartesian_product2(cartesian_product2(singleton(X2),X3),X4),X5,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1385,c_835]) ).
tcf(c_55644,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,cartesian_product2(singleton(X3),X4)),X5) = X0 )
| ( sK4(singleton(X3),X4,sK5(X2,cartesian_product2(singleton(X3),X4),sK2(cartesian_product2(X2,cartesian_product2(singleton(X3),X4)),X5,X0))) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(cartesian_product2(X2,cartesian_product2(singleton(X3),X4)),X5,X0),X1),singleton(sK1(cartesian_product2(X2,cartesian_product2(singleton(X3),X4)),X5,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1385,c_836]) ).
tcf(c_55645,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X2,singleton(X3)),X4),X5) = X0 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X4,sK2(cartesian_product2(cartesian_product2(X2,singleton(X3)),X4),X5,X0))) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(cartesian_product2(cartesian_product2(X2,singleton(X3)),X4),X5,X0),X1),singleton(sK1(cartesian_product2(cartesian_product2(X2,singleton(X3)),X4),X5,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1385,c_861]) ).
tcf(c_55646,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,cartesian_product2(X3,singleton(X4))),X5) = X0 )
| ( sK5(X3,singleton(X4),sK5(X2,cartesian_product2(X3,singleton(X4)),sK2(cartesian_product2(X2,cartesian_product2(X3,singleton(X4))),X5,X0))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK1(cartesian_product2(X2,cartesian_product2(X3,singleton(X4))),X5,X0),X1),singleton(sK1(cartesian_product2(X2,cartesian_product2(X3,singleton(X4))),X5,X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1385,c_862]) ).
tcf(c_55647,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X2,X1),X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5),X6),singleton(sK1(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK2(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_2896]) ).
tcf(c_55648,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5),X6),singleton(sK1(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK2(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_2820]) ).
tcf(c_55649,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X2,X1),X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5),X6),singleton(sK1(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK2(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_2729]) ).
tcf(c_55650,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5),X6),singleton(sK1(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK2(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_2672]) ).
tcf(c_55651,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X2,X1),X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5),X6),singleton(sK1(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK2(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_2340]) ).
tcf(c_55652,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5),X6),singleton(sK1(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK2(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_2282]) ).
tcf(c_55653,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X2,X1),X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5),X6),singleton(sK1(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK2(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_2178]) ).
tcf(c_55654,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5),X6),singleton(sK1(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK2(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_2102]) ).
tcf(c_55655,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5),X6),singleton(sK1(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_2897]) ).
tcf(c_55656,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5),X6),singleton(sK1(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_2821]) ).
tcf(c_55657,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5),X6),singleton(sK1(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_2730]) ).
tcf(c_55658,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5),X6),singleton(sK1(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_2673]) ).
tcf(c_55659,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5),X6),singleton(sK1(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_2341]) ).
tcf(c_55660,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5),X6),singleton(sK1(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_2283]) ).
tcf(c_55661,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5),X6),singleton(sK1(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_2179]) ).
tcf(c_55662,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK1(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5),X6),singleton(sK1(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5)))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1385,c_2103]) ).
tcf(c_57273,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_42941]) ).
tcf(c_57274,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2903]) ).
tcf(c_57275,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_42542]) ).
tcf(c_57276,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2902]) ).
tcf(c_57277,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_42396]) ).
tcf(c_57278,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2901]) ).
tcf(c_57279,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_42068]) ).
tcf(c_57280,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2900]) ).
tcf(c_57281,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_41683]) ).
tcf(c_57282,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2899]) ).
tcf(c_57283,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_40876]) ).
tcf(c_57284,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2898]) ).
tcf(c_57285,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_40020]) ).
tcf(c_57286,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2827]) ).
tcf(c_57287,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_39078]) ).
tcf(c_57288,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2826]) ).
tcf(c_57289,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_38387]) ).
tcf(c_57290,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2825]) ).
tcf(c_57291,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_37946]) ).
tcf(c_57292,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2824]) ).
tcf(c_57293,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_37625]) ).
tcf(c_57294,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2823]) ).
tcf(c_57295,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_36554]) ).
tcf(c_57296,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2736]) ).
tcf(c_57297,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_35937]) ).
tcf(c_57298,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2822]) ).
tcf(c_57299,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_35157]) ).
tcf(c_57300,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2735]) ).
tcf(c_57301,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_34740]) ).
tcf(c_57302,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2734]) ).
tcf(c_57303,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_34537]) ).
tcf(c_57304,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2733]) ).
tcf(c_57305,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_34285]) ).
tcf(c_57306,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2732]) ).
tcf(c_57307,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_33912]) ).
tcf(c_57308,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2679]) ).
tcf(c_57309,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_33513]) ).
tcf(c_57310,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2678]) ).
tcf(c_57311,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_32955]) ).
tcf(c_57312,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2731]) ).
tcf(c_57313,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_31618]) ).
tcf(c_57314,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2677]) ).
tcf(c_57315,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_30471]) ).
tcf(c_57316,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2676]) ).
tcf(c_57317,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_30093]) ).
tcf(c_57318,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2675]) ).
tcf(c_57319,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_29608]) ).
tcf(c_57320,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2347]) ).
tcf(c_57321,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_29355]) ).
tcf(c_57322,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2346]) ).
tcf(c_57323,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_28822]) ).
tcf(c_57324,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2345]) ).
tcf(c_57325,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_28296]) ).
tcf(c_57326,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2674]) ).
tcf(c_57327,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_27575]) ).
tcf(c_57328,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2344]) ).
tcf(c_57329,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_27245]) ).
tcf(c_57330,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2343]) ).
tcf(c_57331,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_26883]) ).
tcf(c_57332,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2289]) ).
tcf(c_57333,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_26385]) ).
tcf(c_57334,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2288]) ).
tcf(c_57335,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_26012]) ).
tcf(c_57336,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2287]) ).
tcf(c_57337,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_25743]) ).
tcf(c_57338,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2286]) ).
tcf(c_57339,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_25328]) ).
tcf(c_57340,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2342]) ).
tcf(c_57341,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_24337]) ).
tcf(c_57342,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2285]) ).
tcf(c_57343,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_23980]) ).
tcf(c_57344,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2185]) ).
tcf(c_57345,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_23739]) ).
tcf(c_57346,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2184]) ).
tcf(c_57347,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_23253]) ).
tcf(c_57348,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2183]) ).
tcf(c_57349,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_22960]) ).
tcf(c_57350,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2182]) ).
tcf(c_57351,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_22721]) ).
tcf(c_57352,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2181]) ).
tcf(c_57353,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_22587]) ).
tcf(c_57354,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2284]) ).
tcf(c_57355,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_21575]) ).
tcf(c_57356,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2109]) ).
tcf(c_57357,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_21200]) ).
tcf(c_57358,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2108]) ).
tcf(c_57359,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_20765]) ).
tcf(c_57360,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2107]) ).
tcf(c_57361,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_20286]) ).
tcf(c_57362,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2106]) ).
tcf(c_57363,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_19855]) ).
tcf(c_57364,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2180]) ).
tcf(c_57365,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_18803]) ).
tcf(c_57366,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2105]) ).
tcf(c_57367,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_18127]) ).
tcf(c_57368,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2104]) ).
tcf(c_57369,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_17483]) ).
tcf(c_57370,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2465]) ).
tcf(c_57371,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_16787]) ).
tcf(c_57372,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2464]) ).
tcf(c_57373,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_16125]) ).
tcf(c_57374,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2463]) ).
tcf(c_57375,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_15658]) ).
tcf(c_57376,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2462]) ).
tcf(c_57377,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_15187]) ).
tcf(c_57378,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2461]) ).
tcf(c_57379,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_14882]) ).
tcf(c_57380,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2460]) ).
tcf(c_57381,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_13234]) ).
tcf(c_57382,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_1863]) ).
tcf(c_57383,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_12125]) ).
tcf(c_57384,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_1862]) ).
tcf(c_57385,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_11834]) ).
tcf(c_57386,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_1861]) ).
tcf(c_57387,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_11410]) ).
tcf(c_57388,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_1860]) ).
tcf(c_57389,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_10829]) ).
tcf(c_57390,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_1859]) ).
tcf(c_57391,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_10535]) ).
tcf(c_57392,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_1858]) ).
tcf(c_57393,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_8720]) ).
tcf(c_57394,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_1575]) ).
tcf(c_57395,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_8554]) ).
tcf(c_57396,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_1574]) ).
tcf(c_57397,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_8285]) ).
tcf(c_57398,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_1573]) ).
tcf(c_57399,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_8027]) ).
tcf(c_57400,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_1572]) ).
tcf(c_57401,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_7766]) ).
tcf(c_57402,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_1571]) ).
tcf(c_57403,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_7495]) ).
tcf(c_57404,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_1570]) ).
tcf(c_57405,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_6164]) ).
tcf(c_57406,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_1156]) ).
tcf(c_57407,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_5987]) ).
tcf(c_57408,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_1155]) ).
tcf(c_57409,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_5758]) ).
tcf(c_57410,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_1154]) ).
tcf(c_57411,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_5518]) ).
tcf(c_57412,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_1153]) ).
tcf(c_57413,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X2),X5),singleton(sK2(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_5291]) ).
tcf(c_57414,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_1152]) ).
tcf(c_57415,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,X1),X5),singleton(sK2(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_4798]) ).
tcf(c_57416,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,X3),X6),singleton(sK2(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_1151]) ).
tcf(c_57417,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X2) = X3 )
| ( sK5(X3,singleton(X4),unordered_pair(singleton(sK1(X0,X2,X3)),unordered_pair(X4,sK1(X0,X2,X3)))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK2(X0,X2,X3),X1),singleton(sK2(X0,X2,X3)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1386,c_2539]) ).
tcf(c_57419,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X2) = X3 )
| ( sK5(X3,singleton(X4),unordered_pair(unordered_pair(X4,sK1(X0,X2,X3)),singleton(sK1(X0,X2,X3)))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK2(X0,X2,X3),X1),singleton(sK2(X0,X2,X3)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1386,c_1929]) ).
tcf(c_57421,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X2) = X3 )
| ( sK5(X3,singleton(X4),unordered_pair(singleton(sK1(X0,X2,X3)),unordered_pair(sK1(X0,X2,X3),X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK2(X0,X2,X3),X1),singleton(sK2(X0,X2,X3)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1386,c_1643]) ).
tcf(c_57423,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X2) = X3 )
| ( sK5(X3,singleton(X4),unordered_pair(unordered_pair(sK1(X0,X2,X3),X4),singleton(sK1(X0,X2,X3)))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK2(X0,X2,X3),X1),singleton(sK2(X0,X2,X3)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1386,c_1306]) ).
tcf(c_57425,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X4) = singleton(X5) )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(sK1(X2,X4,singleton(X5)),X0))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK2(X2,X4,singleton(X5)),X3),singleton(sK2(X2,X4,singleton(X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_907]) ).
tcf(c_57426,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,singleton(X2)),X5),singleton(sK2(X3,X4,singleton(X2))))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK1(X3,X4,singleton(X2))),unordered_pair(X0,sK1(X3,X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_906]) ).
tcf(c_57427,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X4) = singleton(X5) )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(sK1(X2,X4,singleton(X5)),X0),singleton(X0))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK2(X2,X4,singleton(X5)),X3),singleton(sK2(X2,X4,singleton(X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_899]) ).
tcf(c_57428,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,singleton(X2)),X5),singleton(sK2(X3,X4,singleton(X2))))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X0,sK1(X3,X4,singleton(X2))),singleton(sK1(X3,X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_898]) ).
tcf(c_57429,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X4) = singleton(X5) )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X2,X4,singleton(X5))))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK2(X2,X4,singleton(X5)),X3),singleton(sK2(X2,X4,singleton(X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_889]) ).
tcf(c_57430,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,singleton(X2)),X5),singleton(sK2(X3,X4,singleton(X2))))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK1(X3,X4,singleton(X2))),unordered_pair(sK1(X3,X4,singleton(X2)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_888]) ).
tcf(c_57431,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X4) = singleton(X5) )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(X0,sK1(X2,X4,singleton(X5))),singleton(X0))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK2(X2,X4,singleton(X5)),X3),singleton(sK2(X2,X4,singleton(X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_863]) ).
tcf(c_57432,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,singleton(X2)),X5),singleton(sK2(X3,X4,singleton(X2))))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,singleton(X2)),X0),singleton(sK1(X3,X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_837]) ).
tcf(c_57434,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),X6),singleton(sK2(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_16267]) ).
tcf(c_57435,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),X6),singleton(sK2(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_16266]) ).
tcf(c_57436,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),X6),singleton(sK2(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_15723]) ).
tcf(c_57437,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),X6),singleton(sK2(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_15722]) ).
tcf(c_57438,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),X6),singleton(sK2(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_15377]) ).
tcf(c_57439,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),X6),singleton(sK2(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_15376]) ).
tcf(c_57440,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),X6),singleton(sK2(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_12049]) ).
tcf(c_57441,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),X6),singleton(sK2(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_12048]) ).
tcf(c_57442,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),X6),singleton(sK2(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_11518]) ).
tcf(c_57443,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),X6),singleton(sK2(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_11517]) ).
tcf(c_57444,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),X6),singleton(sK2(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_11093]) ).
tcf(c_57445,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),X6),singleton(sK2(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_11092]) ).
tcf(c_57446,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),X6),singleton(sK2(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_8458]) ).
tcf(c_57447,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),X6),singleton(sK2(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_8457]) ).
tcf(c_57448,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),X6),singleton(sK2(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_8152]) ).
tcf(c_57449,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),X6),singleton(sK2(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_8151]) ).
tcf(c_57450,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),X6),singleton(sK2(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_7854]) ).
tcf(c_57451,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),X6),singleton(sK2(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_7853]) ).
tcf(c_57452,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),X6),singleton(sK2(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_5825]) ).
tcf(c_57453,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),X6),singleton(sK2(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_5824]) ).
tcf(c_57454,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),X6),singleton(sK2(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_5642]) ).
tcf(c_57455,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),X6),singleton(sK2(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_5641]) ).
tcf(c_57456,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,X2)),X6),singleton(sK2(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_5396]) ).
tcf(c_57457,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,X3)),X6),singleton(sK2(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_5395]) ).
tcf(c_57458,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,cartesian_product2(X2,X0)),X5),singleton(sK2(X3,X4,cartesian_product2(X2,X0))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))),unordered_pair(X1,sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1386,c_2611]) ).
tcf(c_57459,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,cartesian_product2(X0,X2)),X5),singleton(sK2(X3,X4,cartesian_product2(X0,X2))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))),unordered_pair(X1,sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1386,c_2610]) ).
tcf(c_57460,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,cartesian_product2(X2,X0)),X5),singleton(sK2(X3,X4,cartesian_product2(X2,X0))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))),singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1386,c_2036]) ).
tcf(c_57461,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,cartesian_product2(X0,X2)),X5),singleton(sK2(X3,X4,cartesian_product2(X0,X2))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))),singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1386,c_2035]) ).
tcf(c_57462,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,cartesian_product2(X2,X0)),X5),singleton(sK2(X3,X4,cartesian_product2(X2,X0))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))),unordered_pair(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0))),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1386,c_1703]) ).
tcf(c_57463,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,cartesian_product2(X0,X2)),X5),singleton(sK2(X3,X4,cartesian_product2(X0,X2))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))),unordered_pair(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2))),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1386,c_1702]) ).
tcf(c_57464,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,cartesian_product2(X2,X0)),X5),singleton(sK2(X3,X4,cartesian_product2(X2,X0))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0))),X1),singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1386,c_1389]) ).
tcf(c_57465,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK5(X3,singleton(X5),unordered_pair(unordered_pair(sK2(X3,X4,cartesian_product2(X0,X2)),X5),singleton(sK2(X3,X4,cartesian_product2(X0,X2))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2))),X1),singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1386,c_1388]) ).
tcf(c_57466,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK5(X3,X4,sK1(X0,X2,cartesian_product2(X3,X4))),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK2(X0,X2,cartesian_product2(X3,X4)),X1),singleton(sK2(X0,X2,cartesian_product2(X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1386,c_2459]) ).
tcf(c_57467,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK4(X3,X4,sK1(X0,X2,cartesian_product2(X3,X4))),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK2(X0,X2,cartesian_product2(X3,X4)),X1),singleton(sK2(X0,X2,cartesian_product2(X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1386,c_2458]) ).
tcf(c_57468,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK5(X3,X4,sK1(X0,X2,cartesian_product2(X3,X4))),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK2(X0,X2,cartesian_product2(X3,X4)),X1),singleton(sK2(X0,X2,cartesian_product2(X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1386,c_1857]) ).
tcf(c_57469,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK4(X3,X4,sK1(X0,X2,cartesian_product2(X3,X4))),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK2(X0,X2,cartesian_product2(X3,X4)),X1),singleton(sK2(X0,X2,cartesian_product2(X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1386,c_1856]) ).
tcf(c_57470,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X3,X4,sK1(X0,X2,cartesian_product2(X3,X4)))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK2(X0,X2,cartesian_product2(X3,X4)),X1),singleton(sK2(X0,X2,cartesian_product2(X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1386,c_1569]) ).
tcf(c_57471,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X3,X4,sK1(X0,X2,cartesian_product2(X3,X4)))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK2(X0,X2,cartesian_product2(X3,X4)),X1),singleton(sK2(X0,X2,cartesian_product2(X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1386,c_1568]) ).
tcf(c_57472,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK5(X3,X4,sK1(X0,X2,cartesian_product2(X3,X4)))),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK2(X0,X2,cartesian_product2(X3,X4)),X1),singleton(sK2(X0,X2,cartesian_product2(X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1386,c_1150]) ).
tcf(c_57473,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK4(X3,X4,sK1(X0,X2,cartesian_product2(X3,X4)))),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK2(X0,X2,cartesian_product2(X3,X4)),X1),singleton(sK2(X0,X2,cartesian_product2(X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1386,c_1149]) ).
tcf(c_57474,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( sK5(X2,singleton(X4),unordered_pair(unordered_pair(sK2(X2,X3,cartesian_product2(X0,X1)),X4),singleton(sK2(X2,X3,cartesian_product2(X0,X1))))) = X4 )
| ( unordered_pair(unordered_pair(sK4(X0,X1,sK1(X2,X3,cartesian_product2(X0,X1))),sK5(X0,X1,sK1(X2,X3,cartesian_product2(X0,X1)))),singleton(sK4(X0,X1,sK1(X2,X3,cartesian_product2(X0,X1))))) = sK1(X2,X3,cartesian_product2(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_1386,c_62]) ).
tcf(c_57475,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X6),singleton(sK2(X4,X5,cartesian_product2(singleton(X2),X3))))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_3017]) ).
tcf(c_57476,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X6),singleton(sK2(X4,X5,cartesian_product2(singleton(X2),X3))))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_3015]) ).
tcf(c_57477,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X6),singleton(sK2(X4,X5,cartesian_product2(singleton(X2),X3))))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_3014]) ).
tcf(c_57478,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X6),singleton(sK2(X4,X5,cartesian_product2(singleton(X2),X3))))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3))),unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2961]) ).
tcf(c_57479,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X6),singleton(sK2(X4,X5,cartesian_product2(singleton(X2),X3))))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3))),unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2959]) ).
tcf(c_57480,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X6),singleton(sK2(X4,X5,cartesian_product2(singleton(X2),X3))))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2958]) ).
tcf(c_57481,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X6),singleton(sK2(X4,X5,cartesian_product2(singleton(X2),X3))))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_3012]) ).
tcf(c_57482,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(singleton(X2),X3)),X6),singleton(sK2(X4,X5,cartesian_product2(singleton(X2),X3))))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0),singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2956]) ).
tcf(c_57483,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X5),X6) = cartesian_product2(X2,X4) )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X5),X6,sK1(X2,X4,cartesian_product2(singleton(X5),X6))),X0))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK2(X2,X4,cartesian_product2(singleton(X5),X6)),X3),singleton(sK2(X2,X4,cartesian_product2(singleton(X5),X6))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2545]) ).
tcf(c_57484,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X5),X6) = cartesian_product2(X2,X4) )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(sK4(singleton(X5),X6,sK1(X2,X4,cartesian_product2(singleton(X5),X6))),X0),singleton(X0))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK2(X2,X4,cartesian_product2(singleton(X5),X6)),X3),singleton(sK2(X2,X4,cartesian_product2(singleton(X5),X6))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_1935]) ).
tcf(c_57485,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X5),X6) = cartesian_product2(X2,X4) )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X5),X6,sK1(X2,X4,cartesian_product2(singleton(X5),X6)))))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK2(X2,X4,cartesian_product2(singleton(X5),X6)),X3),singleton(sK2(X2,X4,cartesian_product2(singleton(X5),X6))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_1649]) ).
tcf(c_57486,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X5),X6) = cartesian_product2(X2,X4) )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(X0,sK4(singleton(X5),X6,sK1(X2,X4,cartesian_product2(singleton(X5),X6)))),singleton(X0))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK2(X2,X4,cartesian_product2(singleton(X5),X6)),X3),singleton(sK2(X2,X4,cartesian_product2(singleton(X5),X6))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_1312]) ).
tcf(c_57487,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = cartesian_product2(X0,X2) )
| ( sK4(singleton(X3),X4,sK1(X0,X2,cartesian_product2(singleton(X3),X4))) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK2(X0,X2,cartesian_product2(singleton(X3),X4)),X1),singleton(sK2(X0,X2,cartesian_product2(singleton(X3),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1386,c_787]) ).
tcf(c_57488,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X5,singleton(X6)) = cartesian_product2(X2,X4) )
| ( sK5(X5,singleton(X6),sK5(X1,cartesian_product2(X5,singleton(X6)),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X2,X4,cartesian_product2(X5,singleton(X6))))))) = X6 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK2(X2,X4,cartesian_product2(X5,singleton(X6))),X3),singleton(sK2(X2,X4,cartesian_product2(X5,singleton(X6)))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_3142]) ).
tcf(c_57489,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X5,singleton(X6)) = cartesian_product2(X2,X4) )
| ( sK5(X5,singleton(X6),sK5(X1,cartesian_product2(X5,singleton(X6)),unordered_pair(singleton(X0),unordered_pair(sK1(X2,X4,cartesian_product2(X5,singleton(X6))),X0)))) = X6 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK2(X2,X4,cartesian_product2(X5,singleton(X6))),X3),singleton(sK2(X2,X4,cartesian_product2(X5,singleton(X6)))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_3140]) ).
tcf(c_57490,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X5,singleton(X6)) = cartesian_product2(X2,X4) )
| ( sK5(X5,singleton(X6),sK5(X1,cartesian_product2(X5,singleton(X6)),unordered_pair(unordered_pair(sK1(X2,X4,cartesian_product2(X5,singleton(X6))),X0),singleton(X0)))) = X6 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK2(X2,X4,cartesian_product2(X5,singleton(X6))),X3),singleton(sK2(X2,X4,cartesian_product2(X5,singleton(X6)))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_3139]) ).
tcf(c_57491,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,singleton(X3))),X6),singleton(sK2(X4,X5,cartesian_product2(X2,singleton(X3)))))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_3063]) ).
tcf(c_57492,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,singleton(X3))),X6),singleton(sK2(X4,X5,cartesian_product2(X2,singleton(X3)))))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_3061]) ).
tcf(c_57493,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,singleton(X3))),X6),singleton(sK2(X4,X5,cartesian_product2(X2,singleton(X3)))))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_3060]) ).
tcf(c_57494,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X5,singleton(X6)) = cartesian_product2(X2,X4) )
| ( sK5(X5,singleton(X6),sK5(X1,cartesian_product2(X5,singleton(X6)),unordered_pair(unordered_pair(X0,sK1(X2,X4,cartesian_product2(X5,singleton(X6)))),singleton(X0)))) = X6 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK2(X2,X4,cartesian_product2(X5,singleton(X6))),X3),singleton(sK2(X2,X4,cartesian_product2(X5,singleton(X6)))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_3137]) ).
tcf(c_57495,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X2,singleton(X3))),X6),singleton(sK2(X4,X5,cartesian_product2(X2,singleton(X3)))))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0),singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_3058]) ).
tcf(c_57496,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X5,singleton(X6)) = cartesian_product2(X2,X4) )
| ( sK5(X1,singleton(X6),unordered_pair(singleton(X0),unordered_pair(sK5(X5,singleton(X6),sK1(X2,X4,cartesian_product2(X5,singleton(X6)))),X0))) = X6 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK2(X2,X4,cartesian_product2(X5,singleton(X6))),X3),singleton(sK2(X2,X4,cartesian_product2(X5,singleton(X6)))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_2546]) ).
tcf(c_57497,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X5,singleton(X6)) = cartesian_product2(X2,X4) )
| ( sK5(X1,singleton(X6),unordered_pair(unordered_pair(sK5(X5,singleton(X6),sK1(X2,X4,cartesian_product2(X5,singleton(X6)))),X0),singleton(X0))) = X6 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK2(X2,X4,cartesian_product2(X5,singleton(X6))),X3),singleton(sK2(X2,X4,cartesian_product2(X5,singleton(X6)))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_1936]) ).
tcf(c_57498,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X5,singleton(X6)) = cartesian_product2(X2,X4) )
| ( sK5(X1,singleton(X6),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X5,singleton(X6),sK1(X2,X4,cartesian_product2(X5,singleton(X6))))))) = X6 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK2(X2,X4,cartesian_product2(X5,singleton(X6))),X3),singleton(sK2(X2,X4,cartesian_product2(X5,singleton(X6)))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_1650]) ).
tcf(c_57499,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X5,singleton(X6)) = cartesian_product2(X2,X4) )
| ( sK5(X1,singleton(X6),unordered_pair(unordered_pair(X0,sK5(X5,singleton(X6),sK1(X2,X4,cartesian_product2(X5,singleton(X6))))),singleton(X0))) = X6 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK2(X2,X4,cartesian_product2(X5,singleton(X6))),X3),singleton(sK2(X2,X4,cartesian_product2(X5,singleton(X6)))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1386,c_1313]) ).
tcf(c_57500,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = cartesian_product2(X0,X2) )
| ( sK5(X3,singleton(X4),sK1(X0,X2,cartesian_product2(X3,singleton(X4)))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK2(X0,X2,cartesian_product2(X3,singleton(X4))),X1),singleton(sK2(X0,X2,cartesian_product2(X3,singleton(X4)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1386,c_789]) ).
tcf(c_57501,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X3),X4),X5) = cartesian_product2(X0,X2) )
| ( sK4(singleton(X3),X4,sK4(cartesian_product2(singleton(X3),X4),X5,sK1(X0,X2,cartesian_product2(cartesian_product2(singleton(X3),X4),X5)))) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK2(X0,X2,cartesian_product2(cartesian_product2(singleton(X3),X4),X5)),X1),singleton(sK2(X0,X2,cartesian_product2(cartesian_product2(singleton(X3),X4),X5))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1386,c_835]) ).
tcf(c_57502,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(singleton(X4),X5)) = cartesian_product2(X0,X2) )
| ( sK4(singleton(X4),X5,sK5(X3,cartesian_product2(singleton(X4),X5),sK1(X0,X2,cartesian_product2(X3,cartesian_product2(singleton(X4),X5))))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK2(X0,X2,cartesian_product2(X3,cartesian_product2(singleton(X4),X5))),X1),singleton(sK2(X0,X2,cartesian_product2(X3,cartesian_product2(singleton(X4),X5)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1386,c_836]) ).
tcf(c_57503,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X3,singleton(X4)),X5) = cartesian_product2(X0,X2) )
| ( sK5(X3,singleton(X4),sK4(cartesian_product2(X3,singleton(X4)),X5,sK1(X0,X2,cartesian_product2(cartesian_product2(X3,singleton(X4)),X5)))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK2(X0,X2,cartesian_product2(cartesian_product2(X3,singleton(X4)),X5)),X1),singleton(sK2(X0,X2,cartesian_product2(cartesian_product2(X3,singleton(X4)),X5))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1386,c_861]) ).
tcf(c_57504,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X4,singleton(X5))) = cartesian_product2(X0,X2) )
| ( sK5(X4,singleton(X5),sK5(X3,cartesian_product2(X4,singleton(X5)),sK1(X0,X2,cartesian_product2(X3,cartesian_product2(X4,singleton(X5)))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK2(X0,X2,cartesian_product2(X3,cartesian_product2(X4,singleton(X5)))),X1),singleton(sK2(X0,X2,cartesian_product2(X3,cartesian_product2(X4,singleton(X5))))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1386,c_862]) ).
tcf(c_57505,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)),X6),singleton(sK2(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_2896]) ).
tcf(c_57506,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)),X6),singleton(sK2(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_2820]) ).
tcf(c_57507,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)),X6),singleton(sK2(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_2729]) ).
tcf(c_57508,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)),X6),singleton(sK2(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_2672]) ).
tcf(c_57509,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)),X6),singleton(sK2(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_2340]) ).
tcf(c_57510,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)),X6),singleton(sK2(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_2282]) ).
tcf(c_57511,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)),X6),singleton(sK2(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_2178]) ).
tcf(c_57512,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)),X6),singleton(sK2(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_2102]) ).
tcf(c_57513,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))),X6),singleton(sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_2897]) ).
tcf(c_57514,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))),X6),singleton(sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_2821]) ).
tcf(c_57515,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))),X6),singleton(sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_2730]) ).
tcf(c_57516,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))),X6),singleton(sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_2673]) ).
tcf(c_57517,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))),X6),singleton(sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_2341]) ).
tcf(c_57518,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))),X6),singleton(sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_2283]) ).
tcf(c_57519,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))),X6),singleton(sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_2179]) ).
tcf(c_57520,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK5(X4,singleton(X6),unordered_pair(unordered_pair(sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))),X6),singleton(sK2(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1386,c_2103]) ).
tcf(c_58922,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_42941]) ).
tcf(c_58923,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2903]) ).
tcf(c_58924,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_42542]) ).
tcf(c_58925,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2902]) ).
tcf(c_58926,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_42396]) ).
tcf(c_58927,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2901]) ).
tcf(c_58928,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_42068]) ).
tcf(c_58929,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2900]) ).
tcf(c_58930,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_41683]) ).
tcf(c_58931,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2899]) ).
tcf(c_58932,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_40876]) ).
tcf(c_58933,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2898]) ).
tcf(c_58934,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_40020]) ).
tcf(c_58935,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2827]) ).
tcf(c_58936,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_39078]) ).
tcf(c_58937,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2826]) ).
tcf(c_58938,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_38387]) ).
tcf(c_58939,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2825]) ).
tcf(c_58940,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_37946]) ).
tcf(c_58941,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2824]) ).
tcf(c_58942,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_37625]) ).
tcf(c_58943,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2823]) ).
tcf(c_58944,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_36554]) ).
tcf(c_58945,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2736]) ).
tcf(c_58946,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_35937]) ).
tcf(c_58947,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2822]) ).
tcf(c_58948,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_35157]) ).
tcf(c_58949,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2735]) ).
tcf(c_58950,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_34740]) ).
tcf(c_58951,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2734]) ).
tcf(c_58952,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_34537]) ).
tcf(c_58953,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2733]) ).
tcf(c_58954,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_34285]) ).
tcf(c_58955,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2732]) ).
tcf(c_58956,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_33912]) ).
tcf(c_58957,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2679]) ).
tcf(c_58958,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_33513]) ).
tcf(c_58959,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2678]) ).
tcf(c_58960,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_32955]) ).
tcf(c_58961,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2731]) ).
tcf(c_58962,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_31618]) ).
tcf(c_58963,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2677]) ).
tcf(c_58964,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_30471]) ).
tcf(c_58965,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2676]) ).
tcf(c_58966,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_30093]) ).
tcf(c_58967,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2675]) ).
tcf(c_58968,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_29608]) ).
tcf(c_58969,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2347]) ).
tcf(c_58970,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_29355]) ).
tcf(c_58971,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2346]) ).
tcf(c_58972,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_28822]) ).
tcf(c_58973,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2345]) ).
tcf(c_58974,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_28296]) ).
tcf(c_58975,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2674]) ).
tcf(c_58976,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_27575]) ).
tcf(c_58977,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2344]) ).
tcf(c_58978,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_27245]) ).
tcf(c_58979,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2343]) ).
tcf(c_58980,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_26883]) ).
tcf(c_58981,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2289]) ).
tcf(c_58982,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_26385]) ).
tcf(c_58983,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2288]) ).
tcf(c_58984,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_26012]) ).
tcf(c_58985,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2287]) ).
tcf(c_58986,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_25743]) ).
tcf(c_58987,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2286]) ).
tcf(c_58988,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_25328]) ).
tcf(c_58989,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2342]) ).
tcf(c_58990,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_24337]) ).
tcf(c_58991,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2285]) ).
tcf(c_58992,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(sK1(X3,X4,X2),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_23980]) ).
tcf(c_58993,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2185]) ).
tcf(c_58994,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK1(X3,X4,X2)),unordered_pair(X1,sK1(X3,X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_23739]) ).
tcf(c_58995,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2184]) ).
tcf(c_58996,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK1(X3,X4,X1),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_23253]) ).
tcf(c_58997,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2183]) ).
tcf(c_58998,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_22960]) ).
tcf(c_58999,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2182]) ).
tcf(c_59000,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK1(X3,X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_22721]) ).
tcf(c_59001,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2181]) ).
tcf(c_59002,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_22587]) ).
tcf(c_59003,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2284]) ).
tcf(c_59004,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_21575]) ).
tcf(c_59005,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2109]) ).
tcf(c_59006,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_21200]) ).
tcf(c_59007,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2108]) ).
tcf(c_59008,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_20765]) ).
tcf(c_59009,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2107]) ).
tcf(c_59010,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_20286]) ).
tcf(c_59011,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2106]) ).
tcf(c_59012,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(sK1(X3,X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_19855]) ).
tcf(c_59013,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2180]) ).
tcf(c_59014,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_18803]) ).
tcf(c_59015,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2105]) ).
tcf(c_59016,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_18127]) ).
tcf(c_59017,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2104]) ).
tcf(c_59018,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_17483]) ).
tcf(c_59019,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2465]) ).
tcf(c_59020,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_16787]) ).
tcf(c_59021,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2464]) ).
tcf(c_59022,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_16125]) ).
tcf(c_59023,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2463]) ).
tcf(c_59024,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_15658]) ).
tcf(c_59025,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2462]) ).
tcf(c_59026,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_15187]) ).
tcf(c_59027,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2461]) ).
tcf(c_59028,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_14882]) ).
tcf(c_59029,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2460]) ).
tcf(c_59030,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_13234]) ).
tcf(c_59031,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_1863]) ).
tcf(c_59032,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_12125]) ).
tcf(c_59033,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_1862]) ).
tcf(c_59034,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_11834]) ).
tcf(c_59035,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_1861]) ).
tcf(c_59036,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_11410]) ).
tcf(c_59037,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_1860]) ).
tcf(c_59038,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_10829]) ).
tcf(c_59039,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_1859]) ).
tcf(c_59040,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_10535]) ).
tcf(c_59041,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_1858]) ).
tcf(c_59042,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_8720]) ).
tcf(c_59043,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_1575]) ).
tcf(c_59044,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_8554]) ).
tcf(c_59045,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_1574]) ).
tcf(c_59046,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_8285]) ).
tcf(c_59047,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_1573]) ).
tcf(c_59048,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_8027]) ).
tcf(c_59049,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_1572]) ).
tcf(c_59050,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_7766]) ).
tcf(c_59051,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_1571]) ).
tcf(c_59052,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_7495]) ).
tcf(c_59053,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_1570]) ).
tcf(c_59054,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(sK1(X3,X4,X1),X2))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_6164]) ).
tcf(c_59055,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_1156]) ).
tcf(c_59056,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK1(X3,X4,X1)),unordered_pair(X2,sK1(X3,X4,X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_5987]) ).
tcf(c_59057,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,X3),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_1155]) ).
tcf(c_59058,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK1(X3,X4,X2),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_5758]) ).
tcf(c_59059,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(X0,sK1(X4,X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_1154]) ).
tcf(c_59060,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X2),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_5518]) ).
tcf(c_59061,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(sK1(X4,X5,X3)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_1153]) ).
tcf(c_59062,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X2 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X2),X5),singleton(sK3(X3,X4,X2)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK1(X3,X4,X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_5291]) ).
tcf(c_59063,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK1(X4,X5,X3)),unordered_pair(sK1(X4,X5,X3),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_1152]) ).
tcf(c_59064,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = X1 )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,X1),X5),singleton(sK3(X3,X4,X1)))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK1(X3,X4,X1),X2),singleton(sK1(X3,X4,X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_4798]) ).
tcf(c_59065,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X5) = X3 )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,X3),X6),singleton(sK3(X4,X5,X3)))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK1(X4,X5,X3)),singleton(X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_1151]) ).
tcf(c_59066,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X0) = X3 )
| ( sK5(X3,singleton(X4),unordered_pair(singleton(sK1(X2,X0,X3)),unordered_pair(X4,sK1(X2,X0,X3)))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK3(X2,X0,X3),X1),singleton(sK3(X2,X0,X3)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1387,c_2539]) ).
tcf(c_59068,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X0) = X3 )
| ( sK5(X3,singleton(X4),unordered_pair(unordered_pair(X4,sK1(X2,X0,X3)),singleton(sK1(X2,X0,X3)))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK3(X2,X0,X3),X1),singleton(sK3(X2,X0,X3)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1387,c_1929]) ).
tcf(c_59070,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X0) = X3 )
| ( sK5(X3,singleton(X4),unordered_pair(singleton(sK1(X2,X0,X3)),unordered_pair(sK1(X2,X0,X3),X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK3(X2,X0,X3),X1),singleton(sK3(X2,X0,X3)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1387,c_1643]) ).
tcf(c_59072,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X0) = X3 )
| ( sK5(X3,singleton(X4),unordered_pair(unordered_pair(sK1(X2,X0,X3),X4),singleton(sK1(X2,X0,X3)))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK3(X2,X0,X3),X1),singleton(sK3(X2,X0,X3)))) = X1 ) ),
inference(superposition,[status(thm)],[c_1387,c_1306]) ).
tcf(c_59074,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X2) = singleton(X5) )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(sK1(X4,X2,singleton(X5)),X0))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK3(X4,X2,singleton(X5)),X3),singleton(sK3(X4,X2,singleton(X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_907]) ).
tcf(c_59075,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,singleton(X2)),X5),singleton(sK3(X3,X4,singleton(X2))))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK1(X3,X4,singleton(X2))),unordered_pair(X0,sK1(X3,X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_906]) ).
tcf(c_59076,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X2) = singleton(X5) )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(sK1(X4,X2,singleton(X5)),X0),singleton(X0))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK3(X4,X2,singleton(X5)),X3),singleton(sK3(X4,X2,singleton(X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_899]) ).
tcf(c_59077,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,singleton(X2)),X5),singleton(sK3(X3,X4,singleton(X2))))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X0,sK1(X3,X4,singleton(X2))),singleton(sK1(X3,X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_898]) ).
tcf(c_59078,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X2) = singleton(X5) )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X2,singleton(X5))))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK3(X4,X2,singleton(X5)),X3),singleton(sK3(X4,X2,singleton(X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_889]) ).
tcf(c_59079,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,singleton(X2)),X5),singleton(sK3(X3,X4,singleton(X2))))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK1(X3,X4,singleton(X2))),unordered_pair(sK1(X3,X4,singleton(X2)),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_888]) ).
tcf(c_59080,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,X2) = singleton(X5) )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(X0,sK1(X4,X2,singleton(X5))),singleton(X0))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK3(X4,X2,singleton(X5)),X3),singleton(sK3(X4,X2,singleton(X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_863]) ).
tcf(c_59081,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X4) = singleton(X2) )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,singleton(X2)),X5),singleton(sK3(X3,X4,singleton(X2))))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK1(X3,X4,singleton(X2)),X0),singleton(sK1(X3,X4,singleton(X2))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_837]) ).
tcf(c_59083,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,X2)),X6),singleton(sK3(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_16267]) ).
tcf(c_59084,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X2,X3)),X6),singleton(sK3(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_16266]) ).
tcf(c_59085,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,X2)),X6),singleton(sK3(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_15723]) ).
tcf(c_59086,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X2,X3)),X6),singleton(sK3(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_15722]) ).
tcf(c_59087,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,X2)),X6),singleton(sK3(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_15377]) ).
tcf(c_59088,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X2,X3)),X6),singleton(sK3(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_15376]) ).
tcf(c_59089,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,X2)),X6),singleton(sK3(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_12049]) ).
tcf(c_59090,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X2,X3)),X6),singleton(sK3(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_12048]) ).
tcf(c_59091,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,X2)),X6),singleton(sK3(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_11518]) ).
tcf(c_59092,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X2,X3)),X6),singleton(sK3(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_11517]) ).
tcf(c_59093,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,X2)),X6),singleton(sK3(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_11093]) ).
tcf(c_59094,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X2,X3)),X6),singleton(sK3(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_11092]) ).
tcf(c_59095,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,X2)),X6),singleton(sK3(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_8458]) ).
tcf(c_59096,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X2,X3)),X6),singleton(sK3(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_8457]) ).
tcf(c_59097,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,X2)),X6),singleton(sK3(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_8152]) ).
tcf(c_59098,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X2,X3)),X6),singleton(sK3(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_8151]) ).
tcf(c_59099,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,X2)),X6),singleton(sK3(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_7854]) ).
tcf(c_59100,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X2,X3)),X6),singleton(sK3(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_7853]) ).
tcf(c_59101,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,X2)),X6),singleton(sK3(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_5825]) ).
tcf(c_59102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X2,X3)),X6),singleton(sK3(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_5824]) ).
tcf(c_59103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,X2)),X6),singleton(sK3(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2))),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_5642]) ).
tcf(c_59104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X2,X3)),X6),singleton(sK3(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3))),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_5641]) ).
tcf(c_59105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X2) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,X2)),X6),singleton(sK3(X4,X5,cartesian_product2(X3,X2))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK1(X4,X5,cartesian_product2(X3,X2)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_5396]) ).
tcf(c_59106,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,X3) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X2,X3)),X6),singleton(sK3(X4,X5,cartesian_product2(X2,X3))))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK1(X4,X5,cartesian_product2(X2,X3)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_5395]) ).
tcf(c_59107,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,cartesian_product2(X2,X0)),X5),singleton(sK3(X3,X4,cartesian_product2(X2,X0))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))),unordered_pair(X1,sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1387,c_2611]) ).
tcf(c_59108,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,cartesian_product2(X0,X2)),X5),singleton(sK3(X3,X4,cartesian_product2(X0,X2))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))),unordered_pair(X1,sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1387,c_2610]) ).
tcf(c_59109,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,cartesian_product2(X2,X0)),X5),singleton(sK3(X3,X4,cartesian_product2(X2,X0))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))),singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1387,c_2036]) ).
tcf(c_59110,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,cartesian_product2(X0,X2)),X5),singleton(sK3(X3,X4,cartesian_product2(X0,X2))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))),singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1387,c_2035]) ).
tcf(c_59111,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,cartesian_product2(X2,X0)),X5),singleton(sK3(X3,X4,cartesian_product2(X2,X0))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))),unordered_pair(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0))),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1387,c_1703]) ).
tcf(c_59112,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,cartesian_product2(X0,X2)),X5),singleton(sK3(X3,X4,cartesian_product2(X0,X2))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))),unordered_pair(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2))),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1387,c_1702]) ).
tcf(c_59113,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,cartesian_product2(X2,X0)),X5),singleton(sK3(X3,X4,cartesian_product2(X2,X0))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0))),X1),singleton(sK5(X2,X0,sK1(X3,X4,cartesian_product2(X2,X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1387,c_1389]) ).
tcf(c_59114,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X0,X2) = cartesian_product2(X3,X4) )
| ( sK5(X4,singleton(X5),unordered_pair(unordered_pair(sK3(X3,X4,cartesian_product2(X0,X2)),X5),singleton(sK3(X3,X4,cartesian_product2(X0,X2))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2))),X1),singleton(sK4(X0,X2,sK1(X3,X4,cartesian_product2(X0,X2)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1387,c_1388]) ).
tcf(c_59115,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK5(X3,X4,sK1(X2,X0,cartesian_product2(X3,X4))),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK3(X2,X0,cartesian_product2(X3,X4)),X1),singleton(sK3(X2,X0,cartesian_product2(X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1387,c_2459]) ).
tcf(c_59116,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK4(X3,X4,sK1(X2,X0,cartesian_product2(X3,X4))),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK3(X2,X0,cartesian_product2(X3,X4)),X1),singleton(sK3(X2,X0,cartesian_product2(X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1387,c_2458]) ).
tcf(c_59117,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK5(X3,X4,sK1(X2,X0,cartesian_product2(X3,X4))),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK3(X2,X0,cartesian_product2(X3,X4)),X1),singleton(sK3(X2,X0,cartesian_product2(X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1387,c_1857]) ).
tcf(c_59118,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK4(X3,X4,sK1(X2,X0,cartesian_product2(X3,X4))),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK3(X2,X0,cartesian_product2(X3,X4)),X1),singleton(sK3(X2,X0,cartesian_product2(X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1387,c_1856]) ).
tcf(c_59119,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X3,X4,sK1(X2,X0,cartesian_product2(X3,X4)))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK3(X2,X0,cartesian_product2(X3,X4)),X1),singleton(sK3(X2,X0,cartesian_product2(X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1387,c_1569]) ).
tcf(c_59120,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X3,X4,sK1(X2,X0,cartesian_product2(X3,X4)))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK3(X2,X0,cartesian_product2(X3,X4)),X1),singleton(sK3(X2,X0,cartesian_product2(X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1387,c_1568]) ).
tcf(c_59121,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK5(X3,X4,sK1(X2,X0,cartesian_product2(X3,X4)))),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK3(X2,X0,cartesian_product2(X3,X4)),X1),singleton(sK3(X2,X0,cartesian_product2(X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1387,c_1150]) ).
tcf(c_59122,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X0) = cartesian_product2(X3,X4) )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK4(X3,X4,sK1(X2,X0,cartesian_product2(X3,X4)))),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK3(X2,X0,cartesian_product2(X3,X4)),X1),singleton(sK3(X2,X0,cartesian_product2(X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1387,c_1149]) ).
tcf(c_59123,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( sK5(X3,singleton(X4),unordered_pair(unordered_pair(sK3(X2,X3,cartesian_product2(X0,X1)),X4),singleton(sK3(X2,X3,cartesian_product2(X0,X1))))) = X4 )
| ( unordered_pair(unordered_pair(sK4(X0,X1,sK1(X2,X3,cartesian_product2(X0,X1))),sK5(X0,X1,sK1(X2,X3,cartesian_product2(X0,X1)))),singleton(sK4(X0,X1,sK1(X2,X3,cartesian_product2(X0,X1))))) = sK1(X2,X3,cartesian_product2(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_1387,c_62]) ).
tcf(c_59124,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X6),singleton(sK3(X4,X5,cartesian_product2(singleton(X2),X3))))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_3017]) ).
tcf(c_59125,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X6),singleton(sK3(X4,X5,cartesian_product2(singleton(X2),X3))))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_3015]) ).
tcf(c_59126,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X6),singleton(sK3(X4,X5,cartesian_product2(singleton(X2),X3))))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_3014]) ).
tcf(c_59127,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X6),singleton(sK3(X4,X5,cartesian_product2(singleton(X2),X3))))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3))),unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2961]) ).
tcf(c_59128,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X6),singleton(sK3(X4,X5,cartesian_product2(singleton(X2),X3))))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3))),unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2959]) ).
tcf(c_59129,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X6),singleton(sK3(X4,X5,cartesian_product2(singleton(X2),X3))))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2958]) ).
tcf(c_59130,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X6),singleton(sK3(X4,X5,cartesian_product2(singleton(X2),X3))))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(singleton(X2),X3))),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_3012]) ).
tcf(c_59131,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X2),X3) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(singleton(X2),X3)),X6),singleton(sK3(X4,X5,cartesian_product2(singleton(X2),X3))))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(singleton(X2),X3)),X0),singleton(sK1(X4,X5,cartesian_product2(singleton(X2),X3)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2956]) ).
tcf(c_59132,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X5),X6) = cartesian_product2(X4,X2) )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X5),X6,sK1(X4,X2,cartesian_product2(singleton(X5),X6))),X0))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK3(X4,X2,cartesian_product2(singleton(X5),X6)),X3),singleton(sK3(X4,X2,cartesian_product2(singleton(X5),X6))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2545]) ).
tcf(c_59133,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X5),X6) = cartesian_product2(X4,X2) )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(sK4(singleton(X5),X6,sK1(X4,X2,cartesian_product2(singleton(X5),X6))),X0),singleton(X0))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK3(X4,X2,cartesian_product2(singleton(X5),X6)),X3),singleton(sK3(X4,X2,cartesian_product2(singleton(X5),X6))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_1935]) ).
tcf(c_59134,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X5),X6) = cartesian_product2(X4,X2) )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X5),X6,sK1(X4,X2,cartesian_product2(singleton(X5),X6)))))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK3(X4,X2,cartesian_product2(singleton(X5),X6)),X3),singleton(sK3(X4,X2,cartesian_product2(singleton(X5),X6))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_1649]) ).
tcf(c_59135,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(singleton(X5),X6) = cartesian_product2(X4,X2) )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(X0,sK4(singleton(X5),X6,sK1(X4,X2,cartesian_product2(singleton(X5),X6)))),singleton(X0))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK3(X4,X2,cartesian_product2(singleton(X5),X6)),X3),singleton(sK3(X4,X2,cartesian_product2(singleton(X5),X6))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_1312]) ).
tcf(c_59136,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(singleton(X3),X4) = cartesian_product2(X2,X0) )
| ( sK4(singleton(X3),X4,sK1(X2,X0,cartesian_product2(singleton(X3),X4))) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK3(X2,X0,cartesian_product2(singleton(X3),X4)),X1),singleton(sK3(X2,X0,cartesian_product2(singleton(X3),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1387,c_787]) ).
tcf(c_59137,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X5,singleton(X6)) = cartesian_product2(X4,X2) )
| ( sK5(X5,singleton(X6),sK5(X1,cartesian_product2(X5,singleton(X6)),unordered_pair(singleton(X0),unordered_pair(X0,sK1(X4,X2,cartesian_product2(X5,singleton(X6))))))) = X6 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK3(X4,X2,cartesian_product2(X5,singleton(X6))),X3),singleton(sK3(X4,X2,cartesian_product2(X5,singleton(X6)))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_3142]) ).
tcf(c_59138,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X5,singleton(X6)) = cartesian_product2(X4,X2) )
| ( sK5(X5,singleton(X6),sK5(X1,cartesian_product2(X5,singleton(X6)),unordered_pair(singleton(X0),unordered_pair(sK1(X4,X2,cartesian_product2(X5,singleton(X6))),X0)))) = X6 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK3(X4,X2,cartesian_product2(X5,singleton(X6))),X3),singleton(sK3(X4,X2,cartesian_product2(X5,singleton(X6)))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_3140]) ).
tcf(c_59139,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X5,singleton(X6)) = cartesian_product2(X4,X2) )
| ( sK5(X5,singleton(X6),sK5(X1,cartesian_product2(X5,singleton(X6)),unordered_pair(unordered_pair(sK1(X4,X2,cartesian_product2(X5,singleton(X6))),X0),singleton(X0)))) = X6 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK3(X4,X2,cartesian_product2(X5,singleton(X6))),X3),singleton(sK3(X4,X2,cartesian_product2(X5,singleton(X6)))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_3139]) ).
tcf(c_59140,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X2,singleton(X3))),X6),singleton(sK3(X4,X5,cartesian_product2(X2,singleton(X3)))))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_3063]) ).
tcf(c_59141,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X2,singleton(X3))),X6),singleton(sK3(X4,X5,cartesian_product2(X2,singleton(X3)))))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_3061]) ).
tcf(c_59142,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X2,singleton(X3))),X6),singleton(sK3(X4,X5,cartesian_product2(X2,singleton(X3)))))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(X0,sK1(X4,X5,cartesian_product2(X2,singleton(X3)))),singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_3060]) ).
tcf(c_59143,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X5,singleton(X6)) = cartesian_product2(X4,X2) )
| ( sK5(X5,singleton(X6),sK5(X1,cartesian_product2(X5,singleton(X6)),unordered_pair(unordered_pair(X0,sK1(X4,X2,cartesian_product2(X5,singleton(X6)))),singleton(X0)))) = X6 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK3(X4,X2,cartesian_product2(X5,singleton(X6))),X3),singleton(sK3(X4,X2,cartesian_product2(X5,singleton(X6)))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_3137]) ).
tcf(c_59144,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X2,singleton(X3)) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X2,singleton(X3))),X6),singleton(sK3(X4,X5,cartesian_product2(X2,singleton(X3)))))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(sK1(X4,X5,cartesian_product2(X2,singleton(X3))),X0),singleton(sK1(X4,X5,cartesian_product2(X2,singleton(X3))))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_3058]) ).
tcf(c_59145,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X5,singleton(X6)) = cartesian_product2(X4,X2) )
| ( sK5(X1,singleton(X6),unordered_pair(singleton(X0),unordered_pair(sK5(X5,singleton(X6),sK1(X4,X2,cartesian_product2(X5,singleton(X6)))),X0))) = X6 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK3(X4,X2,cartesian_product2(X5,singleton(X6))),X3),singleton(sK3(X4,X2,cartesian_product2(X5,singleton(X6)))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_2546]) ).
tcf(c_59146,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X5,singleton(X6)) = cartesian_product2(X4,X2) )
| ( sK5(X1,singleton(X6),unordered_pair(unordered_pair(sK5(X5,singleton(X6),sK1(X4,X2,cartesian_product2(X5,singleton(X6)))),X0),singleton(X0))) = X6 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK3(X4,X2,cartesian_product2(X5,singleton(X6))),X3),singleton(sK3(X4,X2,cartesian_product2(X5,singleton(X6)))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_1936]) ).
tcf(c_59147,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X5,singleton(X6)) = cartesian_product2(X4,X2) )
| ( sK5(X1,singleton(X6),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X5,singleton(X6),sK1(X4,X2,cartesian_product2(X5,singleton(X6))))))) = X6 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK3(X4,X2,cartesian_product2(X5,singleton(X6))),X3),singleton(sK3(X4,X2,cartesian_product2(X5,singleton(X6)))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_1650]) ).
tcf(c_59148,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X5,singleton(X6)) = cartesian_product2(X4,X2) )
| ( sK5(X1,singleton(X6),unordered_pair(unordered_pair(X0,sK5(X5,singleton(X6),sK1(X4,X2,cartesian_product2(X5,singleton(X6))))),singleton(X0))) = X6 )
| ( sK5(X2,singleton(X3),unordered_pair(unordered_pair(sK3(X4,X2,cartesian_product2(X5,singleton(X6))),X3),singleton(sK3(X4,X2,cartesian_product2(X5,singleton(X6)))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1387,c_1313]) ).
tcf(c_59149,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X3,singleton(X4)) = cartesian_product2(X2,X0) )
| ( sK5(X3,singleton(X4),sK1(X2,X0,cartesian_product2(X3,singleton(X4)))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK3(X2,X0,cartesian_product2(X3,singleton(X4))),X1),singleton(sK3(X2,X0,cartesian_product2(X3,singleton(X4)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1387,c_789]) ).
tcf(c_59150,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X3),X4),X5) = cartesian_product2(X2,X0) )
| ( sK4(singleton(X3),X4,sK4(cartesian_product2(singleton(X3),X4),X5,sK1(X2,X0,cartesian_product2(cartesian_product2(singleton(X3),X4),X5)))) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK3(X2,X0,cartesian_product2(cartesian_product2(singleton(X3),X4),X5)),X1),singleton(sK3(X2,X0,cartesian_product2(cartesian_product2(singleton(X3),X4),X5))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1387,c_835]) ).
tcf(c_59151,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(singleton(X4),X5)) = cartesian_product2(X2,X0) )
| ( sK4(singleton(X4),X5,sK5(X3,cartesian_product2(singleton(X4),X5),sK1(X2,X0,cartesian_product2(X3,cartesian_product2(singleton(X4),X5))))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK3(X2,X0,cartesian_product2(X3,cartesian_product2(singleton(X4),X5))),X1),singleton(sK3(X2,X0,cartesian_product2(X3,cartesian_product2(singleton(X4),X5)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1387,c_836]) ).
tcf(c_59152,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X3,singleton(X4)),X5) = cartesian_product2(X2,X0) )
| ( sK5(X3,singleton(X4),sK4(cartesian_product2(X3,singleton(X4)),X5,sK1(X2,X0,cartesian_product2(cartesian_product2(X3,singleton(X4)),X5)))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK3(X2,X0,cartesian_product2(cartesian_product2(X3,singleton(X4)),X5)),X1),singleton(sK3(X2,X0,cartesian_product2(cartesian_product2(X3,singleton(X4)),X5))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1387,c_861]) ).
tcf(c_59153,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X4,singleton(X5))) = cartesian_product2(X2,X0) )
| ( sK5(X4,singleton(X5),sK5(X3,cartesian_product2(X4,singleton(X5)),sK1(X2,X0,cartesian_product2(X3,cartesian_product2(X4,singleton(X5)))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK3(X2,X0,cartesian_product2(X3,cartesian_product2(X4,singleton(X5)))),X1),singleton(sK3(X2,X0,cartesian_product2(X3,cartesian_product2(X4,singleton(X5))))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1387,c_862]) ).
tcf(c_59154,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)),X6),singleton(sK3(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_2896]) ).
tcf(c_59155,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)),X6),singleton(sK3(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_2820]) ).
tcf(c_59156,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)),X6),singleton(sK3(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_2729]) ).
tcf(c_59157,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)),X6),singleton(sK3(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_2672]) ).
tcf(c_59158,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)),X6),singleton(sK3(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_2340]) ).
tcf(c_59159,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)),X6),singleton(sK3(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_2282]) ).
tcf(c_59160,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X1),X3) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3)),X6),singleton(sK3(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X2,X1),X3))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_2178]) ).
tcf(c_59161,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X1,X2),X3) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3)),X6),singleton(sK3(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK1(X4,X5,cartesian_product2(cartesian_product2(X1,X2),X3))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_2102]) ).
tcf(c_59162,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))),X6),singleton(sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_2897]) ).
tcf(c_59163,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))),X6),singleton(sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_2821]) ).
tcf(c_59164,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))),X6),singleton(sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_2730]) ).
tcf(c_59165,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))),X6),singleton(sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_2673]) ).
tcf(c_59166,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))),X6),singleton(sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_2341]) ).
tcf(c_59167,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))),X6),singleton(sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_2283]) ).
tcf(c_59168,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X1)) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1))),X6),singleton(sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X2,X1)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_2179]) ).
tcf(c_59169,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,cartesian_product2(X1,X2)) = cartesian_product2(X4,X5) )
| ( sK5(X5,singleton(X6),unordered_pair(unordered_pair(sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2))),X6),singleton(sK3(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK1(X4,X5,cartesian_product2(X3,cartesian_product2(X1,X2)))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1387,c_2103]) ).
tcf(c_61189,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,singleton(X3))
| ( cartesian_product2(X2,singleton(X3)) = singleton(X0) )
| ( sK1(X2,singleton(X3),singleton(X0)) = X0 )
| ( sK5(singleton(X0),singleton(X1),unordered_pair(singleton(sK1(X2,singleton(X3),singleton(X0))),unordered_pair(sK1(X2,singleton(X3),singleton(X0)),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1032,c_1698]) ).
tcf(c_61190,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X2,X4)),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(sK3(X3,X2,X4),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_42941]) ).
tcf(c_61191,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2903]) ).
tcf(c_61192,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X2,X4)),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(X1,sK3(X3,X2,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_42542]) ).
tcf(c_61193,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2902]) ).
tcf(c_61194,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X1,X4)),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK3(X3,X1,X4),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_42396]) ).
tcf(c_61195,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2901]) ).
tcf(c_61196,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X1,X4)),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_42068]) ).
tcf(c_61197,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2900]) ).
tcf(c_61198,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X1,X4)),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK3(X3,X1,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_41683]) ).
tcf(c_61199,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2899]) ).
tcf(c_61200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X2,X4)),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(sK3(X3,X2,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_40876]) ).
tcf(c_61201,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2898]) ).
tcf(c_61202,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X1,X4)),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_40020]) ).
tcf(c_61203,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2827]) ).
tcf(c_61204,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X1,X4)),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_39078]) ).
tcf(c_61205,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2826]) ).
tcf(c_61206,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X2,X4)),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_38387]) ).
tcf(c_61207,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2825]) ).
tcf(c_61208,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X2,X4)),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_37946]) ).
tcf(c_61209,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2824]) ).
tcf(c_61210,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X2,X4)),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_37625]) ).
tcf(c_61211,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2823]) ).
tcf(c_61212,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X2,X4)),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(sK3(X3,X2,X4),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_36554]) ).
tcf(c_61213,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2736]) ).
tcf(c_61214,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X1,X4)),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_35937]) ).
tcf(c_61215,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2822]) ).
tcf(c_61216,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X2,X4)),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(X1,sK3(X3,X2,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_35157]) ).
tcf(c_61217,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2735]) ).
tcf(c_61218,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X1,X4)),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK3(X3,X1,X4),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_34740]) ).
tcf(c_61219,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2734]) ).
tcf(c_61220,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X1,X4)),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_34537]) ).
tcf(c_61221,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2733]) ).
tcf(c_61222,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X1,X4)),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK3(X3,X1,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_34285]) ).
tcf(c_61223,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2732]) ).
tcf(c_61224,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X1,X4)),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_33912]) ).
tcf(c_61225,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2679]) ).
tcf(c_61226,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X1,X4)),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_33513]) ).
tcf(c_61227,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2678]) ).
tcf(c_61228,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X2,X4)),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(sK3(X3,X2,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_32955]) ).
tcf(c_61229,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2731]) ).
tcf(c_61230,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X2,X4)),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_31618]) ).
tcf(c_61231,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2677]) ).
tcf(c_61232,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X2,X4)),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_30471]) ).
tcf(c_61233,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2676]) ).
tcf(c_61234,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X2,X4)),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_30093]) ).
tcf(c_61235,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2675]) ).
tcf(c_61236,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X2,X4)),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(sK3(X3,X2,X4),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_29608]) ).
tcf(c_61237,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2347]) ).
tcf(c_61238,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X2,X4)),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(X1,sK3(X3,X2,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_29355]) ).
tcf(c_61239,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2346]) ).
tcf(c_61240,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X1,X4)),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK3(X3,X1,X4),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_28822]) ).
tcf(c_61241,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2345]) ).
tcf(c_61242,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X1,X4)),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_28296]) ).
tcf(c_61243,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2674]) ).
tcf(c_61244,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X1,X4)),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_27575]) ).
tcf(c_61245,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2344]) ).
tcf(c_61246,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X1,X4)),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK3(X3,X1,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_27245]) ).
tcf(c_61247,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2343]) ).
tcf(c_61248,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X1,X4)),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_26883]) ).
tcf(c_61249,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2289]) ).
tcf(c_61250,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X1,X4)),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_26385]) ).
tcf(c_61251,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2288]) ).
tcf(c_61252,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X2,X4)),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_26012]) ).
tcf(c_61253,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2287]) ).
tcf(c_61254,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X2,X4)),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_25743]) ).
tcf(c_61255,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2286]) ).
tcf(c_61256,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X2,X4)),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(sK3(X3,X2,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_25328]) ).
tcf(c_61257,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2342]) ).
tcf(c_61258,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X2,X4)),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_24337]) ).
tcf(c_61259,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2285]) ).
tcf(c_61260,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X2,X4)),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(sK3(X3,X2,X4),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_23980]) ).
tcf(c_61261,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2185]) ).
tcf(c_61262,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X2,X4)),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK3(X3,X2,X4)),unordered_pair(X1,sK3(X3,X2,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_23739]) ).
tcf(c_61263,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2184]) ).
tcf(c_61264,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X1,X4)),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK3(X3,X1,X4),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_23253]) ).
tcf(c_61265,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2183]) ).
tcf(c_61266,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X1,X4)),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_22960]) ).
tcf(c_61267,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2182]) ).
tcf(c_61268,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X1,X4)),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK3(X3,X1,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_22721]) ).
tcf(c_61269,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2181]) ).
tcf(c_61270,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X1,X4)),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_22587]) ).
tcf(c_61271,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2284]) ).
tcf(c_61272,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X1,X4)),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_21575]) ).
tcf(c_61273,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2109]) ).
tcf(c_61274,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X1,X4)),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_21200]) ).
tcf(c_61275,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2108]) ).
tcf(c_61276,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X2,X4)),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_20765]) ).
tcf(c_61277,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2107]) ).
tcf(c_61278,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X2,X4)),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_20286]) ).
tcf(c_61279,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2106]) ).
tcf(c_61280,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X2,X4)),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(sK3(X3,X2,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_19855]) ).
tcf(c_61281,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2180]) ).
tcf(c_61282,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X2,X4)),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_18803]) ).
tcf(c_61283,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2105]) ).
tcf(c_61284,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X1,X4)),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_18127]) ).
tcf(c_61285,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2104]) ).
tcf(c_61286,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X1,X4)),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_17483]) ).
tcf(c_61287,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2465]) ).
tcf(c_61288,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X1,X4)),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_16787]) ).
tcf(c_61289,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2464]) ).
tcf(c_61290,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X2,X4)),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_16125]) ).
tcf(c_61291,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2463]) ).
tcf(c_61292,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X2,X4)),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_15658]) ).
tcf(c_61293,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2462]) ).
tcf(c_61294,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X2,X4)),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_15187]) ).
tcf(c_61295,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2461]) ).
tcf(c_61296,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X1,X4)),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_14882]) ).
tcf(c_61297,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2460]) ).
tcf(c_61298,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X1,X4)),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_13234]) ).
tcf(c_61299,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_1863]) ).
tcf(c_61300,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X1,X4)),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_12125]) ).
tcf(c_61301,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_1862]) ).
tcf(c_61302,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X2,X4)),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_11834]) ).
tcf(c_61303,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_1861]) ).
tcf(c_61304,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X2,X4)),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_11410]) ).
tcf(c_61305,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_1860]) ).
tcf(c_61306,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X2,X4)),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_10829]) ).
tcf(c_61307,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_1859]) ).
tcf(c_61308,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X1,X4)),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_10535]) ).
tcf(c_61309,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_1858]) ).
tcf(c_61310,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X1,X4)),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_8720]) ).
tcf(c_61311,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_1575]) ).
tcf(c_61312,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X1,X4)),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_8554]) ).
tcf(c_61313,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_1574]) ).
tcf(c_61314,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X2,X4)),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_8285]) ).
tcf(c_61315,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_1573]) ).
tcf(c_61316,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X2,X4)),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_8027]) ).
tcf(c_61317,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_1572]) ).
tcf(c_61318,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X2,X4)),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_7766]) ).
tcf(c_61319,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_1571]) ).
tcf(c_61320,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X1,X4)),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_7495]) ).
tcf(c_61321,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_1570]) ).
tcf(c_61322,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X1,X4)),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(sK3(X3,X1,X4),X2))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_6164]) ).
tcf(c_61323,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,X3,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_1156]) ).
tcf(c_61324,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X1,X4)),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK3(X3,X1,X4)),unordered_pair(X2,sK3(X3,X1,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_5987]) ).
tcf(c_61325,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK3(X4,X3,X5),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_1155]) ).
tcf(c_61326,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X2,X4)),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK3(X3,X2,X4),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_5758]) ).
tcf(c_61327,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(X0,sK3(X4,X3,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_1154]) ).
tcf(c_61328,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X2,X4)),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK3(X3,X2,X4),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_5518]) ).
tcf(c_61329,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(sK3(X4,X3,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_1153]) ).
tcf(c_61330,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X2) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X2,X4)),unordered_pair(sK1(X3,X2,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK3(X3,X2,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_5291]) ).
tcf(c_61331,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK3(X4,X3,X5)),unordered_pair(sK3(X4,X3,X5),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_1152]) ).
tcf(c_61332,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,X1) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,X1,X4)),unordered_pair(sK1(X3,X1,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK3(X3,X1,X4),X2),singleton(sK3(X3,X1,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_4798]) ).
tcf(c_61333,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,X3) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,X3,X5)),unordered_pair(sK1(X4,X3,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK3(X4,X3,X5)),singleton(X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_1151]) ).
tcf(c_61334,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK5(X3,singleton(X4),unordered_pair(singleton(sK3(X2,X3,X0)),unordered_pair(X4,sK3(X2,X3,X0)))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,X3,X0)),unordered_pair(sK1(X2,X3,X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1698,c_2539]) ).
tcf(c_61336,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK5(X3,singleton(X4),unordered_pair(unordered_pair(X4,sK3(X2,X3,X0)),singleton(sK3(X2,X3,X0)))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,X3,X0)),unordered_pair(sK1(X2,X3,X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1698,c_1929]) ).
tcf(c_61338,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK5(X3,singleton(X4),unordered_pair(singleton(sK3(X2,X3,X0)),unordered_pair(sK3(X2,X3,X0),X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,X3,X0)),unordered_pair(sK1(X2,X3,X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1698,c_1643]) ).
tcf(c_61340,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK5(X3,singleton(X4),unordered_pair(unordered_pair(sK3(X2,X3,X0),X4),singleton(sK3(X2,X3,X0)))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,X3,X0)),unordered_pair(sK1(X2,X3,X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1698,c_1306]) ).
tcf(c_61342,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X2 )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(sK3(X4,singleton(X5),X2),X0))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(singleton(sK1(X4,singleton(X5),X2)),unordered_pair(sK1(X4,singleton(X5),X2),X3))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_907]) ).
tcf(c_61343,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,singleton(X2)) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,singleton(X2),X4)),unordered_pair(sK1(X3,singleton(X2),X4),X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK3(X3,singleton(X2),X4)),unordered_pair(X0,sK3(X3,singleton(X2),X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_906]) ).
tcf(c_61344,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X2 )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(sK3(X4,singleton(X5),X2),X0),singleton(X0))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(singleton(sK1(X4,singleton(X5),X2)),unordered_pair(sK1(X4,singleton(X5),X2),X3))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_899]) ).
tcf(c_61345,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,singleton(X2)) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,singleton(X2),X4)),unordered_pair(sK1(X3,singleton(X2),X4),X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X0,sK3(X3,singleton(X2),X4)),singleton(sK3(X3,singleton(X2),X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_898]) ).
tcf(c_61346,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X2 )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,singleton(X5),X2)))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(singleton(sK1(X4,singleton(X5),X2)),unordered_pair(sK1(X4,singleton(X5),X2),X3))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_889]) ).
tcf(c_61347,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,singleton(X2)) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,singleton(X2),X4)),unordered_pair(sK1(X3,singleton(X2),X4),X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK3(X3,singleton(X2),X4)),unordered_pair(sK3(X3,singleton(X2),X4),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_888]) ).
tcf(c_61348,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X4,singleton(X5)) = X2 )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(X0,sK3(X4,singleton(X5),X2)),singleton(X0))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(singleton(sK1(X4,singleton(X5),X2)),unordered_pair(sK1(X4,singleton(X5),X2),X3))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_863]) ).
tcf(c_61349,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,singleton(X2)) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,singleton(X2),X4)),unordered_pair(sK1(X3,singleton(X2),X4),X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK3(X3,singleton(X2),X4),X0),singleton(sK3(X3,singleton(X2),X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_837]) ).
tcf(c_61351,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(X3,X2),X5)),unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_16267]) ).
tcf(c_61352,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(X2,X3),X5)),unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_16266]) ).
tcf(c_61353,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(X3,X2),X5)),unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_15723]) ).
tcf(c_61354,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(X2,X3),X5)),unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_15722]) ).
tcf(c_61355,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(X3,X2),X5)),unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_15377]) ).
tcf(c_61356,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(X2,X3),X5)),unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_15376]) ).
tcf(c_61357,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(X3,X2),X5)),unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_12049]) ).
tcf(c_61358,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(X2,X3),X5)),unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_12048]) ).
tcf(c_61359,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(X3,X2),X5)),unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_11518]) ).
tcf(c_61360,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(X2,X3),X5)),unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_11517]) ).
tcf(c_61361,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(X3,X2),X5)),unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_11093]) ).
tcf(c_61362,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(X2,X3),X5)),unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_11092]) ).
tcf(c_61363,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(X3,X2),X5)),unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_8458]) ).
tcf(c_61364,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(X2,X3),X5)),unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_8457]) ).
tcf(c_61365,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(X3,X2),X5)),unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_8152]) ).
tcf(c_61366,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(X2,X3),X5)),unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_8151]) ).
tcf(c_61367,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(X3,X2),X5)),unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_7854]) ).
tcf(c_61368,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(X2,X3),X5)),unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_7853]) ).
tcf(c_61369,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(X3,X2),X5)),unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_5825]) ).
tcf(c_61370,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(X2,X3),X5)),unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_5824]) ).
tcf(c_61371,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(X3,X2),X5)),unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5)),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_5642]) ).
tcf(c_61372,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(X2,X3),X5)),unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5)),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_5641]) ).
tcf(c_61373,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,X2)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(X3,X2),X5)),unordered_pair(sK1(X4,cartesian_product2(X3,X2),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK3(X4,cartesian_product2(X3,X2),X5))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_5396]) ).
tcf(c_61374,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(X2,X3),X5)),unordered_pair(sK1(X4,cartesian_product2(X2,X3),X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK3(X4,cartesian_product2(X2,X3),X5))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_5395]) ).
tcf(c_61375,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X0)) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,cartesian_product2(X2,X0),X4)),unordered_pair(sK1(X3,cartesian_product2(X2,X0),X4),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))),unordered_pair(X1,sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1698,c_2611]) ).
tcf(c_61376,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X0,X2)) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,cartesian_product2(X0,X2),X4)),unordered_pair(sK1(X3,cartesian_product2(X0,X2),X4),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))),unordered_pair(X1,sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1698,c_2610]) ).
tcf(c_61377,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X0)) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,cartesian_product2(X2,X0),X4)),unordered_pair(sK1(X3,cartesian_product2(X2,X0),X4),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))),singleton(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1698,c_2036]) ).
tcf(c_61378,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X0,X2)) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,cartesian_product2(X0,X2),X4)),unordered_pair(sK1(X3,cartesian_product2(X0,X2),X4),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))),singleton(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1698,c_2035]) ).
tcf(c_61379,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X0)) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,cartesian_product2(X2,X0),X4)),unordered_pair(sK1(X3,cartesian_product2(X2,X0),X4),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))),unordered_pair(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4)),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1698,c_1703]) ).
tcf(c_61380,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X0,X2)) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,cartesian_product2(X0,X2),X4)),unordered_pair(sK1(X3,cartesian_product2(X0,X2),X4),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))),unordered_pair(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4)),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1698,c_1702]) ).
tcf(c_61381,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X2,X0)) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,cartesian_product2(X2,X0),X4)),unordered_pair(sK1(X3,cartesian_product2(X2,X0),X4),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4)),X1),singleton(sK5(X2,X0,sK3(X3,cartesian_product2(X2,X0),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1698,c_1389]) ).
tcf(c_61382,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X3,cartesian_product2(X0,X2)) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X3,cartesian_product2(X0,X2),X4)),unordered_pair(sK1(X3,cartesian_product2(X0,X2),X4),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4)),X1),singleton(sK4(X0,X2,sK3(X3,cartesian_product2(X0,X2),X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1698,c_1388]) ).
tcf(c_61383,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(X3,X4)) = X0 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(sK5(X3,X4,sK3(X2,cartesian_product2(X3,X4),X0)),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,cartesian_product2(X3,X4),X0)),unordered_pair(sK1(X2,cartesian_product2(X3,X4),X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1698,c_2459]) ).
tcf(c_61384,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(X3,X4)) = X0 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK4(X3,X4,sK3(X2,cartesian_product2(X3,X4),X0)),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,cartesian_product2(X3,X4),X0)),unordered_pair(sK1(X2,cartesian_product2(X3,X4),X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1698,c_2458]) ).
tcf(c_61385,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(X3,X4)) = X0 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(sK5(X3,X4,sK3(X2,cartesian_product2(X3,X4),X0)),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,cartesian_product2(X3,X4),X0)),unordered_pair(sK1(X2,cartesian_product2(X3,X4),X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1698,c_1857]) ).
tcf(c_61386,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(X3,X4)) = X0 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK4(X3,X4,sK3(X2,cartesian_product2(X3,X4),X0)),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,cartesian_product2(X3,X4),X0)),unordered_pair(sK1(X2,cartesian_product2(X3,X4),X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1698,c_1856]) ).
tcf(c_61387,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(X3,X4)) = X0 )
| ( sK4(singleton(X5),X4,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X3,X4,sK3(X2,cartesian_product2(X3,X4),X0))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,cartesian_product2(X3,X4),X0)),unordered_pair(sK1(X2,cartesian_product2(X3,X4),X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1698,c_1569]) ).
tcf(c_61388,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(X3,X4)) = X0 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X3,X4,sK3(X2,cartesian_product2(X3,X4),X0))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,cartesian_product2(X3,X4),X0)),unordered_pair(sK1(X2,cartesian_product2(X3,X4),X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1698,c_1568]) ).
tcf(c_61389,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(X3,X4)) = X0 )
| ( sK4(singleton(X5),X4,unordered_pair(unordered_pair(X5,sK5(X3,X4,sK3(X2,cartesian_product2(X3,X4),X0))),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,cartesian_product2(X3,X4),X0)),unordered_pair(sK1(X2,cartesian_product2(X3,X4),X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1698,c_1150]) ).
tcf(c_61390,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(X3,X4)) = X0 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK4(X3,X4,sK3(X2,cartesian_product2(X3,X4),X0))),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,cartesian_product2(X3,X4),X0)),unordered_pair(sK1(X2,cartesian_product2(X3,X4),X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1698,c_1149]) ).
tcf(c_61391,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,cartesian_product2(X0,X1)) = X3 )
| ( sK5(X3,singleton(X4),unordered_pair(singleton(sK1(X2,cartesian_product2(X0,X1),X3)),unordered_pair(sK1(X2,cartesian_product2(X0,X1),X3),X4))) = X4 )
| ( unordered_pair(unordered_pair(sK4(X0,X1,sK3(X2,cartesian_product2(X0,X1),X3)),sK5(X0,X1,sK3(X2,cartesian_product2(X0,X1),X3))),singleton(sK4(X0,X1,sK3(X2,cartesian_product2(X0,X1),X3)))) = sK3(X2,cartesian_product2(X0,X1),X3) ) ),
inference(superposition,[status(thm)],[c_1698,c_62]) ).
tcf(c_61392,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(singleton(X2),X3),X5)),unordered_pair(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,cartesian_product2(singleton(X2),X3),X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_3017]) ).
tcf(c_61393,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(singleton(X2),X3),X5)),unordered_pair(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(sK3(X4,cartesian_product2(singleton(X2),X3),X5),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_3015]) ).
tcf(c_61394,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(singleton(X2),X3),X5)),unordered_pair(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(sK3(X4,cartesian_product2(singleton(X2),X3),X5),X0),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_3014]) ).
tcf(c_61395,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(singleton(X2),X3),X5)),unordered_pair(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK3(X4,cartesian_product2(singleton(X2),X3),X5)),unordered_pair(sK3(X4,cartesian_product2(singleton(X2),X3),X5),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2961]) ).
tcf(c_61396,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(singleton(X2),X3),X5)),unordered_pair(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK3(X4,cartesian_product2(singleton(X2),X3),X5)),unordered_pair(X0,sK3(X4,cartesian_product2(singleton(X2),X3),X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2959]) ).
tcf(c_61397,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(singleton(X2),X3),X5)),unordered_pair(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(X0,sK3(X4,cartesian_product2(singleton(X2),X3),X5)),singleton(sK3(X4,cartesian_product2(singleton(X2),X3),X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2958]) ).
tcf(c_61398,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(singleton(X2),X3),X5)),unordered_pair(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(X0,sK3(X4,cartesian_product2(singleton(X2),X3),X5)),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_3012]) ).
tcf(c_61399,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X2),X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(singleton(X2),X3),X5)),unordered_pair(sK1(X4,cartesian_product2(singleton(X2),X3),X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(sK3(X4,cartesian_product2(singleton(X2),X3),X5),X0),singleton(sK3(X4,cartesian_product2(singleton(X2),X3),X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2956]) ).
tcf(c_61400,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X5),X6)) = X2 )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X5),X6,sK3(X4,cartesian_product2(singleton(X5),X6),X2)),X0))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(singleton(sK1(X4,cartesian_product2(singleton(X5),X6),X2)),unordered_pair(sK1(X4,cartesian_product2(singleton(X5),X6),X2),X3))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2545]) ).
tcf(c_61401,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X5),X6)) = X2 )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(sK4(singleton(X5),X6,sK3(X4,cartesian_product2(singleton(X5),X6),X2)),X0),singleton(X0))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(singleton(sK1(X4,cartesian_product2(singleton(X5),X6),X2)),unordered_pair(sK1(X4,cartesian_product2(singleton(X5),X6),X2),X3))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_1935]) ).
tcf(c_61402,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X5),X6)) = X2 )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X5),X6,sK3(X4,cartesian_product2(singleton(X5),X6),X2))))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(singleton(sK1(X4,cartesian_product2(singleton(X5),X6),X2)),unordered_pair(sK1(X4,cartesian_product2(singleton(X5),X6),X2),X3))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_1649]) ).
tcf(c_61403,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(singleton(X5),X6)) = X2 )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(X0,sK4(singleton(X5),X6,sK3(X4,cartesian_product2(singleton(X5),X6),X2))),singleton(X0))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(singleton(sK1(X4,cartesian_product2(singleton(X5),X6),X2)),unordered_pair(sK1(X4,cartesian_product2(singleton(X5),X6),X2),X3))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_1312]) ).
tcf(c_61404,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,cartesian_product2(singleton(X3),X4)) = X0 )
| ( sK4(singleton(X3),X4,sK3(X2,cartesian_product2(singleton(X3),X4),X0)) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,cartesian_product2(singleton(X3),X4),X0)),unordered_pair(sK1(X2,cartesian_product2(singleton(X3),X4),X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1698,c_787]) ).
tcf(c_61405,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X5,singleton(X6))) = X2 )
| ( sK5(X5,singleton(X6),sK5(X1,cartesian_product2(X5,singleton(X6)),unordered_pair(singleton(X0),unordered_pair(X0,sK3(X4,cartesian_product2(X5,singleton(X6)),X2))))) = X6 )
| ( sK5(X2,singleton(X3),unordered_pair(singleton(sK1(X4,cartesian_product2(X5,singleton(X6)),X2)),unordered_pair(sK1(X4,cartesian_product2(X5,singleton(X6)),X2),X3))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_3142]) ).
tcf(c_61406,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X5,singleton(X6))) = X2 )
| ( sK5(X5,singleton(X6),sK5(X1,cartesian_product2(X5,singleton(X6)),unordered_pair(singleton(X0),unordered_pair(sK3(X4,cartesian_product2(X5,singleton(X6)),X2),X0)))) = X6 )
| ( sK5(X2,singleton(X3),unordered_pair(singleton(sK1(X4,cartesian_product2(X5,singleton(X6)),X2)),unordered_pair(sK1(X4,cartesian_product2(X5,singleton(X6)),X2),X3))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_3140]) ).
tcf(c_61407,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X5,singleton(X6))) = X2 )
| ( sK5(X5,singleton(X6),sK5(X1,cartesian_product2(X5,singleton(X6)),unordered_pair(unordered_pair(sK3(X4,cartesian_product2(X5,singleton(X6)),X2),X0),singleton(X0)))) = X6 )
| ( sK5(X2,singleton(X3),unordered_pair(singleton(sK1(X4,cartesian_product2(X5,singleton(X6)),X2)),unordered_pair(sK1(X4,cartesian_product2(X5,singleton(X6)),X2),X3))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_3139]) ).
tcf(c_61408,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(X2,singleton(X3)),X5)),unordered_pair(sK1(X4,cartesian_product2(X2,singleton(X3)),X5),X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK3(X4,cartesian_product2(X2,singleton(X3)),X5)),unordered_pair(sK3(X4,cartesian_product2(X2,singleton(X3)),X5),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_3063]) ).
tcf(c_61409,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(X2,singleton(X3)),X5)),unordered_pair(sK1(X4,cartesian_product2(X2,singleton(X3)),X5),X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK3(X4,cartesian_product2(X2,singleton(X3)),X5)),unordered_pair(X0,sK3(X4,cartesian_product2(X2,singleton(X3)),X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_3061]) ).
tcf(c_61410,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(X2,singleton(X3)),X5)),unordered_pair(sK1(X4,cartesian_product2(X2,singleton(X3)),X5),X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(X0,sK3(X4,cartesian_product2(X2,singleton(X3)),X5)),singleton(sK3(X4,cartesian_product2(X2,singleton(X3)),X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_3060]) ).
tcf(c_61411,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X5,singleton(X6))) = X2 )
| ( sK5(X5,singleton(X6),sK5(X1,cartesian_product2(X5,singleton(X6)),unordered_pair(unordered_pair(X0,sK3(X4,cartesian_product2(X5,singleton(X6)),X2)),singleton(X0)))) = X6 )
| ( sK5(X2,singleton(X3),unordered_pair(singleton(sK1(X4,cartesian_product2(X5,singleton(X6)),X2)),unordered_pair(sK1(X4,cartesian_product2(X5,singleton(X6)),X2),X3))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_3137]) ).
tcf(c_61412,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X2,singleton(X3))) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(X2,singleton(X3)),X5)),unordered_pair(sK1(X4,cartesian_product2(X2,singleton(X3)),X5),X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(sK3(X4,cartesian_product2(X2,singleton(X3)),X5),X0),singleton(sK3(X4,cartesian_product2(X2,singleton(X3)),X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_3058]) ).
tcf(c_61413,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X5,singleton(X6))) = X2 )
| ( sK5(X1,singleton(X6),unordered_pair(singleton(X0),unordered_pair(sK5(X5,singleton(X6),sK3(X4,cartesian_product2(X5,singleton(X6)),X2)),X0))) = X6 )
| ( sK5(X2,singleton(X3),unordered_pair(singleton(sK1(X4,cartesian_product2(X5,singleton(X6)),X2)),unordered_pair(sK1(X4,cartesian_product2(X5,singleton(X6)),X2),X3))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_2546]) ).
tcf(c_61414,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X5,singleton(X6))) = X2 )
| ( sK5(X1,singleton(X6),unordered_pair(unordered_pair(sK5(X5,singleton(X6),sK3(X4,cartesian_product2(X5,singleton(X6)),X2)),X0),singleton(X0))) = X6 )
| ( sK5(X2,singleton(X3),unordered_pair(singleton(sK1(X4,cartesian_product2(X5,singleton(X6)),X2)),unordered_pair(sK1(X4,cartesian_product2(X5,singleton(X6)),X2),X3))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_1936]) ).
tcf(c_61415,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X5,singleton(X6))) = X2 )
| ( sK5(X1,singleton(X6),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X5,singleton(X6),sK3(X4,cartesian_product2(X5,singleton(X6)),X2))))) = X6 )
| ( sK5(X2,singleton(X3),unordered_pair(singleton(sK1(X4,cartesian_product2(X5,singleton(X6)),X2)),unordered_pair(sK1(X4,cartesian_product2(X5,singleton(X6)),X2),X3))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_1650]) ).
tcf(c_61416,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X5,singleton(X6))) = X2 )
| ( sK5(X1,singleton(X6),unordered_pair(unordered_pair(X0,sK5(X5,singleton(X6),sK3(X4,cartesian_product2(X5,singleton(X6)),X2))),singleton(X0))) = X6 )
| ( sK5(X2,singleton(X3),unordered_pair(singleton(sK1(X4,cartesian_product2(X5,singleton(X6)),X2)),unordered_pair(sK1(X4,cartesian_product2(X5,singleton(X6)),X2),X3))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1698,c_1313]) ).
tcf(c_61417,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,cartesian_product2(X3,singleton(X4))) = X0 )
| ( sK5(X3,singleton(X4),sK3(X2,cartesian_product2(X3,singleton(X4)),X0)) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,cartesian_product2(X3,singleton(X4)),X0)),unordered_pair(sK1(X2,cartesian_product2(X3,singleton(X4)),X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1698,c_789]) ).
tcf(c_61418,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(cartesian_product2(singleton(X3),X4),X5)) = X0 )
| ( sK4(singleton(X3),X4,sK4(cartesian_product2(singleton(X3),X4),X5,sK3(X2,cartesian_product2(cartesian_product2(singleton(X3),X4),X5),X0))) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,cartesian_product2(cartesian_product2(singleton(X3),X4),X5),X0)),unordered_pair(sK1(X2,cartesian_product2(cartesian_product2(singleton(X3),X4),X5),X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1698,c_835]) ).
tcf(c_61419,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(X3,cartesian_product2(singleton(X4),X5))) = X0 )
| ( sK4(singleton(X4),X5,sK5(X3,cartesian_product2(singleton(X4),X5),sK3(X2,cartesian_product2(X3,cartesian_product2(singleton(X4),X5)),X0))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,cartesian_product2(X3,cartesian_product2(singleton(X4),X5)),X0)),unordered_pair(sK1(X2,cartesian_product2(X3,cartesian_product2(singleton(X4),X5)),X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1698,c_836]) ).
tcf(c_61420,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(cartesian_product2(X3,singleton(X4)),X5)) = X0 )
| ( sK5(X3,singleton(X4),sK4(cartesian_product2(X3,singleton(X4)),X5,sK3(X2,cartesian_product2(cartesian_product2(X3,singleton(X4)),X5),X0))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,cartesian_product2(cartesian_product2(X3,singleton(X4)),X5),X0)),unordered_pair(sK1(X2,cartesian_product2(cartesian_product2(X3,singleton(X4)),X5),X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1698,c_861]) ).
tcf(c_61421,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,cartesian_product2(X3,cartesian_product2(X4,singleton(X5)))) = X0 )
| ( sK5(X4,singleton(X5),sK5(X3,cartesian_product2(X4,singleton(X5)),sK3(X2,cartesian_product2(X3,cartesian_product2(X4,singleton(X5))),X0))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,cartesian_product2(X3,cartesian_product2(X4,singleton(X5))),X0)),unordered_pair(sK1(X2,cartesian_product2(X3,cartesian_product2(X4,singleton(X5))),X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1698,c_862]) ).
tcf(c_61422,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X2,X1),X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5)),unordered_pair(sK1(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK3(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_2896]) ).
tcf(c_61423,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X1,X2),X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5)),unordered_pair(sK1(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK3(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_2820]) ).
tcf(c_61424,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X2,X1),X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5)),unordered_pair(sK1(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK3(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_2729]) ).
tcf(c_61425,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X1,X2),X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5)),unordered_pair(sK1(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK3(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_2672]) ).
tcf(c_61426,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X2,X1),X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5)),unordered_pair(sK1(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK3(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_2340]) ).
tcf(c_61427,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X1,X2),X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5)),unordered_pair(sK1(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK3(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_2282]) ).
tcf(c_61428,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X2,X1),X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5)),unordered_pair(sK1(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK3(X4,cartesian_product2(cartesian_product2(X2,X1),X3),X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_2178]) ).
tcf(c_61429,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(cartesian_product2(X1,X2),X3)) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5)),unordered_pair(sK1(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK3(X4,cartesian_product2(cartesian_product2(X1,X2),X3),X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_2102]) ).
tcf(c_61430,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X2,X1))) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5)),unordered_pair(sK1(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK3(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_2897]) ).
tcf(c_61431,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X1,X2))) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5)),unordered_pair(sK1(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK3(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_2821]) ).
tcf(c_61432,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X2,X1))) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5)),unordered_pair(sK1(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK3(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_2730]) ).
tcf(c_61433,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X1,X2))) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5)),unordered_pair(sK1(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK3(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_2673]) ).
tcf(c_61434,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X2,X1))) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5)),unordered_pair(sK1(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK3(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_2341]) ).
tcf(c_61435,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X1,X2))) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5)),unordered_pair(sK1(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK3(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_2283]) ).
tcf(c_61436,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X2,X1))) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5)),unordered_pair(sK1(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK3(X4,cartesian_product2(X3,cartesian_product2(X2,X1)),X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_2179]) ).
tcf(c_61437,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X4,cartesian_product2(X3,cartesian_product2(X1,X2))) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5)),unordered_pair(sK1(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK3(X4,cartesian_product2(X3,cartesian_product2(X1,X2)),X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1698,c_2103]) ).
tcf(c_62952,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X2,singleton(X2))
| ( cartesian_product2(singleton(X2),X3) = singleton(X0) )
| ( sK1(singleton(X2),X3,singleton(X0)) = X0 )
| ( sK5(singleton(X0),singleton(X1),unordered_pair(singleton(sK1(singleton(X2),X3,singleton(X0))),unordered_pair(sK1(singleton(X2),X3,singleton(X0)),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1009,c_1699]) ).
tcf(c_62953,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X2,X3,X4)),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(sK2(X2,X3,X4),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_42941]) ).
tcf(c_62954,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2903]) ).
tcf(c_62955,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X2,X3,X4)),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(X1,sK2(X2,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_42542]) ).
tcf(c_62956,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2902]) ).
tcf(c_62957,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X1,X3,X4)),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK2(X1,X3,X4),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_42396]) ).
tcf(c_62958,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2901]) ).
tcf(c_62959,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X1,X3,X4)),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_42068]) ).
tcf(c_62960,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2900]) ).
tcf(c_62961,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X1,X3,X4)),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK2(X1,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_41683]) ).
tcf(c_62962,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2899]) ).
tcf(c_62963,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X2,X3,X4)),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(sK2(X2,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_40876]) ).
tcf(c_62964,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2898]) ).
tcf(c_62965,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X1,X3,X4)),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_40020]) ).
tcf(c_62966,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2827]) ).
tcf(c_62967,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X1,X3,X4)),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_39078]) ).
tcf(c_62968,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2826]) ).
tcf(c_62969,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X2,X3,X4)),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_38387]) ).
tcf(c_62970,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2825]) ).
tcf(c_62971,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X2,X3,X4)),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_37946]) ).
tcf(c_62972,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2824]) ).
tcf(c_62973,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X2,X3,X4)),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_37625]) ).
tcf(c_62974,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2823]) ).
tcf(c_62975,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X2,X3,X4)),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(sK2(X2,X3,X4),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_36554]) ).
tcf(c_62976,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2736]) ).
tcf(c_62977,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X1,X3,X4)),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_35937]) ).
tcf(c_62978,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2822]) ).
tcf(c_62979,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X2,X3,X4)),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(X1,sK2(X2,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_35157]) ).
tcf(c_62980,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2735]) ).
tcf(c_62981,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X1,X3,X4)),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK2(X1,X3,X4),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_34740]) ).
tcf(c_62982,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2734]) ).
tcf(c_62983,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X1,X3,X4)),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_34537]) ).
tcf(c_62984,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2733]) ).
tcf(c_62985,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X1,X3,X4)),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK2(X1,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_34285]) ).
tcf(c_62986,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2732]) ).
tcf(c_62987,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X1,X3,X4)),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_33912]) ).
tcf(c_62988,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2679]) ).
tcf(c_62989,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X1,X3,X4)),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_33513]) ).
tcf(c_62990,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2678]) ).
tcf(c_62991,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X2,X3,X4)),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(sK2(X2,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_32955]) ).
tcf(c_62992,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK5(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2731]) ).
tcf(c_62993,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X2,X3,X4)),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_31618]) ).
tcf(c_62994,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2677]) ).
tcf(c_62995,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X2,X3,X4)),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_30471]) ).
tcf(c_62996,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2676]) ).
tcf(c_62997,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X2,X3,X4)),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_30093]) ).
tcf(c_62998,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2675]) ).
tcf(c_62999,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X2,X3,X4)),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(sK2(X2,X3,X4),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_29608]) ).
tcf(c_63000,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2347]) ).
tcf(c_63001,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X2,X3,X4)),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(X1,sK2(X2,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_29355]) ).
tcf(c_63002,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2346]) ).
tcf(c_63003,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X1,X3,X4)),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK2(X1,X3,X4),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_28822]) ).
tcf(c_63004,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2345]) ).
tcf(c_63005,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X1,X3,X4)),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_28296]) ).
tcf(c_63006,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK4(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2674]) ).
tcf(c_63007,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X1,X3,X4)),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_27575]) ).
tcf(c_63008,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2344]) ).
tcf(c_63009,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X1,X3,X4)),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK2(X1,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_27245]) ).
tcf(c_63010,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2343]) ).
tcf(c_63011,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X1,X3,X4)),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_26883]) ).
tcf(c_63012,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2289]) ).
tcf(c_63013,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X1,X3,X4)),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_26385]) ).
tcf(c_63014,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2288]) ).
tcf(c_63015,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X2,X3,X4)),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_26012]) ).
tcf(c_63016,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2287]) ).
tcf(c_63017,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X2,X3,X4)),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_25743]) ).
tcf(c_63018,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2286]) ).
tcf(c_63019,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X2,X3,X4)),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(sK2(X2,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_25328]) ).
tcf(c_63020,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2342]) ).
tcf(c_63021,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X2,X3,X4)),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_24337]) ).
tcf(c_63022,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2285]) ).
tcf(c_63023,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X2,X3,X4)),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(sK2(X2,X3,X4),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_23980]) ).
tcf(c_63024,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2185]) ).
tcf(c_63025,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X2,X3,X4)),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(singleton(sK2(X2,X3,X4)),unordered_pair(X1,sK2(X2,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_23739]) ).
tcf(c_63026,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2184]) ).
tcf(c_63027,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X1,X3,X4)),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(sK2(X1,X3,X4),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_23253]) ).
tcf(c_63028,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2183]) ).
tcf(c_63029,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X1,X3,X4)),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_22960]) ).
tcf(c_63030,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2182]) ).
tcf(c_63031,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X1,X3,X4)),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK2(X1,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_22721]) ).
tcf(c_63032,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK5(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2181]) ).
tcf(c_63033,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X1,X3,X4)),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_22587]) ).
tcf(c_63034,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(X2),unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2284]) ).
tcf(c_63035,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X1,X3,X4)),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_21575]) ).
tcf(c_63036,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2109]) ).
tcf(c_63037,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X1,X3,X4)),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_21200]) ).
tcf(c_63038,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2108]) ).
tcf(c_63039,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X2,X3,X4)),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_20765]) ).
tcf(c_63040,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2107]) ).
tcf(c_63041,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X2,X3,X4)),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_20286]) ).
tcf(c_63042,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2106]) ).
tcf(c_63043,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X2,X3,X4)),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK5(X2,singleton(X1),unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(sK2(X2,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_19855]) ).
tcf(c_63044,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK5(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2180]) ).
tcf(c_63045,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X2,X3,X4)),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),singleton(X1),unordered_pair(unordered_pair(X0,sK4(singleton(X1),X2,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_18803]) ).
tcf(c_63046,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,unordered_pair(unordered_pair(X2,sK4(X3,X1,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2105]) ).
tcf(c_63047,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X1,X3,X4)),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,singleton(X2),unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_18127]) ).
tcf(c_63048,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X2,sK4(X1,X3,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2104]) ).
tcf(c_63049,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X1,X3,X4)),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_17483]) ).
tcf(c_63050,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2465]) ).
tcf(c_63051,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X1,X3,X4)),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_16787]) ).
tcf(c_63052,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2464]) ).
tcf(c_63053,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X2,X3,X4)),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_16125]) ).
tcf(c_63054,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2463]) ).
tcf(c_63055,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X2,X3,X4)),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_15658]) ).
tcf(c_63056,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2462]) ).
tcf(c_63057,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X2,X3,X4)),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_15187]) ).
tcf(c_63058,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2461]) ).
tcf(c_63059,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X1,X3,X4)),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_14882]) ).
tcf(c_63060,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)),X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2460]) ).
tcf(c_63061,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X1,X3,X4)),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_13234]) ).
tcf(c_63062,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_1863]) ).
tcf(c_63063,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X1,X3,X4)),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_12125]) ).
tcf(c_63064,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_1862]) ).
tcf(c_63065,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X2,X3,X4)),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_11834]) ).
tcf(c_63066,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_1861]) ).
tcf(c_63067,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X2,X3,X4)),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_11410]) ).
tcf(c_63068,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5))),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_1860]) ).
tcf(c_63069,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X2,X3,X4)),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_10829]) ).
tcf(c_63070,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_1859]) ).
tcf(c_63071,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X1,X3,X4)),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_10535]) ).
tcf(c_63072,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0)),X2),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_1858]) ).
tcf(c_63073,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X1,X3,X4)),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_8720]) ).
tcf(c_63074,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_1575]) ).
tcf(c_63075,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X1,X3,X4)),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_8554]) ).
tcf(c_63076,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_1574]) ).
tcf(c_63077,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X2,X3,X4)),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_8285]) ).
tcf(c_63078,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_1573]) ).
tcf(c_63079,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X2,X3,X4)),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_8027]) ).
tcf(c_63080,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_1572]) ).
tcf(c_63081,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X2,X3,X4)),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_7766]) ).
tcf(c_63082,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_1571]) ).
tcf(c_63083,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X1,X3,X4)),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_7495]) ).
tcf(c_63084,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_1570]) ).
tcf(c_63085,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X1,X3,X4)),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(sK2(X1,X3,X4),X2))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_6164]) ).
tcf(c_63086,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(X0,sK2(X3,X4,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_1156]) ).
tcf(c_63087,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X1,X3,X4)),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(singleton(sK2(X1,X3,X4)),unordered_pair(X2,sK2(X1,X3,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_5987]) ).
tcf(c_63088,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(singleton(X0),unordered_pair(sK2(X3,X4,X5),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_1155]) ).
tcf(c_63089,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X2,X3,X4)),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK2(X2,X3,X4),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_5758]) ).
tcf(c_63090,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(X0,sK2(X3,X4,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_1154]) ).
tcf(c_63091,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X2,X3,X4)),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK2(X2,X3,X4),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_5518]) ).
tcf(c_63092,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(sK2(X3,X4,X5)))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_1153]) ).
tcf(c_63093,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X2,X3,X4)),unordered_pair(sK1(X2,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK2(X2,X3,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_5291]) ).
tcf(c_63094,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X3,X1),unordered_pair(unordered_pair(X2,unordered_pair(singleton(sK2(X3,X4,X5)),unordered_pair(sK2(X3,X4,X5),X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_1152]) ).
tcf(c_63095,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(X1,X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(X1,X3,X4)),unordered_pair(sK1(X1,X3,X4),X5))) = X5 )
| ( sK4(singleton(X0),cartesian_product2(X1,singleton(X2)),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK2(X1,X3,X4),X2),singleton(sK2(X1,X3,X4)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_4798]) ).
tcf(c_63096,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(X3,X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(X3,X4,X5)),unordered_pair(sK1(X3,X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),cartesian_product2(X1,X3),unordered_pair(unordered_pair(X2,unordered_pair(unordered_pair(X0,sK2(X3,X4,X5)),singleton(X0))),singleton(X2))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_1151]) ).
tcf(c_63097,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK5(X2,singleton(X4),unordered_pair(singleton(sK2(X2,X3,X0)),unordered_pair(X4,sK2(X2,X3,X0)))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,X3,X0)),unordered_pair(sK1(X2,X3,X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1699,c_2539]) ).
tcf(c_63099,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK5(X2,singleton(X4),unordered_pair(unordered_pair(X4,sK2(X2,X3,X0)),singleton(sK2(X2,X3,X0)))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,X3,X0)),unordered_pair(sK1(X2,X3,X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1699,c_1929]) ).
tcf(c_63101,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK5(X2,singleton(X4),unordered_pair(singleton(sK2(X2,X3,X0)),unordered_pair(sK2(X2,X3,X0),X4))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,X3,X0)),unordered_pair(sK1(X2,X3,X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1699,c_1643]) ).
tcf(c_63103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X0 )
| ( sK5(X2,singleton(X4),unordered_pair(unordered_pair(sK2(X2,X3,X0),X4),singleton(sK2(X2,X3,X0)))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(X2,X3,X0)),unordered_pair(sK1(X2,X3,X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1699,c_1306]) ).
tcf(c_63105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X2 )
| ( sK5(X1,singleton(X4),unordered_pair(singleton(X0),unordered_pair(sK2(singleton(X4),X5,X2),X0))) = X4 )
| ( sK5(X2,singleton(X3),unordered_pair(singleton(sK1(singleton(X4),X5,X2)),unordered_pair(sK1(singleton(X4),X5,X2),X3))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_907]) ).
tcf(c_63106,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(singleton(X2),X3,X4)),unordered_pair(sK1(singleton(X2),X3,X4),X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK2(singleton(X2),X3,X4)),unordered_pair(X0,sK2(singleton(X2),X3,X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_906]) ).
tcf(c_63107,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X2 )
| ( sK5(X1,singleton(X4),unordered_pair(unordered_pair(sK2(singleton(X4),X5,X2),X0),singleton(X0))) = X4 )
| ( sK5(X2,singleton(X3),unordered_pair(singleton(sK1(singleton(X4),X5,X2)),unordered_pair(sK1(singleton(X4),X5,X2),X3))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_899]) ).
tcf(c_63108,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(singleton(X2),X3,X4)),unordered_pair(sK1(singleton(X2),X3,X4),X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(X0,sK2(singleton(X2),X3,X4)),singleton(sK2(singleton(X2),X3,X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_898]) ).
tcf(c_63109,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X2 )
| ( sK5(X1,singleton(X4),unordered_pair(singleton(X0),unordered_pair(X0,sK2(singleton(X4),X5,X2)))) = X4 )
| ( sK5(X2,singleton(X3),unordered_pair(singleton(sK1(singleton(X4),X5,X2)),unordered_pair(sK1(singleton(X4),X5,X2),X3))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_889]) ).
tcf(c_63110,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(singleton(X2),X3,X4)),unordered_pair(sK1(singleton(X2),X3,X4),X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(singleton(sK2(singleton(X2),X3,X4)),unordered_pair(sK2(singleton(X2),X3,X4),X0))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_888]) ).
tcf(c_63111,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X4),X5) = X2 )
| ( sK5(X1,singleton(X4),unordered_pair(unordered_pair(X0,sK2(singleton(X4),X5,X2)),singleton(X0))) = X4 )
| ( sK5(X2,singleton(X3),unordered_pair(singleton(sK1(singleton(X4),X5,X2)),unordered_pair(sK1(singleton(X4),X5,X2),X3))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_863]) ).
tcf(c_63112,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(singleton(X2),X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(singleton(X2),X3,X4)),unordered_pair(sK1(singleton(X2),X3,X4),X5))) = X5 )
| ( sK4(singleton(X2),X1,unordered_pair(unordered_pair(sK2(singleton(X2),X3,X4),X0),singleton(sK2(singleton(X2),X3,X4)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_837]) ).
tcf(c_63114,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(X3,X2),X4,X5)),unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_16267]) ).
tcf(c_63115,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(X2,X3),X4,X5)),unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_16266]) ).
tcf(c_63116,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(X3,X2),X4,X5)),unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_15723]) ).
tcf(c_63117,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(X2,X3),X4,X5)),unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1),singleton(X1)),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_15722]) ).
tcf(c_63118,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(X3,X2),X4,X5)),unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_15377]) ).
tcf(c_63119,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(X2,X3),X4,X5)),unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_15376]) ).
tcf(c_63120,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(X3,X2),X4,X5)),unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_12049]) ).
tcf(c_63121,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(X2,X3),X4,X5)),unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_12048]) ).
tcf(c_63122,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(X3,X2),X4,X5)),unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_11518]) ).
tcf(c_63123,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(X2,X3),X4,X5)),unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1),singleton(X1)),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_11517]) ).
tcf(c_63124,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(X3,X2),X4,X5)),unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_11093]) ).
tcf(c_63125,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(X2,X3),X4,X5)),unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_11092]) ).
tcf(c_63126,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(X3,X2),X4,X5)),unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_8458]) ).
tcf(c_63127,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(X2,X3),X4,X5)),unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_8457]) ).
tcf(c_63128,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(X3,X2),X4,X5)),unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_8152]) ).
tcf(c_63129,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(X2,X3),X4,X5)),unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1),singleton(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_8151]) ).
tcf(c_63130,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(X3,X2),X4,X5)),unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_7854]) ).
tcf(c_63131,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(X2,X3),X4,X5)),unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_7853]) ).
tcf(c_63132,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(X3,X2),X4,X5)),unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_5825]) ).
tcf(c_63133,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(X2,X3),X4,X5)),unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_5824]) ).
tcf(c_63134,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(X3,X2),X4,X5)),unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5)),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_5642]) ).
tcf(c_63135,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(X2,X3),X4,X5)),unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5)),X1),singleton(X1))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_5641]) ).
tcf(c_63136,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,X2),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(X3,X2),X4,X5)),unordered_pair(sK1(cartesian_product2(X3,X2),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X3,X2,sK2(cartesian_product2(X3,X2),X4,X5))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_5396]) ).
tcf(c_63137,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(X2,X3),X4,X5)),unordered_pair(sK1(cartesian_product2(X2,X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),cartesian_product2(singleton(X1),X2),unordered_pair(unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X5))))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_5395]) ).
tcf(c_63138,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X0),X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(cartesian_product2(X2,X0),X3,X4)),unordered_pair(sK1(cartesian_product2(X2,X0),X3,X4),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))),unordered_pair(X1,sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1699,c_2611]) ).
tcf(c_63139,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X0,X2),X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(cartesian_product2(X0,X2),X3,X4)),unordered_pair(sK1(cartesian_product2(X0,X2),X3,X4),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))),unordered_pair(X1,sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1699,c_2610]) ).
tcf(c_63140,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X0),X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(cartesian_product2(X2,X0),X3,X4)),unordered_pair(sK1(cartesian_product2(X2,X0),X3,X4),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))),singleton(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1699,c_2036]) ).
tcf(c_63141,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X0,X2),X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(cartesian_product2(X0,X2),X3,X4)),unordered_pair(sK1(cartesian_product2(X0,X2),X3,X4),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(X1,sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))),singleton(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1699,c_2035]) ).
tcf(c_63142,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X0),X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(cartesian_product2(X2,X0),X3,X4)),unordered_pair(sK1(cartesian_product2(X2,X0),X3,X4),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))),unordered_pair(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4)),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1699,c_1703]) ).
tcf(c_63143,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X0,X2),X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(cartesian_product2(X0,X2),X3,X4)),unordered_pair(sK1(cartesian_product2(X0,X2),X3,X4),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))),unordered_pair(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4)),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1699,c_1702]) ).
tcf(c_63144,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X0),X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(cartesian_product2(X2,X0),X3,X4)),unordered_pair(sK1(cartesian_product2(X2,X0),X3,X4),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4)),X1),singleton(sK5(X2,X0,sK2(cartesian_product2(X2,X0),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1699,c_1389]) ).
tcf(c_63145,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X0,X2),X3) = X4 )
| ( sK5(X4,singleton(X5),unordered_pair(singleton(sK1(cartesian_product2(X0,X2),X3,X4)),unordered_pair(sK1(cartesian_product2(X0,X2),X3,X4),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(unordered_pair(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4)),X1),singleton(sK4(X0,X2,sK2(cartesian_product2(X0,X2),X3,X4))))) = X1 ) ),
inference(superposition,[status(thm)],[c_1699,c_1388]) ).
tcf(c_63146,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X0 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(sK5(X2,X3,sK2(cartesian_product2(X2,X3),X4,X0)),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(cartesian_product2(X2,X3),X4,X0)),unordered_pair(sK1(cartesian_product2(X2,X3),X4,X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1699,c_2459]) ).
tcf(c_63147,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X0 )
| ( sK4(singleton(X5),X2,unordered_pair(singleton(X5),unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X0)),X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(cartesian_product2(X2,X3),X4,X0)),unordered_pair(sK1(cartesian_product2(X2,X3),X4,X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1699,c_2458]) ).
tcf(c_63148,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X0 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(sK5(X2,X3,sK2(cartesian_product2(X2,X3),X4,X0)),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(cartesian_product2(X2,X3),X4,X0)),unordered_pair(sK1(cartesian_product2(X2,X3),X4,X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1699,c_1857]) ).
tcf(c_63149,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X0 )
| ( sK4(singleton(X5),X2,unordered_pair(unordered_pair(sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X0)),X5),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(cartesian_product2(X2,X3),X4,X0)),unordered_pair(sK1(cartesian_product2(X2,X3),X4,X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1699,c_1856]) ).
tcf(c_63150,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X0 )
| ( sK4(singleton(X5),X3,unordered_pair(singleton(X5),unordered_pair(X5,sK5(X2,X3,sK2(cartesian_product2(X2,X3),X4,X0))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(cartesian_product2(X2,X3),X4,X0)),unordered_pair(sK1(cartesian_product2(X2,X3),X4,X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1699,c_1569]) ).
tcf(c_63151,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X0 )
| ( sK4(singleton(X5),X2,unordered_pair(singleton(X5),unordered_pair(X5,sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X0))))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(cartesian_product2(X2,X3),X4,X0)),unordered_pair(sK1(cartesian_product2(X2,X3),X4,X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1699,c_1568]) ).
tcf(c_63152,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X0 )
| ( sK4(singleton(X5),X3,unordered_pair(unordered_pair(X5,sK5(X2,X3,sK2(cartesian_product2(X2,X3),X4,X0))),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(cartesian_product2(X2,X3),X4,X0)),unordered_pair(sK1(cartesian_product2(X2,X3),X4,X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1699,c_1150]) ).
tcf(c_63153,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,X3),X4) = X0 )
| ( sK4(singleton(X5),X2,unordered_pair(unordered_pair(X5,sK4(X2,X3,sK2(cartesian_product2(X2,X3),X4,X0))),singleton(X5))) = X5 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(cartesian_product2(X2,X3),X4,X0)),unordered_pair(sK1(cartesian_product2(X2,X3),X4,X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1699,c_1149]) ).
tcf(c_63154,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(X0,X1),X2) = X3 )
| ( sK5(X3,singleton(X4),unordered_pair(singleton(sK1(cartesian_product2(X0,X1),X2,X3)),unordered_pair(sK1(cartesian_product2(X0,X1),X2,X3),X4))) = X4 )
| ( unordered_pair(unordered_pair(sK4(X0,X1,sK2(cartesian_product2(X0,X1),X2,X3)),sK5(X0,X1,sK2(cartesian_product2(X0,X1),X2,X3))),singleton(sK4(X0,X1,sK2(cartesian_product2(X0,X1),X2,X3)))) = sK2(cartesian_product2(X0,X1),X2,X3) ) ),
inference(superposition,[status(thm)],[c_1699,c_62]) ).
tcf(c_63155,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(singleton(X2),X3),X4,X5)),unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(X0,sK2(cartesian_product2(singleton(X2),X3),X4,X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_3017]) ).
tcf(c_63156,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(singleton(X2),X3),X4,X5)),unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(singleton(X0),unordered_pair(sK2(cartesian_product2(singleton(X2),X3),X4,X5),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_3015]) ).
tcf(c_63157,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(singleton(X2),X3),X4,X5)),unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(sK2(cartesian_product2(singleton(X2),X3),X4,X5),X0),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_3014]) ).
tcf(c_63158,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(singleton(X2),X3),X4,X5)),unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK2(cartesian_product2(singleton(X2),X3),X4,X5)),unordered_pair(sK2(cartesian_product2(singleton(X2),X3),X4,X5),X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2961]) ).
tcf(c_63159,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(singleton(X2),X3),X4,X5)),unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(singleton(sK2(cartesian_product2(singleton(X2),X3),X4,X5)),unordered_pair(X0,sK2(cartesian_product2(singleton(X2),X3),X4,X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2959]) ).
tcf(c_63160,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(singleton(X2),X3),X4,X5)),unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(X0,sK2(cartesian_product2(singleton(X2),X3),X4,X5)),singleton(sK2(cartesian_product2(singleton(X2),X3),X4,X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2958]) ).
tcf(c_63161,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(singleton(X2),X3),X4,X5)),unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK5(X1,cartesian_product2(singleton(X2),X3),unordered_pair(unordered_pair(X0,sK2(cartesian_product2(singleton(X2),X3),X4,X5)),singleton(X0)))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_3012]) ).
tcf(c_63162,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(singleton(X2),X3),X4,X5)),unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X1,unordered_pair(unordered_pair(sK2(cartesian_product2(singleton(X2),X3),X4,X5),X0),singleton(sK2(cartesian_product2(singleton(X2),X3),X4,X5))))) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2956]) ).
tcf(c_63163,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X4),X5),X6) = X2 )
| ( sK5(X1,singleton(X4),unordered_pair(singleton(X0),unordered_pair(sK4(singleton(X4),X5,sK2(cartesian_product2(singleton(X4),X5),X6,X2)),X0))) = X4 )
| ( sK5(X2,singleton(X3),unordered_pair(singleton(sK1(cartesian_product2(singleton(X4),X5),X6,X2)),unordered_pair(sK1(cartesian_product2(singleton(X4),X5),X6,X2),X3))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2545]) ).
tcf(c_63164,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X4),X5),X6) = X2 )
| ( sK5(X1,singleton(X4),unordered_pair(unordered_pair(sK4(singleton(X4),X5,sK2(cartesian_product2(singleton(X4),X5),X6,X2)),X0),singleton(X0))) = X4 )
| ( sK5(X2,singleton(X3),unordered_pair(singleton(sK1(cartesian_product2(singleton(X4),X5),X6,X2)),unordered_pair(sK1(cartesian_product2(singleton(X4),X5),X6,X2),X3))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_1935]) ).
tcf(c_63165,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X4),X5),X6) = X2 )
| ( sK5(X1,singleton(X4),unordered_pair(singleton(X0),unordered_pair(X0,sK4(singleton(X4),X5,sK2(cartesian_product2(singleton(X4),X5),X6,X2))))) = X4 )
| ( sK5(X2,singleton(X3),unordered_pair(singleton(sK1(cartesian_product2(singleton(X4),X5),X6,X2)),unordered_pair(sK1(cartesian_product2(singleton(X4),X5),X6,X2),X3))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_1649]) ).
tcf(c_63166,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X4),X5),X6) = X2 )
| ( sK5(X1,singleton(X4),unordered_pair(unordered_pair(X0,sK4(singleton(X4),X5,sK2(cartesian_product2(singleton(X4),X5),X6,X2))),singleton(X0))) = X4 )
| ( sK5(X2,singleton(X3),unordered_pair(singleton(sK1(cartesian_product2(singleton(X4),X5),X6,X2)),unordered_pair(sK1(cartesian_product2(singleton(X4),X5),X6,X2),X3))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_1312]) ).
tcf(c_63167,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(singleton(X2),X3),X4) = X0 )
| ( sK4(singleton(X2),X3,sK2(cartesian_product2(singleton(X2),X3),X4,X0)) = X2 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(cartesian_product2(singleton(X2),X3),X4,X0)),unordered_pair(sK1(cartesian_product2(singleton(X2),X3),X4,X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1699,c_787]) ).
tcf(c_63168,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X4,singleton(X5)),X6) = X2 )
| ( sK5(X4,singleton(X5),sK5(X1,cartesian_product2(X4,singleton(X5)),unordered_pair(singleton(X0),unordered_pair(X0,sK2(cartesian_product2(X4,singleton(X5)),X6,X2))))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(singleton(sK1(cartesian_product2(X4,singleton(X5)),X6,X2)),unordered_pair(sK1(cartesian_product2(X4,singleton(X5)),X6,X2),X3))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_3142]) ).
tcf(c_63169,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X4,singleton(X5)),X6) = X2 )
| ( sK5(X4,singleton(X5),sK5(X1,cartesian_product2(X4,singleton(X5)),unordered_pair(singleton(X0),unordered_pair(sK2(cartesian_product2(X4,singleton(X5)),X6,X2),X0)))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(singleton(sK1(cartesian_product2(X4,singleton(X5)),X6,X2)),unordered_pair(sK1(cartesian_product2(X4,singleton(X5)),X6,X2),X3))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_3140]) ).
tcf(c_63170,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X4,singleton(X5)),X6) = X2 )
| ( sK5(X4,singleton(X5),sK5(X1,cartesian_product2(X4,singleton(X5)),unordered_pair(unordered_pair(sK2(cartesian_product2(X4,singleton(X5)),X6,X2),X0),singleton(X0)))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(singleton(sK1(cartesian_product2(X4,singleton(X5)),X6,X2)),unordered_pair(sK1(cartesian_product2(X4,singleton(X5)),X6,X2),X3))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_3139]) ).
tcf(c_63171,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(X2,singleton(X3)),X4,X5)),unordered_pair(sK1(cartesian_product2(X2,singleton(X3)),X4,X5),X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK2(cartesian_product2(X2,singleton(X3)),X4,X5)),unordered_pair(sK2(cartesian_product2(X2,singleton(X3)),X4,X5),X0)))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_3063]) ).
tcf(c_63172,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(X2,singleton(X3)),X4,X5)),unordered_pair(sK1(cartesian_product2(X2,singleton(X3)),X4,X5),X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(singleton(sK2(cartesian_product2(X2,singleton(X3)),X4,X5)),unordered_pair(X0,sK2(cartesian_product2(X2,singleton(X3)),X4,X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_3061]) ).
tcf(c_63173,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(X2,singleton(X3)),X4,X5)),unordered_pair(sK1(cartesian_product2(X2,singleton(X3)),X4,X5),X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(X0,sK2(cartesian_product2(X2,singleton(X3)),X4,X5)),singleton(sK2(cartesian_product2(X2,singleton(X3)),X4,X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_3060]) ).
tcf(c_63174,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X4,singleton(X5)),X6) = X2 )
| ( sK5(X4,singleton(X5),sK5(X1,cartesian_product2(X4,singleton(X5)),unordered_pair(unordered_pair(X0,sK2(cartesian_product2(X4,singleton(X5)),X6,X2)),singleton(X0)))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(singleton(sK1(cartesian_product2(X4,singleton(X5)),X6,X2)),unordered_pair(sK1(cartesian_product2(X4,singleton(X5)),X6,X2),X3))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_3137]) ).
tcf(c_63175,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(X2,singleton(X3)),X4,X5)),unordered_pair(sK1(cartesian_product2(X2,singleton(X3)),X4,X5),X6))) = X6 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X1,unordered_pair(unordered_pair(sK2(cartesian_product2(X2,singleton(X3)),X4,X5),X0),singleton(sK2(cartesian_product2(X2,singleton(X3)),X4,X5))))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_3058]) ).
tcf(c_63176,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X4,singleton(X5)),X6) = X2 )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(sK5(X4,singleton(X5),sK2(cartesian_product2(X4,singleton(X5)),X6,X2)),X0))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(singleton(sK1(cartesian_product2(X4,singleton(X5)),X6,X2)),unordered_pair(sK1(cartesian_product2(X4,singleton(X5)),X6,X2),X3))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_2546]) ).
tcf(c_63177,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X4,singleton(X5)),X6) = X2 )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(sK5(X4,singleton(X5),sK2(cartesian_product2(X4,singleton(X5)),X6,X2)),X0),singleton(X0))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(singleton(sK1(cartesian_product2(X4,singleton(X5)),X6,X2)),unordered_pair(sK1(cartesian_product2(X4,singleton(X5)),X6,X2),X3))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_1936]) ).
tcf(c_63178,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X4,singleton(X5)),X6) = X2 )
| ( sK5(X1,singleton(X5),unordered_pair(singleton(X0),unordered_pair(X0,sK5(X4,singleton(X5),sK2(cartesian_product2(X4,singleton(X5)),X6,X2))))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(singleton(sK1(cartesian_product2(X4,singleton(X5)),X6,X2)),unordered_pair(sK1(cartesian_product2(X4,singleton(X5)),X6,X2),X3))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_1650]) ).
tcf(c_63179,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X4,singleton(X5)),X6) = X2 )
| ( sK5(X1,singleton(X5),unordered_pair(unordered_pair(X0,sK5(X4,singleton(X5),sK2(cartesian_product2(X4,singleton(X5)),X6,X2))),singleton(X0))) = X5 )
| ( sK5(X2,singleton(X3),unordered_pair(singleton(sK1(cartesian_product2(X4,singleton(X5)),X6,X2)),unordered_pair(sK1(cartesian_product2(X4,singleton(X5)),X6,X2),X3))) = X3 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1699,c_1313]) ).
tcf(c_63180,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(cartesian_product2(X2,singleton(X3)),X4) = X0 )
| ( sK5(X2,singleton(X3),sK2(cartesian_product2(X2,singleton(X3)),X4,X0)) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(cartesian_product2(X2,singleton(X3)),X4,X0)),unordered_pair(sK1(cartesian_product2(X2,singleton(X3)),X4,X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1699,c_789]) ).
tcf(c_63181,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(singleton(X2),X3),X4),X5) = X0 )
| ( sK4(singleton(X2),X3,sK4(cartesian_product2(singleton(X2),X3),X4,sK2(cartesian_product2(cartesian_product2(singleton(X2),X3),X4),X5,X0))) = X2 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(cartesian_product2(cartesian_product2(singleton(X2),X3),X4),X5,X0)),unordered_pair(sK1(cartesian_product2(cartesian_product2(singleton(X2),X3),X4),X5,X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1699,c_835]) ).
tcf(c_63182,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,cartesian_product2(singleton(X3),X4)),X5) = X0 )
| ( sK4(singleton(X3),X4,sK5(X2,cartesian_product2(singleton(X3),X4),sK2(cartesian_product2(X2,cartesian_product2(singleton(X3),X4)),X5,X0))) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(cartesian_product2(X2,cartesian_product2(singleton(X3),X4)),X5,X0)),unordered_pair(sK1(cartesian_product2(X2,cartesian_product2(singleton(X3),X4)),X5,X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1699,c_836]) ).
tcf(c_63183,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X2,singleton(X3)),X4),X5) = X0 )
| ( sK5(X2,singleton(X3),sK4(cartesian_product2(X2,singleton(X3)),X4,sK2(cartesian_product2(cartesian_product2(X2,singleton(X3)),X4),X5,X0))) = X3 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(cartesian_product2(cartesian_product2(X2,singleton(X3)),X4),X5,X0)),unordered_pair(sK1(cartesian_product2(cartesian_product2(X2,singleton(X3)),X4),X5,X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1699,c_861]) ).
tcf(c_63184,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cartesian_product2(cartesian_product2(X2,cartesian_product2(X3,singleton(X4))),X5) = X0 )
| ( sK5(X3,singleton(X4),sK5(X2,cartesian_product2(X3,singleton(X4)),sK2(cartesian_product2(X2,cartesian_product2(X3,singleton(X4))),X5,X0))) = X4 )
| ( sK5(X0,singleton(X1),unordered_pair(singleton(sK1(cartesian_product2(X2,cartesian_product2(X3,singleton(X4))),X5,X0)),unordered_pair(sK1(cartesian_product2(X2,cartesian_product2(X3,singleton(X4))),X5,X0),X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_1699,c_862]) ).
tcf(c_63185,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X2,X1),X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5)),unordered_pair(sK1(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK2(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_2896]) ).
tcf(c_63186,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5)),unordered_pair(sK1(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK2(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_2820]) ).
tcf(c_63187,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X2,X1),X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5)),unordered_pair(sK1(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK2(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_2729]) ).
tcf(c_63188,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5)),unordered_pair(sK1(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK2(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_2672]) ).
tcf(c_63189,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X2,X1),X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5)),unordered_pair(sK1(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK2(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_2340]) ).
tcf(c_63190,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5)),unordered_pair(sK1(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK2(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_2282]) ).
tcf(c_63191,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X2,X1),X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5)),unordered_pair(sK1(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK4(cartesian_product2(X2,X1),X3,sK2(cartesian_product2(cartesian_product2(X2,X1),X3),X4,X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_2178]) ).
tcf(c_63192,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X3),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5)),unordered_pair(sK1(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK4(cartesian_product2(X1,X2),X3,sK2(cartesian_product2(cartesian_product2(X1,X2),X3),X4,X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_2102]) ).
tcf(c_63193,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5)),unordered_pair(sK1(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_2897]) ).
tcf(c_63194,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5)),unordered_pair(sK1(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5))),X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_2821]) ).
tcf(c_63195,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5)),unordered_pair(sK1(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_2730]) ).
tcf(c_63196,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5)),unordered_pair(sK1(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5))),X0),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_2673]) ).
tcf(c_63197,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5)),unordered_pair(sK1(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_2341]) ).
tcf(c_63198,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5)),unordered_pair(sK1(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_2283]) ).
tcf(c_63199,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5)),unordered_pair(sK1(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK5(X2,X1,sK5(X3,cartesian_product2(X2,X1),sK2(cartesian_product2(X3,cartesian_product2(X2,X1)),X4,X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_2179]) ).
tcf(c_63200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( cartesian_product2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4) = X5 )
| ( sK5(X5,singleton(X6),unordered_pair(singleton(sK1(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5)),unordered_pair(sK1(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5),X6))) = X6 )
| ( sK4(singleton(X0),X1,unordered_pair(unordered_pair(X0,sK4(X1,X2,sK5(X3,cartesian_product2(X1,X2),sK2(cartesian_product2(X3,cartesian_product2(X1,X2)),X4,X5)))),singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_1699,c_2103]) ).
tcf(c_65504,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_63200,c_63199,c_63198,c_63197,c_63196,c_63195,c_63194,c_63193,c_63192,c_63191,c_63190,c_63189,c_63188,c_63187,c_63186,c_63185,c_63184,c_63183,c_63182,c_63181,c_63180,c_63179,c_63178,c_63177,c_63176,c_63175,c_63174,c_63173,c_63172,c_63171,c_63170,c_63169,c_63168,c_63167,c_63166,c_63165,c_63164,c_63163,c_63162,c_63161,c_63160,c_63159,c_63158,c_63157,c_63156,c_63155,c_63154,c_63153,c_63152,c_63151,c_63150,c_63149,c_63148,c_63147,c_63146,c_63145,c_63144,c_63143,c_63142,c_63141,c_63140,c_63139,c_63138,c_63137,c_63136,c_63135,c_63134,c_63133,c_63132,c_63131,c_63130,c_63129,c_63128,c_63127,c_63126,c_63125,c_63124,c_63123,c_63122,c_63121,c_63120,c_63119,c_63118,c_63117,c_63116,c_63115,c_63114,c_63112,c_63111,c_63110,c_63109,c_63108,c_63107,c_63106,c_63105,c_63103,c_63101,c_63099,c_63097,c_63096,c_63095,c_63094,c_63093,c_63092,c_63091,c_63090,c_63089,c_63088,c_63087,c_63086,c_63085,c_63084,c_63083,c_63082,c_63081,c_63080,c_63079,c_63078,c_63077,c_63076,c_63075,c_63074,c_63073,c_63072,c_63071,c_63070,c_63069,c_63068,c_63067,c_63066,c_63065,c_63064,c_63063,c_63062,c_63061,c_63060,c_63059,c_63058,c_63057,c_63056,c_63055,c_63054,c_63053,c_63052,c_63051,c_63050,c_63049,c_63048,c_63047,c_63046,c_63045,c_63044,c_63043,c_63042,c_63041,c_63040,c_63039,c_63038,c_63037,c_63036,c_63035,c_63034,c_63033,c_63032,c_63031,c_63030,c_63029,c_63028,c_63027,c_63026,c_63025,c_63024,c_63023,c_63022,c_63021,c_63020,c_63019,c_63018,c_63017,c_63016,c_63015,c_63014,c_63013,c_63012,c_63011,c_63010,c_63009,c_63008,c_63007,c_63006,c_63005,c_63004,c_63003,c_63002,c_63001,c_63000,c_62999,c_62998,c_62997,c_62996,c_62995,c_62994,c_62993,c_62992,c_62991,c_62990,c_62989,c_62988,c_62987,c_62986,c_62985,c_62984,c_62983,c_62982,c_62981,c_62980,c_62979,c_62978,c_62977,c_62976,c_62975,c_62974,c_62973,c_62972,c_62971,c_62970,c_62969,c_62968,c_62967,c_62966,c_62965,c_62964,c_62963,c_62962,c_62961,c_62960,c_62959,c_62958,c_62957,c_62956,c_62955,c_62954,c_62953,c_62952,c_61437,c_61436,c_61435,c_61434,c_61433,c_61432,c_61431,c_61430,c_61429,c_61428,c_61427,c_61426,c_61425,c_61424,c_61423,c_61422,c_61421,c_61420,c_61419,c_61418,c_61417,c_61416,c_61415,c_61414,c_61413,c_61412,c_61411,c_61410,c_61409,c_61408,c_61407,c_61406,c_61405,c_61404,c_61403,c_61402,c_61401,c_61400,c_61399,c_61398,c_61397,c_61396,c_61395,c_61394,c_61393,c_61392,c_61391,c_61390,c_61389,c_61388,c_61387,c_61386,c_61385,c_61384,c_61383,c_61382,c_61381,c_61380,c_61379,c_61378,c_61377,c_61376,c_61375,c_61374,c_61373,c_61372,c_61371,c_61370,c_61369,c_61368,c_61367,c_61366,c_61365,c_61364,c_61363,c_61362,c_61361,c_61360,c_61359,c_61358,c_61357,c_61356,c_61355,c_61354,c_61353,c_61352,c_61351,c_61349,c_61348,c_61347,c_61346,c_61345,c_61344,c_61343,c_61342,c_61340,c_61338,c_61336,c_61334,c_61333,c_61332,c_61331,c_61330,c_61329,c_61328,c_61327,c_61326,c_61325,c_61324,c_61323,c_61322,c_61321,c_61320,c_61319,c_61318,c_61317,c_61316,c_61315,c_61314,c_61313,c_61312,c_61311,c_61310,c_61309,c_61308,c_61307,c_61306,c_61305,c_61304,c_61303,c_61302,c_61301,c_61300,c_61299,c_61298,c_61297,c_61296,c_61295,c_61294,c_61293,c_61292,c_61291,c_61290,c_61289,c_61288,c_61287,c_61286,c_61285,c_61284,c_61283,c_61282,c_61281,c_61280,c_61279,c_61278,c_61277,c_61276,c_61275,c_61274,c_61273,c_61272,c_61271,c_61270,c_61269,c_61268,c_61267,c_61266,c_61265,c_61264,c_61263,c_61262,c_61261,c_61260,c_61259,c_61258,c_61257,c_61256,c_61255,c_61254,c_61253,c_61252,c_61251,c_61250,c_61249,c_61248,c_61247,c_61246,c_61245,c_61244,c_61243,c_61242,c_61241,c_61240,c_61239,c_61238,c_61237,c_61236,c_61235,c_61234,c_61233,c_61232,c_61231,c_61230,c_61229,c_61228,c_61227,c_61226,c_61225,c_61224,c_61223,c_61222,c_61221,c_61220,c_61219,c_61218,c_61217,c_61216,c_61215,c_61214,c_61213,c_61212,c_61211,c_61210,c_61209,c_61208,c_61207,c_61206,c_61205,c_61204,c_61203,c_61202,c_61201,c_61200,c_61199,c_61198,c_61197,c_61196,c_61195,c_61194,c_61193,c_61192,c_61191,c_61190,c_61189,c_59169,c_59168,c_59167,c_59166,c_59165,c_59164,c_59163,c_59162,c_59161,c_59160,c_59159,c_59158,c_59157,c_59156,c_59155,c_59154,c_59153,c_59152,c_59151,c_59150,c_59149,c_59148,c_59147,c_59146,c_59145,c_59144,c_59143,c_59142,c_59141,c_59140,c_59139,c_59138,c_59137,c_59136,c_59135,c_59134,c_59133,c_59132,c_59131,c_59130,c_59129,c_59128,c_59127,c_59126,c_59125,c_59124,c_59123,c_59122,c_59121,c_59120,c_59119,c_59118,c_59117,c_59116,c_59115,c_59114,c_59113,c_59112,c_59111,c_59110,c_59109,c_59108,c_59107,c_59106,c_59105,c_59104,c_59103,c_59102,c_59101,c_59100,c_59099,c_59098,c_59097,c_59096,c_59095,c_59094,c_59093,c_59092,c_59091,c_59090,c_59089,c_59088,c_59087,c_59086,c_59085,c_59084,c_59083,c_59081,c_59080,c_59079,c_59078,c_59077,c_59076,c_59075,c_59074,c_59072,c_59070,c_59068,c_59066,c_59065,c_59064,c_59063,c_59062,c_59061,c_59060,c_59059,c_59058,c_59057,c_59056,c_59055,c_59054,c_59053,c_59052,c_59051,c_59050,c_59049,c_59048,c_59047,c_59046,c_59045,c_59044,c_59043,c_59042,c_59041,c_59040,c_59039,c_59038,c_59037,c_59036,c_59035,c_59034,c_59033,c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).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET894+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.42 % Computer : n011.cluster.edu
% 0.09/0.42 % Model : x86_64 x86_64
% 0.09/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.42 % Memory : 8046.5625MB
% 0.09/0.42 % OS : Linux 6.8.0-71-generic
% 0.09/0.42 % CPULimit : 300
% 0.09/0.42 % WCLimit : 300
% 0.09/0.42 % DateTime : Thu Sep 24 12:20:43 UTC 2026
% 0.09/0.42 % CPUTime :
% 0.09/0.42 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.46 Running first-order theorem proving
% 0.09/0.46 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.47
% 0.09/0.47 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.47
% 0.09/0.47 % Detected problem language: tptp
% 0.09/0.48 % Proving...
% 189.39/27.09 % SZS status Started for theBenchmark.p
% 189.39/27.09 % SZS status Theorem for theBenchmark.p
% 189.39/27.09
% 189.39/27.09 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 189.39/27.09
% 189.39/27.09 % ------ iProver source info
% 189.39/27.09
% 189.39/27.09 % git: date: 2026-07-19 20:42:38 +0200
% 189.39/27.09 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 189.39/27.09 % git: non_committed_changes: false
% 189.39/27.09
% 189.39/27.09 % ------ Parsing...
% 189.39/27.09 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 189.39/27.09
% 189.39/27.09 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 189.39/27.09
% 189.39/27.09 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 189.39/27.09
% 189.39/27.09 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 189.39/27.09 % ------ Proving...
% 189.39/27.09 % ------ Problem Properties
% 189.39/27.09
% 189.39/27.09 %
% 189.39/27.09 % clauses 22
% 189.39/27.09 % conjectures 1
% 189.39/27.09 % EPR 3
% 189.39/27.09 % Horn 17
% 189.39/27.09 % unary 6
% 189.39/27.09 % binary 7
% 189.39/27.09 % lits 49
% 189.39/27.09 % lits eq 16
% 189.39/27.09 % fd_pure 0
% 189.39/27.09 % fd_pseudo 0
% 189.39/27.09 % fd_cond 0
% 189.39/27.09 % fd_pseudo_cond 8
% 189.39/27.09 % AC symbols 0
% 189.39/27.09
% 189.39/27.09 % ------ Input Options Time Limit: Unbounded
% 189.39/27.09
% 189.39/27.09
% 189.39/27.09 % ------
% 189.39/27.09 % Current options:
% 189.39/27.09 % ------
% 189.39/27.09
% 189.39/27.09
% 189.39/27.09 %
% 189.39/27.09
% 189.39/27.09 % ------ Proving...
% 189.39/27.09 %
% 189.39/27.09
% 189.39/27.09 % ------ Proving...
% 189.39/27.09 %
% 189.39/27.09
% 189.39/27.09 % ------ Proving...
% 189.39/27.09 %
% 189.39/27.09
% 189.39/27.09 % SZS status Theorem for theBenchmark.p
% 189.39/27.09
% 189.39/27.09 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 198.70/27.39
% 198.70/27.39
%------------------------------------------------------------------------------