%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU278+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n015.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 02:56:27 PM UTC 2026
% Result : Theorem 20.38s 4.80s
% Output : CNFRefutation 15.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 6
% Syntax : Number of formulae : 170 ( 18 unt; 0 def)
% Number of atoms : 750 ( 61 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 1025 ( 445 ~; 493 |; 72 &)
% ( 8 <=>; 5 =>; 0 <=; 2 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 3 con; 0-3 aty)
% Number of variables : 382 ( 0 sgn 334 !; 48 ?; 188 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2)
& relation(X1) )
=> ? [X3] :
( ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ( in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1)
& in(X5,X0)
& in(X4,X0) ) )
& relation(X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_relat_1__e6_21__wellord2) ).
fof(f2,negated_conjecture,
~ ! [X0,X1,X2] :
( ( function(X2)
& relation(X2)
& relation(X1) )
=> ? [X3] :
( ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ( in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1)
& in(X5,X0)
& in(X4,X0) ) )
& relation(X3) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f15,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f20,axiom,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2)
& relation(X1) )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( ? [X5,X6] :
( in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
& X4 = ordered_pair(X5,X6) )
& in(X4,cartesian_product2(X0,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e6_21__wellord2__1) ).
fof(f22,axiom,
! [X0] :
( relation(X0)
<=> ! [X1] :
~ ( ! [X2,X3] : X1 != ordered_pair(X2,X3)
& in(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_1) ).
fof(f35,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',t106_zfmisc_1) ).
fof(f38,axiom,
! [X0,X1,X2,X3] :
( ordered_pair(X0,X1) = ordered_pair(X2,X3)
=> ( X1 = X3
& X0 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_zfmisc_1) ).
fof(f42,plain,
? [X0,X1,X2] :
( function(X2)
& relation(X2)
& relation(X1)
& ! [X3] :
( ? [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<~> ( in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1)
& in(X5,X0)
& in(X4,X0) ) )
| ~ relation(X3) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f43,plain,
? [X0,X1,X2] :
( function(X2)
& relation(X2)
& relation(X1)
& ! [X3] :
( ? [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<~> ( in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1)
& in(X5,X0)
& in(X4,X0) ) )
| ~ relation(X3) ) ),
inference(flattening,[],[f42]) ).
fof(f44,plain,
! [X0,X1,X2,X3] :
( ordered_pair(X0,X1) != ordered_pair(X2,X3)
| ( X1 = X3
& X0 = X2 ) ),
inference(ennf_transformation,[],[f38]) ).
fof(f45,plain,
! [X0] :
( relation(X0)
<=> ! [X1] :
( ? [X2,X3] : ordered_pair(X2,X3) = X1
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f22]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( ? [X5,X6] :
( in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
& X4 = ordered_pair(X5,X6) )
& in(X4,cartesian_product2(X0,X0)) ) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( ? [X5,X6] :
( in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
& X4 = ordered_pair(X5,X6) )
& in(X4,cartesian_product2(X0,X0)) ) ) ),
inference(flattening,[],[f46]) ).
fof(f50,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f54,plain,
? [X0,X1,X2] :
( function(X2)
& relation(X2)
& relation(X1)
& ! [X3] :
( ? [X4,X5] :
( ( in(ordered_pair(X4,X5),X3)
| ( in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1)
& in(X5,X0)
& in(X4,X0) ) )
& ( ~ in(ordered_pair(X4,X5),X3)
| ~ in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1)
| ~ in(X5,X0)
| ~ in(X4,X0) ) )
| ~ relation(X3) ) ),
inference(nnf_transformation,[],[f43]) ).
fof(f55,plain,
? [X0,X1,X2] :
( function(X2)
& relation(X2)
& relation(X1)
& ! [X3] :
( ? [X4,X5] :
( ( in(ordered_pair(X4,X5),X3)
| ( in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1)
& in(X5,X0)
& in(X4,X0) ) )
& ( ~ in(ordered_pair(X4,X5),X3)
| ~ in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1)
| ~ in(X5,X0)
| ~ in(X4,X0) ) )
| ~ relation(X3) ) ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
( function(sK2)
& relation(sK2)
& relation(sK1)
& ! [X3] :
( ( ( in(ordered_pair(sK3(X3),sK4(X3)),X3)
| ( in(ordered_pair(apply(sK2,sK3(X3)),apply(sK2,sK4(X3))),sK1)
& in(sK4(X3),sK0)
& in(sK3(X3),sK0) ) )
& ( ~ in(ordered_pair(sK3(X3),sK4(X3)),X3)
| ~ in(ordered_pair(apply(sK2,sK3(X3)),apply(sK2,sK4(X3))),sK1)
| ~ in(sK4(X3),sK0)
| ~ in(sK3(X3),sK0) ) )
| ~ relation(X3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X4,sK3(X3)),skolemize(X5,sK4(X3))],[f55]) ).
fof(f57,plain,
! [X0] :
( ( ~ relation(X0)
| ! [X1] :
( ? [X2,X3] : ordered_pair(X2,X3) = X1
| ~ in(X1,X0) ) )
& ( ? [X1] :
( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) )
| relation(X0) ) ),
inference(nnf_transformation,[],[f45]) ).
fof(f58,plain,
! [X0] :
( ( ~ relation(X0)
| ! [X4] :
( ? [X5,X6] : ordered_pair(X5,X6) = X4
| ~ in(X4,X0) ) )
& ( ? [X1] :
( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) )
| relation(X0) ) ),
inference(rectify,[],[f57]) ).
fof(f59,plain,
! [X0] :
( ( ~ relation(X0)
| ! [X4] :
( ordered_pair(sK6(X4),sK7(X4)) = X4
| ~ in(X4,X0) ) )
& ( ( ! [X2,X3] : ordered_pair(X2,X3) != sK5(X0)
& in(sK5(X0),X0) )
| relation(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X1,sK5(X0)),skolemize(X5,sK6(X4)),skolemize(X6,sK7(X4))],[f58]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ? [X3] :
! [X4] :
( ( ~ in(X4,X3)
| ( ? [X5,X6] :
( in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
& X4 = ordered_pair(X5,X6) )
& in(X4,cartesian_product2(X0,X0)) ) )
& ( ! [X5,X6] :
( ~ in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(X0,X0))
| in(X4,X3) ) ) ),
inference(nnf_transformation,[],[f47]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ? [X3] :
! [X4] :
( ( ~ in(X4,X3)
| ( ? [X5,X6] :
( in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
& X4 = ordered_pair(X5,X6) )
& in(X4,cartesian_product2(X0,X0)) ) )
& ( ! [X5,X6] :
( ~ in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(X0,X0))
| in(X4,X3) ) ) ),
inference(flattening,[],[f63]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ? [X3] :
! [X4] :
( ( ~ in(X4,X3)
| ( ? [X7,X8] :
( in(ordered_pair(apply(X2,X7),apply(X2,X8)),X1)
& ordered_pair(X7,X8) = X4 )
& in(X4,cartesian_product2(X0,X0)) ) )
& ( ! [X5,X6] :
( ~ in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(X0,X0))
| in(X4,X3) ) ) ),
inference(rectify,[],[f64]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ! [X4] :
( ( ~ in(X4,sK11(X0,X1,X2))
| ( in(ordered_pair(apply(X2,sK12(X1,X2,X4)),apply(X2,sK13(X1,X2,X4))),X1)
& ordered_pair(sK12(X1,X2,X4),sK13(X1,X2,X4)) = X4
& in(X4,cartesian_product2(X0,X0)) ) )
& ( ! [X5,X6] :
( ~ in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(X0,X0))
| in(X4,sK11(X0,X1,X2)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13]),skolemize(X3,sK11(X0,X1,X2)),skolemize(X7,sK12(X1,X2,X4)),skolemize(X8,sK13(X1,X2,X4))],[f65]) ).
fof(f69,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,[],[f35]) ).
fof(f70,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,[],[f69]) ).
fof(f71,plain,
function(sK2),
inference(cnf_transformation,[],[f56]) ).
fof(f72,plain,
relation(sK2),
inference(cnf_transformation,[],[f56]) ).
fof(f73,plain,
relation(sK1),
inference(cnf_transformation,[],[f56]) ).
fof(f74,plain,
! [X3] :
( in(ordered_pair(sK3(X3),sK4(X3)),X3)
| in(ordered_pair(apply(sK2,sK3(X3)),apply(sK2,sK4(X3))),sK1)
| ~ relation(X3) ),
inference(cnf_transformation,[],[f56]) ).
fof(f75,plain,
! [X3] :
( in(ordered_pair(sK3(X3),sK4(X3)),X3)
| in(sK4(X3),sK0)
| ~ relation(X3) ),
inference(cnf_transformation,[],[f56]) ).
fof(f76,plain,
! [X3] :
( in(ordered_pair(sK3(X3),sK4(X3)),X3)
| in(sK3(X3),sK0)
| ~ relation(X3) ),
inference(cnf_transformation,[],[f56]) ).
fof(f77,plain,
! [X3] :
( ~ in(ordered_pair(sK3(X3),sK4(X3)),X3)
| ~ in(ordered_pair(apply(sK2,sK3(X3)),apply(sK2,sK4(X3))),sK1)
| ~ in(sK4(X3),sK0)
| ~ in(sK3(X3),sK0)
| ~ relation(X3) ),
inference(cnf_transformation,[],[f56]) ).
fof(f78,plain,
! [X2,X3,X0,X1] :
( ordered_pair(X0,X1) != ordered_pair(X2,X3)
| X1 = X3 ),
inference(cnf_transformation,[],[f44]) ).
fof(f79,plain,
! [X2,X3,X0,X1] :
( ordered_pair(X0,X1) != ordered_pair(X2,X3)
| X0 = X2 ),
inference(cnf_transformation,[],[f44]) ).
fof(f81,plain,
! [X2,X3,X0] :
( ordered_pair(X2,X3) != sK5(X0)
| relation(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f82,plain,
! [X0] :
( in(sK5(X0),X0)
| relation(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f91,plain,
! [X2,X0,X1,X4] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X4,sK11(X0,X1,X2))
| in(ordered_pair(apply(X2,sK12(X1,X2,X4)),apply(X2,sK13(X1,X2,X4))),X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f92,plain,
! [X2,X0,X1,X4] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X4,sK11(X0,X1,X2))
| ordered_pair(sK12(X1,X2,X4),sK13(X1,X2,X4)) = X4 ),
inference(cnf_transformation,[],[f66]) ).
fof(f93,plain,
! [X2,X0,X1,X4] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X4,sK11(X0,X1,X2))
| in(X4,cartesian_product2(X0,X0)) ),
inference(cnf_transformation,[],[f66]) ).
fof(f94,plain,
! [X2,X0,X1,X6,X4,X5] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
| ordered_pair(X5,X6) != X4
| ~ in(X4,cartesian_product2(X0,X0))
| in(X4,sK11(X0,X1,X2)) ),
inference(cnf_transformation,[],[f66]) ).
fof(f97,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f101,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f70]) ).
fof(f102,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f70]) ).
fof(f103,plain,
! [X2,X3,X0,X1] :
( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f70]) ).
fof(f105,plain,
! [X2,X0,X1,X6,X5] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
| ~ in(ordered_pair(X5,X6),cartesian_product2(X0,X0))
| in(ordered_pair(X5,X6),sK11(X0,X1,X2)) ),
inference(equality_resolution,[],[f94]) ).
tcf(c_49,negated_conjecture,
! [X0: $i] :
( ~ relation(X0)
| ~ in(sK4(X0),sK0)
| ~ in(sK3(X0),sK0)
| ~ in(ordered_pair(sK3(X0),sK4(X0)),X0)
| ~ in(ordered_pair(apply(sK2,sK3(X0)),apply(sK2,sK4(X0))),sK1) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_50,negated_conjecture,
! [X0: $i] :
( in(sK3(X0),sK0)
| in(ordered_pair(sK3(X0),sK4(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_51,negated_conjecture,
! [X0: $i] :
( in(sK4(X0),sK0)
| in(ordered_pair(sK3(X0),sK4(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_52,negated_conjecture,
! [X0: $i] :
( in(ordered_pair(sK3(X0),sK4(X0)),X0)
| in(ordered_pair(apply(sK2,sK3(X0)),apply(sK2,sK4(X0))),sK1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_53,negated_conjecture,
relation(sK1),
inference(cnf_transformation,[],[f73]) ).
tcf(c_54,negated_conjecture,
relation(sK2),
inference(cnf_transformation,[],[f72]) ).
tcf(c_55,negated_conjecture,
function(sK2),
inference(cnf_transformation,[],[f71]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X2 )
| ( ordered_pair(X0,X1) != ordered_pair(X2,X3) ) ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X3 )
| ( ordered_pair(X0,X1) != ordered_pair(X2,X3) ) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_58,plain,
! [X0: $i] :
( relation(X0)
| in(sK5(X0),X0) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(X2)
| ( ordered_pair(X0,X1) != sK5(X2) ) ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(ordered_pair(X1,X2),sK11(X4,X3,X0))
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X0)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X4,X4))
| ~ in(ordered_pair(apply(X0,X1),apply(X0,X2)),X3) ),
inference(cnf_transformation,[],[f105]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,cartesian_product2(X1,X1))
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(X0,sK11(X1,X2,X3)) ),
inference(cnf_transformation,[],[f93]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ordered_pair(sK12(X2,X3,X0),sK13(X2,X3,X0)) = X0 )
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(X0,sK11(X1,X2,X3)) ),
inference(cnf_transformation,[],[f92]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(apply(X3,sK12(X2,X3,X0)),apply(X3,sK13(X2,X3,X0))),X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(X0,sK11(X1,X2,X3)) ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(X0,X2),cartesian_product2(X1,X3))
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f101]) ).
tcf(c_1776,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK3(sK11(X0,X1,X2)),sK4(sK11(X0,X1,X2))),cartesian_product2(X0,X0))
| in(ordered_pair(apply(sK2,sK3(sK11(X0,X1,X2))),apply(sK2,sK4(sK11(X0,X1,X2)))),sK1)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(sK11(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_52,c_70]) ).
tcf(c_1777,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(sK11(X0,X1,X2)),sK0)
| in(ordered_pair(sK3(sK11(X0,X1,X2)),sK4(sK11(X0,X1,X2))),cartesian_product2(X0,X0))
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(sK11(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_51,c_70]) ).
tcf(c_1778,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(sK11(X0,X1,X2)),sK0)
| in(ordered_pair(sK3(sK11(X0,X1,X2)),sK4(sK11(X0,X1,X2))),cartesian_product2(X0,X0))
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(sK11(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_50,c_70]) ).
tcf(c_2028,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK3(X0),sK4(X0)),X0)
| in(ordered_pair(sK3(X0),sK4(X0)),sK11(X1,sK1,sK2))
| ~ function(sK2)
| ~ relation(sK1)
| ~ relation(sK2)
| ~ relation(X0)
| ~ in(ordered_pair(sK3(X0),sK4(X0)),cartesian_product2(X1,X1)) ),
inference(superposition,[status(thm)],[c_52,c_69]) ).
tcf(c_2036,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK3(X0),sK4(X0)),X0)
| in(ordered_pair(sK3(X0),sK4(X0)),sK11(X1,sK1,sK2))
| ~ relation(X0)
| ~ in(ordered_pair(sK3(X0),sK4(X0)),cartesian_product2(X1,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2028,c_55,c_53,c_54]) ).
tcf(c_2123,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK3(X0),sK4(X0)),X0)
| in(ordered_pair(sK3(X0),sK4(X0)),sK11(X1,sK1,sK2))
| ~ relation(X0)
| ~ in(sK4(X0),X1)
| ~ in(sK3(X0),X1) ),
inference(superposition,[status(thm)],[c_79,c_2036]) ).
tcf(c_2211,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(sK11(X0,X1,X2)),sK0)
| in(sK4(sK11(X0,X1,X2)),X0)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(sK11(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_1777,c_81]) ).
tcf(c_2212,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(sK11(X0,X1,X2)),sK0)
| in(sK3(sK11(X0,X1,X2)),X0)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(sK11(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_1777,c_80]) ).
tcf(c_2348,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(sK11(X0,X1,X2)),sK0)
| in(sK3(sK11(X0,X1,X2)),X0)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(sK11(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_1778,c_80]) ).
tcf(c_2788,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ relation(sK11(X0,X1,X2))
| ~ in(sK4(sK11(X0,X1,X2)),sK0)
| ~ in(sK3(sK11(X0,X1,X2)),sK0)
| ~ in(ordered_pair(sK3(sK11(X0,X1,X2)),sK4(sK11(X0,X1,X2))),sK11(X0,X1,X2))
| ~ in(ordered_pair(apply(sK2,sK3(sK11(X0,X1,X2))),apply(sK2,sK4(sK11(X0,X1,X2)))),sK1) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_2908,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(sK11(X0,X1,X2)),X0)
| in(ordered_pair(apply(sK2,sK3(sK11(X0,X1,X2))),apply(sK2,sK4(sK11(X0,X1,X2)))),sK1)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(sK11(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_1776,c_80]) ).
tcf(c_4576,plain,
! [X0: $i,X1: $i] :
( in(sK4(sK11(sK0,X0,X1)),sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(sK11(sK0,X0,X1)) ),
inference(equality_factoring,[status(thm)],[c_2211]) ).
tcf(c_5169,plain,
! [X0: $i,X1: $i] :
( in(sK3(sK11(sK0,X0,X1)),sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(sK11(sK0,X0,X1)) ),
inference(equality_factoring,[status(thm)],[c_2348]) ).
tcf(c_5250,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(sK3(sK11(X0,X1,X2)),sK4(sK11(X0,X1,X2))),sK11(X3,sK1,sK2))
| in(ordered_pair(apply(X2,sK12(X1,X2,ordered_pair(sK3(sK11(X0,X1,X2)),sK4(sK11(X0,X1,X2))))),apply(X2,sK13(X1,X2,ordered_pair(sK3(sK11(X0,X1,X2)),sK4(sK11(X0,X1,X2)))))),X1)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(sK11(X0,X1,X2))
| ~ in(sK4(sK11(X0,X1,X2)),X3)
| ~ in(sK3(sK11(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_2123,c_72]) ).
tcf(c_5266,plain,
! [X0: $i] :
( in(ordered_pair(sK3(sK11(X0,sK1,sK2)),sK4(sK11(X0,sK1,sK2))),sK11(X0,sK1,sK2))
| ~ relation(sK11(X0,sK1,sK2))
| ~ in(sK4(sK11(X0,sK1,sK2)),X0)
| ~ in(sK3(sK11(X0,sK1,sK2)),X0) ),
inference(equality_factoring,[status(thm)],[c_2123]) ).
tcf(c_9890,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(sK11(X0,X1,X2)),X0)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(sK11(X0,X1,X2))
| ~ in(sK4(sK11(X0,X1,X2)),sK0)
| ~ in(sK3(sK11(X0,X1,X2)),sK0)
| ~ in(ordered_pair(sK3(sK11(X0,X1,X2)),sK4(sK11(X0,X1,X2))),sK11(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_2908,c_49]) ).
tcf(c_10002,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(sK11(X0,X1,X2)),X0)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(sK11(X0,X1,X2))
| ~ in(ordered_pair(sK3(sK11(X0,X1,X2)),sK4(sK11(X0,X1,X2))),sK11(X0,X1,X2)) ),
inference(global_subsumption_just,[status(thm)],[c_9890,c_2212,c_2348,c_2788,c_2908]) ).
tcf(c_25107,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK3(sK11(X0,X1,X2)),sK4(sK11(X0,X1,X2))),cartesian_product2(X0,X0))
| in(ordered_pair(apply(sK2,sK3(sK11(X0,X1,X2))),apply(sK2,sK4(sK11(X0,X1,X2)))),sK1)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(sK11(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_52,c_70]) ).
tcf(c_25108,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(sK11(X0,X1,X2)),sK0)
| in(ordered_pair(sK3(sK11(X0,X1,X2)),sK4(sK11(X0,X1,X2))),cartesian_product2(X0,X0))
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(sK11(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_51,c_70]) ).
tcf(c_25109,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(sK11(X0,X1,X2)),sK0)
| in(ordered_pair(sK3(sK11(X0,X1,X2)),sK4(sK11(X0,X1,X2))),cartesian_product2(X0,X0))
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(sK11(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_50,c_70]) ).
tcf(c_25175,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(sK11(X2,X0,X1))
| ( ordered_pair(sK12(X0,X1,sK5(sK11(X2,X0,X1))),sK13(X0,X1,sK5(sK11(X2,X0,X1)))) = sK5(sK11(X2,X0,X1)) )
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_58,c_71]) ).
tcf(c_25239,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(sK11(X0,X1,X2)),sK0)
| in(ordered_pair(apply(X2,sK12(X1,X2,ordered_pair(sK3(sK11(X0,X1,X2)),sK4(sK11(X0,X1,X2))))),apply(X2,sK13(X1,X2,ordered_pair(sK3(sK11(X0,X1,X2)),sK4(sK11(X0,X1,X2)))))),X1)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(sK11(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_50,c_72]) ).
tcf(c_25336,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(sK11(X0,X1,X2)),sK0)
| in(sK4(sK11(X0,X1,X2)),X0)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(sK11(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_25108,c_81]) ).
tcf(c_25385,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(sK11(X0,X1,X2)),sK0)
| in(sK3(sK11(X0,X1,X2)),X0)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(sK11(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_25109,c_80]) ).
tcf(c_25474,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(sK11(X0,X1,X2)),X0)
| in(ordered_pair(apply(sK2,sK3(sK11(X0,X1,X2))),apply(sK2,sK4(sK11(X0,X1,X2)))),sK1)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(sK11(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_25107,c_80]) ).
tcf(c_25616,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK3(X0),sK4(X0)),X0)
| in(ordered_pair(sK3(X0),sK4(X0)),sK11(X1,sK1,sK2))
| ~ function(sK2)
| ~ relation(sK1)
| ~ relation(sK2)
| ~ relation(X0)
| ~ in(ordered_pair(sK3(X0),sK4(X0)),cartesian_product2(X1,X1)) ),
inference(superposition,[status(thm)],[c_52,c_69]) ).
tcf(c_25626,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK3(X0),sK4(X0)),X0)
| in(ordered_pair(sK3(X0),sK4(X0)),sK11(X1,sK1,sK2))
| ~ relation(X0)
| ~ in(ordered_pair(sK3(X0),sK4(X0)),cartesian_product2(X1,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25616,c_55,c_53,c_54]) ).
tcf(c_25795,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK3(X0),sK4(X0)),X0)
| in(ordered_pair(sK3(X0),sK4(X0)),sK11(X1,sK1,sK2))
| ~ relation(X0)
| ~ in(sK4(X0),X1)
| ~ in(sK3(X0),X1) ),
inference(superposition,[status(thm)],[c_79,c_25626]) ).
tcf(c_26468,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(sK11(X2,X0,X1)),sK0)
| in(ordered_pair(sK12(X0,X1,ordered_pair(sK3(sK11(X2,X0,X1)),sK4(sK11(X2,X0,X1)))),sK13(X0,X1,ordered_pair(sK3(sK11(X2,X0,X1)),sK4(sK11(X2,X0,X1))))),sK11(X3,X0,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(sK11(X2,X0,X1))
| ~ in(ordered_pair(sK12(X0,X1,ordered_pair(sK3(sK11(X2,X0,X1)),sK4(sK11(X2,X0,X1)))),sK13(X0,X1,ordered_pair(sK3(sK11(X2,X0,X1)),sK4(sK11(X2,X0,X1))))),cartesian_product2(X3,X3)) ),
inference(superposition,[status(thm)],[c_25239,c_69]) ).
tcf(c_27605,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(sK11(X0,X1,X2)),X0)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(sK11(X0,X1,X2))
| ~ in(sK4(sK11(X0,X1,X2)),sK0)
| ~ in(sK3(sK11(X0,X1,X2)),sK0)
| ~ in(ordered_pair(sK3(sK11(X0,X1,X2)),sK4(sK11(X0,X1,X2))),sK11(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_25474,c_49]) ).
tcf(c_27820,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(sK11(X0,X1,X2)),X0)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(sK11(X0,X1,X2))
| ~ in(ordered_pair(sK3(sK11(X0,X1,X2)),sK4(sK11(X0,X1,X2))),sK11(X0,X1,X2)) ),
inference(global_subsumption_just,[status(thm)],[c_27605,c_10002]) ).
tcf(c_28011,plain,
! [X0: $i] :
( in(ordered_pair(sK3(sK11(X0,sK1,sK2)),sK4(sK11(X0,sK1,sK2))),sK11(X0,sK1,sK2))
| ~ relation(sK11(X0,sK1,sK2))
| ~ in(sK4(sK11(X0,sK1,sK2)),X0)
| ~ in(sK3(sK11(X0,sK1,sK2)),X0) ),
inference(equality_factoring,[status(thm)],[c_25795]) ).
tcf(c_39973,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(apply(sK2,sK12(sK1,sK2,ordered_pair(sK3(sK11(X0,X1,X2)),sK4(sK11(X0,X1,X2))))),apply(sK2,sK13(sK1,sK2,ordered_pair(sK3(sK11(X0,X1,X2)),sK4(sK11(X0,X1,X2)))))),sK1)
| in(ordered_pair(apply(X2,sK12(X1,X2,ordered_pair(sK3(sK11(X0,X1,X2)),sK4(sK11(X0,X1,X2))))),apply(X2,sK13(X1,X2,ordered_pair(sK3(sK11(X0,X1,X2)),sK4(sK11(X0,X1,X2)))))),X1)
| ~ function(sK2)
| ~ relation(sK1)
| ~ relation(sK2)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(sK11(X0,X1,X2))
| ~ in(sK4(sK11(X0,X1,X2)),X3)
| ~ in(sK3(sK11(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_5250,c_72]) ).
tcf(c_40057,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(apply(sK2,sK12(sK1,sK2,ordered_pair(sK3(sK11(X0,X1,X2)),sK4(sK11(X0,X1,X2))))),apply(sK2,sK13(sK1,sK2,ordered_pair(sK3(sK11(X0,X1,X2)),sK4(sK11(X0,X1,X2)))))),sK1)
| in(ordered_pair(apply(X2,sK12(X1,X2,ordered_pair(sK3(sK11(X0,X1,X2)),sK4(sK11(X0,X1,X2))))),apply(X2,sK13(X1,X2,ordered_pair(sK3(sK11(X0,X1,X2)),sK4(sK11(X0,X1,X2)))))),X1)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(sK11(X0,X1,X2))
| ~ in(sK4(sK11(X0,X1,X2)),X3)
| ~ in(sK3(sK11(X0,X1,X2)),X3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39973,c_55,c_53,c_54]) ).
tcf(c_44017,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(sK11(X2,X0,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25175,c_59]) ).
tcf(c_44030,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(sK11(X0,X1,X2)),X0)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(ordered_pair(sK3(sK11(X0,X1,X2)),sK4(sK11(X0,X1,X2))),sK11(X0,X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_27820,c_44017]) ).
tcf(c_44036,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(sK11(X2,X0,X1)),sK0)
| in(sK4(sK11(X2,X0,X1)),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_25336,c_44017]) ).
tcf(c_44045,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(sK11(X2,X0,X1)),sK0)
| in(sK3(sK11(X2,X0,X1)),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_25385,c_44017]) ).
tcf(c_44055,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(sK11(X2,X0,X1)),sK0)
| in(ordered_pair(sK3(sK11(X2,X0,X1)),sK4(sK11(X2,X0,X1))),cartesian_product2(X2,X2))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_25109,c_44017]) ).
tcf(c_44059,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(sK11(X2,X0,X1)),sK0)
| in(ordered_pair(sK3(sK11(X2,X0,X1)),sK4(sK11(X2,X0,X1))),cartesian_product2(X2,X2))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_25108,c_44017]) ).
tcf(c_44072,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK3(sK11(X2,X0,X1)),sK4(sK11(X2,X0,X1))),cartesian_product2(X2,X2))
| in(ordered_pair(apply(sK2,sK3(sK11(X2,X0,X1))),apply(sK2,sK4(sK11(X2,X0,X1)))),sK1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_25107,c_44017]) ).
tcf(c_47670,plain,
! [X0: $i] :
( ( ordered_pair(sK12(sK1,sK2,ordered_pair(sK3(sK11(X0,sK1,sK2)),sK4(sK11(X0,sK1,sK2)))),sK13(sK1,sK2,ordered_pair(sK3(sK11(X0,sK1,sK2)),sK4(sK11(X0,sK1,sK2))))) = ordered_pair(sK3(sK11(X0,sK1,sK2)),sK4(sK11(X0,sK1,sK2))) )
| ~ function(sK2)
| ~ relation(sK1)
| ~ relation(sK2)
| ~ relation(sK11(X0,sK1,sK2))
| ~ in(sK4(sK11(X0,sK1,sK2)),X0)
| ~ in(sK3(sK11(X0,sK1,sK2)),X0) ),
inference(superposition,[status(thm)],[c_28011,c_71]) ).
tcf(c_47703,plain,
! [X0: $i] :
( ( ordered_pair(sK12(sK1,sK2,ordered_pair(sK3(sK11(X0,sK1,sK2)),sK4(sK11(X0,sK1,sK2)))),sK13(sK1,sK2,ordered_pair(sK3(sK11(X0,sK1,sK2)),sK4(sK11(X0,sK1,sK2))))) = ordered_pair(sK3(sK11(X0,sK1,sK2)),sK4(sK11(X0,sK1,sK2))) )
| ~ relation(sK11(X0,sK1,sK2))
| ~ in(sK4(sK11(X0,sK1,sK2)),X0)
| ~ in(sK3(sK11(X0,sK1,sK2)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_47670,c_55,c_53,c_54]) ).
tcf(c_47727,plain,
! [X0: $i] :
( ( ordered_pair(sK12(sK1,sK2,ordered_pair(sK3(sK11(X0,sK1,sK2)),sK4(sK11(X0,sK1,sK2)))),sK13(sK1,sK2,ordered_pair(sK3(sK11(X0,sK1,sK2)),sK4(sK11(X0,sK1,sK2))))) = ordered_pair(sK3(sK11(X0,sK1,sK2)),sK4(sK11(X0,sK1,sK2))) )
| ~ function(sK2)
| ~ relation(sK1)
| ~ relation(sK2)
| ~ relation(sK11(X0,sK1,sK2))
| ~ in(sK4(sK11(X0,sK1,sK2)),X0)
| ~ in(sK3(sK11(X0,sK1,sK2)),X0) ),
inference(superposition,[status(thm)],[c_5266,c_71]) ).
tcf(c_47760,plain,
! [X0: $i] :
( ( ordered_pair(sK12(sK1,sK2,ordered_pair(sK3(sK11(X0,sK1,sK2)),sK4(sK11(X0,sK1,sK2)))),sK13(sK1,sK2,ordered_pair(sK3(sK11(X0,sK1,sK2)),sK4(sK11(X0,sK1,sK2))))) = ordered_pair(sK3(sK11(X0,sK1,sK2)),sK4(sK11(X0,sK1,sK2))) )
| ~ relation(sK11(X0,sK1,sK2))
| ~ in(sK4(sK11(X0,sK1,sK2)),X0)
| ~ in(sK3(sK11(X0,sK1,sK2)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_47727,c_55,c_53,c_54]) ).
tcf(c_48187,plain,
! [X0: $i] :
( in(sK4(sK11(X0,sK1,sK2)),sK0)
| ( ordered_pair(sK12(sK1,sK2,ordered_pair(sK3(sK11(X0,sK1,sK2)),sK4(sK11(X0,sK1,sK2)))),sK13(sK1,sK2,ordered_pair(sK3(sK11(X0,sK1,sK2)),sK4(sK11(X0,sK1,sK2))))) = ordered_pair(sK3(sK11(X0,sK1,sK2)),sK4(sK11(X0,sK1,sK2))) )
| ~ function(sK2)
| ~ relation(sK1)
| ~ relation(sK2)
| ~ relation(sK11(X0,sK1,sK2))
| ~ in(sK3(sK11(X0,sK1,sK2)),X0) ),
inference(superposition,[status(thm)],[c_44036,c_47703]) ).
tcf(c_48192,plain,
! [X0: $i] :
( in(sK4(sK11(X0,sK1,sK2)),sK0)
| ( ordered_pair(sK12(sK1,sK2,ordered_pair(sK3(sK11(X0,sK1,sK2)),sK4(sK11(X0,sK1,sK2)))),sK13(sK1,sK2,ordered_pair(sK3(sK11(X0,sK1,sK2)),sK4(sK11(X0,sK1,sK2))))) = ordered_pair(sK3(sK11(X0,sK1,sK2)),sK4(sK11(X0,sK1,sK2))) )
| ~ relation(sK11(X0,sK1,sK2))
| ~ in(sK3(sK11(X0,sK1,sK2)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_48187,c_55,c_53,c_54]) ).
tcf(c_48624,plain,
( in(sK4(sK11(sK0,sK1,sK2)),sK0)
| in(sK3(sK11(sK0,sK1,sK2)),sK0)
| ( ordered_pair(sK12(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2)))),sK13(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2))))) = ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2))) )
| ~ function(sK2)
| ~ relation(sK1)
| ~ relation(sK2)
| ~ relation(sK11(sK0,sK1,sK2)) ),
inference(superposition,[status(thm)],[c_44045,c_48192]) ).
tcf(c_48637,plain,
( in(sK4(sK11(sK0,sK1,sK2)),sK0)
| in(sK3(sK11(sK0,sK1,sK2)),sK0)
| ( ordered_pair(sK12(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2)))),sK13(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2))))) = ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2))) )
| ~ relation(sK11(sK0,sK1,sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_48624,c_55,c_53,c_54]) ).
tcf(c_48664,plain,
( ( ordered_pair(sK12(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2)))),sK13(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2))))) = ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2))) )
| ~ function(sK2)
| ~ relation(sK1)
| ~ relation(sK2)
| ~ relation(sK11(sK0,sK1,sK2))
| ~ in(sK3(sK11(sK0,sK1,sK2)),sK0) ),
inference(superposition,[status(thm)],[c_4576,c_47760]) ).
tcf(c_48666,plain,
( ( ordered_pair(sK12(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2)))),sK13(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2))))) = ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2))) )
| ~ relation(sK11(sK0,sK1,sK2))
| ~ in(sK3(sK11(sK0,sK1,sK2)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_48664,c_55,c_53,c_54]) ).
tcf(c_48702,plain,
( ( ordered_pair(sK12(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2)))),sK13(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2))))) = ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2))) )
| ~ function(sK2)
| ~ relation(sK1)
| ~ relation(sK2)
| ~ relation(sK11(sK0,sK1,sK2)) ),
inference(superposition,[status(thm)],[c_5169,c_48666]) ).
tcf(c_48704,plain,
( ( ordered_pair(sK12(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2)))),sK13(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2))))) = ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2))) )
| ~ relation(sK11(sK0,sK1,sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_48702,c_55,c_53,c_54]) ).
tcf(c_49094,plain,
( ( ordered_pair(sK12(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2)))),sK13(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2))))) = ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2))) )
| ~ relation(sK11(sK0,sK1,sK2)) ),
inference(global_subsumption_just,[status(thm)],[c_48637,c_48704]) ).
tcf(c_49100,plain,
( ( ordered_pair(sK12(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2)))),sK13(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2))))) = ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2))) )
| ~ function(sK2)
| ~ relation(sK1)
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_44017,c_49094]) ).
tcf(c_49101,plain,
ordered_pair(sK12(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2)))),sK13(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2))))) = ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2))),
inference(forward_subsumption_resolution,[status(thm)],[c_49100,c_55,c_53,c_54]) ).
tcf(c_49126,plain,
! [X0: $i,X1: $i] :
( in(sK13(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2)))),X1)
| ~ in(ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2))),cartesian_product2(X0,X1)) ),
inference(superposition,[status(thm)],[c_49101,c_81]) ).
tcf(c_49127,plain,
! [X0: $i,X1: $i] :
( in(sK12(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2)))),X0)
| ~ in(ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2))),cartesian_product2(X0,X1)) ),
inference(superposition,[status(thm)],[c_49101,c_80]) ).
tcf(c_49986,plain,
ordered_pair(sK12(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2)))),sK13(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2))))) = ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2))),
inference(global_subsumption_just,[status(thm)],[c_48704,c_49101]) ).
tcf(c_50025,plain,
! [X0: $i,X1: $i] :
( in(sK13(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2)))),X1)
| ~ in(ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2))),cartesian_product2(X0,X1)) ),
inference(superposition,[status(thm)],[c_49986,c_81]) ).
tcf(c_50032,plain,
! [X0: $i,X1: $i] :
( ( sK13(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2)))) = X1 )
| ( ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2))) != ordered_pair(X0,X1) ) ),
inference(superposition,[status(thm)],[c_49986,c_57]) ).
tcf(c_50033,plain,
! [X0: $i,X1: $i] :
( ( sK12(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2)))) = X0 )
| ( ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2))) != ordered_pair(X0,X1) ) ),
inference(superposition,[status(thm)],[c_49986,c_56]) ).
tcf(c_53047,plain,
( in(sK4(sK11(sK0,sK1,sK2)),sK0)
| in(sK13(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2)))),sK0)
| ~ function(sK2)
| ~ relation(sK1)
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_44059,c_49126]) ).
tcf(c_53048,plain,
( in(sK3(sK11(sK0,sK1,sK2)),sK0)
| in(sK13(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2)))),sK0)
| ~ function(sK2)
| ~ relation(sK1)
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_44055,c_49126]) ).
tcf(c_53049,plain,
( in(sK3(sK11(sK0,sK1,sK2)),sK0)
| in(sK13(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2)))),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_53048,c_55,c_53,c_54]) ).
tcf(c_53052,plain,
( in(sK4(sK11(sK0,sK1,sK2)),sK0)
| in(sK13(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2)))),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_53047,c_55,c_53,c_54]) ).
tcf(c_53413,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(sK11(X2,X0,X1)),sK0)
| in(ordered_pair(sK12(X0,X1,ordered_pair(sK3(sK11(X2,X0,X1)),sK4(sK11(X2,X0,X1)))),sK13(X0,X1,ordered_pair(sK3(sK11(X2,X0,X1)),sK4(sK11(X2,X0,X1))))),sK11(X3,X0,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(ordered_pair(sK12(X0,X1,ordered_pair(sK3(sK11(X2,X0,X1)),sK4(sK11(X2,X0,X1)))),sK13(X0,X1,ordered_pair(sK3(sK11(X2,X0,X1)),sK4(sK11(X2,X0,X1))))),cartesian_product2(X3,X3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26468,c_44017]) ).
tcf(c_53433,plain,
! [X0: $i] :
( in(sK3(sK11(sK0,sK1,sK2)),sK0)
| in(ordered_pair(sK12(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2)))),sK13(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2))))),sK11(X0,sK1,sK2))
| ~ function(sK2)
| ~ relation(sK1)
| ~ relation(sK2)
| ~ in(ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2))),cartesian_product2(X0,X0)) ),
inference(superposition,[status(thm)],[c_49101,c_53413]) ).
tcf(c_53434,plain,
! [X0: $i] :
( in(sK3(sK11(sK0,sK1,sK2)),sK0)
| in(ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2))),sK11(X0,sK1,sK2))
| ~ function(sK2)
| ~ relation(sK1)
| ~ relation(sK2)
| ~ in(ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2))),cartesian_product2(X0,X0)) ),
inference(light_normalisation,[status(thm)],[c_53433,c_49101]) ).
tcf(c_53435,plain,
! [X0: $i] :
( in(sK3(sK11(sK0,sK1,sK2)),sK0)
| in(ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2))),sK11(X0,sK1,sK2))
| ~ in(ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2))),cartesian_product2(X0,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_53434,c_55,c_53,c_54]) ).
tcf(c_53492,plain,
! [X0: $i,X1: $i] :
( in(sK13(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2)))),X1)
| ~ in(sK4(sK11(sK0,sK1,sK2)),X1)
| ~ in(sK3(sK11(sK0,sK1,sK2)),X0) ),
inference(superposition,[status(thm)],[c_79,c_50025]) ).
tcf(c_53495,plain,
( in(sK3(sK11(sK0,sK1,sK2)),sK0)
| in(sK13(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2)))),sK0)
| ~ function(sK2)
| ~ relation(sK1)
| ~ relation(sK2)
| ~ relation(sK11(sK0,sK1,sK2)) ),
inference(superposition,[status(thm)],[c_1778,c_50025]) ).
tcf(c_53496,plain,
( in(sK4(sK11(sK0,sK1,sK2)),sK0)
| in(sK13(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2)))),sK0)
| ~ function(sK2)
| ~ relation(sK1)
| ~ relation(sK2)
| ~ relation(sK11(sK0,sK1,sK2)) ),
inference(superposition,[status(thm)],[c_1777,c_50025]) ).
tcf(c_53500,plain,
( in(sK4(sK11(sK0,sK1,sK2)),sK0)
| in(sK13(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2)))),sK0)
| ~ relation(sK11(sK0,sK1,sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_53496,c_55,c_53,c_54]) ).
tcf(c_53504,plain,
( in(sK3(sK11(sK0,sK1,sK2)),sK0)
| in(sK13(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2)))),sK0)
| ~ relation(sK11(sK0,sK1,sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_53495,c_55,c_53,c_54]) ).
tcf(c_53599,plain,
( in(sK4(sK11(sK0,sK1,sK2)),sK0)
| in(sK13(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2)))),sK0) ),
inference(global_subsumption_just,[status(thm)],[c_53500,c_53052]) ).
tcf(c_53618,plain,
( in(sK3(sK11(sK0,sK1,sK2)),sK0)
| in(sK13(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2)))),sK0) ),
inference(global_subsumption_just,[status(thm)],[c_53504,c_53049]) ).
tcf(c_53625,plain,
( in(sK3(sK11(sK0,sK1,sK2)),sK0)
| ~ in(sK0,sK13(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2))))) ),
inference(superposition,[status(thm)],[c_53618,c_75]) ).
tcf(c_54273,plain,
( in(sK3(sK11(sK0,sK1,sK2)),sK0)
| in(ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2))),sK11(sK0,sK1,sK2))
| ~ function(sK2)
| ~ relation(sK1)
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_44055,c_53435]) ).
tcf(c_54274,plain,
( in(sK3(sK11(sK0,sK1,sK2)),sK0)
| in(ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2))),sK11(sK0,sK1,sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_54273,c_55,c_53,c_54]) ).
tcf(c_54357,plain,
( in(sK3(sK11(sK0,sK1,sK2)),sK0)
| ~ function(sK2)
| ~ relation(sK1)
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_54274,c_44030]) ).
tcf(c_54362,plain,
in(sK3(sK11(sK0,sK1,sK2)),sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_54357,c_55,c_53,c_54]) ).
tcf(c_54629,plain,
in(sK3(sK11(sK0,sK1,sK2)),sK0),
inference(global_subsumption_just,[status(thm)],[c_53625,c_54362]) ).
tcf(c_54636,plain,
! [X0: $i] :
( in(sK13(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2)))),X0)
| ~ in(sK4(sK11(sK0,sK1,sK2)),X0) ),
inference(superposition,[status(thm)],[c_54629,c_53492]) ).
tcf(c_54650,plain,
in(sK13(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2)))),sK0),
inference(backward_subsumption_resolution,[status(thm)],[c_53599,c_54636]) ).
tcf(c_57633,plain,
sK13(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2)))) = sK4(sK11(sK0,sK1,sK2)),
inference(equality_resolution,[status(thm)],[c_50032]) ).
tcf(c_57680,plain,
in(sK4(sK11(sK0,sK1,sK2)),sK0),
inference(demodulation,[status(thm)],[c_54650,c_57633]) ).
tcf(c_57770,plain,
sK12(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2)))) = sK3(sK11(sK0,sK1,sK2)),
inference(equality_resolution,[status(thm)],[c_50033]) ).
tcf(c_57858,plain,
( in(ordered_pair(apply(sK2,sK12(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2))))),apply(sK2,sK13(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2)))))),sK1)
| ~ function(sK2)
| ~ relation(sK1)
| ~ relation(sK2)
| ~ relation(sK11(sK0,sK1,sK2))
| ~ in(sK3(sK11(sK0,sK1,sK2)),sK0) ),
inference(superposition,[status(thm)],[c_57680,c_40057]) ).
tcf(c_57869,plain,
( in(ordered_pair(apply(sK2,sK3(sK11(sK0,sK1,sK2))),apply(sK2,sK4(sK11(sK0,sK1,sK2)))),sK1)
| ~ function(sK2)
| ~ relation(sK1)
| ~ relation(sK2)
| ~ relation(sK11(sK0,sK1,sK2))
| ~ in(sK3(sK11(sK0,sK1,sK2)),sK0) ),
inference(light_normalisation,[status(thm)],[c_57858,c_57633,c_57770]) ).
tcf(c_57870,plain,
( in(ordered_pair(apply(sK2,sK3(sK11(sK0,sK1,sK2))),apply(sK2,sK4(sK11(sK0,sK1,sK2)))),sK1)
| ~ relation(sK11(sK0,sK1,sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_57869,c_55,c_53,c_54,c_54629]) ).
tcf(c_57907,plain,
( ~ relation(sK11(sK0,sK1,sK2))
| ~ in(sK4(sK11(sK0,sK1,sK2)),sK0)
| ~ in(sK3(sK11(sK0,sK1,sK2)),sK0)
| ~ in(ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2))),sK11(sK0,sK1,sK2)) ),
inference(superposition,[status(thm)],[c_57870,c_49]) ).
tcf(c_57914,plain,
( ~ relation(sK11(sK0,sK1,sK2))
| ~ in(ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2))),sK11(sK0,sK1,sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_57907,c_57680,c_54629]) ).
tcf(c_58328,plain,
( ~ relation(sK11(sK0,sK1,sK2))
| ~ in(sK4(sK11(sK0,sK1,sK2)),sK0)
| ~ in(sK3(sK11(sK0,sK1,sK2)),sK0) ),
inference(superposition,[status(thm)],[c_5266,c_57914]) ).
tcf(c_58330,plain,
~ relation(sK11(sK0,sK1,sK2)),
inference(forward_subsumption_resolution,[status(thm)],[c_58328,c_57680,c_54629]) ).
tcf(c_60743,plain,
( in(sK12(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2)))),sK0)
| in(ordered_pair(apply(sK2,sK3(sK11(sK0,sK1,sK2))),apply(sK2,sK4(sK11(sK0,sK1,sK2)))),sK1)
| ~ function(sK2)
| ~ relation(sK1)
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_44072,c_49127]) ).
tcf(c_60744,plain,
( in(sK4(sK11(sK0,sK1,sK2)),sK0)
| in(sK12(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2)))),sK0)
| ~ function(sK2)
| ~ relation(sK1)
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_44059,c_49127]) ).
tcf(c_60746,plain,
( in(sK4(sK11(sK0,sK1,sK2)),sK0)
| in(sK12(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2)))),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_60744,c_55,c_53,c_54]) ).
tcf(c_60752,plain,
( in(sK12(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2)))),sK0)
| in(ordered_pair(apply(sK2,sK3(sK11(sK0,sK1,sK2))),apply(sK2,sK4(sK11(sK0,sK1,sK2)))),sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_60743,c_55,c_53,c_54]) ).
tcf(c_60758,plain,
in(sK4(sK11(sK0,sK1,sK2)),sK0),
inference(global_subsumption_just,[status(thm)],[c_60746,c_57680]) ).
tcf(c_60777,plain,
( in(sK12(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2)))),sK0)
| ~ relation(sK11(sK0,sK1,sK2))
| ~ in(sK4(sK11(sK0,sK1,sK2)),sK0)
| ~ in(sK3(sK11(sK0,sK1,sK2)),sK0)
| ~ in(ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2))),sK11(sK0,sK1,sK2)) ),
inference(superposition,[status(thm)],[c_60752,c_49]) ).
tcf(c_60784,plain,
( in(sK12(sK1,sK2,ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2)))),sK0)
| ~ relation(sK11(sK0,sK1,sK2))
| ~ in(ordered_pair(sK3(sK11(sK0,sK1,sK2)),sK4(sK11(sK0,sK1,sK2))),sK11(sK0,sK1,sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_60777,c_60758,c_54362]) ).
tcf(c_62073,plain,
~ relation(sK11(sK0,sK1,sK2)),
inference(global_subsumption_just,[status(thm)],[c_60784,c_58330]) ).
tcf(c_62075,plain,
( ~ function(sK2)
| ~ relation(sK1)
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_44017,c_62073]) ).
tcf(c_62076,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_62075,c_55,c_53,c_54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU278+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.39 % Computer : n015.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Thu Sep 24 13:33:58 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/0.46 Running first-order theorem proving
% 0.16/0.46 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
% 0.16/0.48
% 0.16/0.48 % ======== iProver multi-core TPTP/SMT =========
% 0.16/0.48
% 0.16/0.48 % Detected problem language: tptp
% 0.16/0.50 % Proving...
% 20.38/4.80 % SZS status Started for theBenchmark.p
% 20.38/4.80 % SZS status Theorem for theBenchmark.p
% 20.38/4.80
% 20.38/4.80 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 20.38/4.80
% 20.38/4.80 % ------ iProver source info
% 20.38/4.80
% 20.38/4.80 % git: date: 2026-07-19 20:42:38 +0200
% 20.38/4.80 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 20.38/4.80 % git: non_committed_changes: false
% 20.38/4.80
% 20.38/4.80 % ------ Parsing...
% 20.38/4.80 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 20.38/4.80
% 20.38/4.80 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 20.38/4.80
% 20.38/4.80 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 20.38/4.80
% 20.38/4.80 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 20.38/4.80 % ------ Proving...
% 20.38/4.80 % ------ Problem Properties
% 20.38/4.80
% 20.38/4.80 %
% 20.38/4.80 % clauses 34
% 20.38/4.80 % conjectures 7
% 20.38/4.80 % EPR 16
% 20.38/4.80 % Horn 29
% 20.38/4.80 % unary 13
% 20.38/4.80 % binary 9
% 20.38/4.80 % lits 78
% 20.38/4.80 % lits eq 8
% 20.38/4.80 % fd_pure 0
% 20.38/4.80 % fd_pseudo 0
% 20.38/4.80 % fd_cond 0
% 20.38/4.80 % fd_pseudo_cond 3
% 20.38/4.80 % AC symbols 0
% 20.38/4.80
% 20.38/4.80 % ------ Schedule dynamic 5 is on
% 20.38/4.80
% 20.38/4.80 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 20.38/4.80
% 20.38/4.80
% 20.38/4.80 % ------
% 20.38/4.80 % Current options:
% 20.38/4.80 % ------
% 20.38/4.80
% 20.38/4.80
% 20.38/4.80 %
% 20.38/4.80
% 20.38/4.80 % ------ Proving...
% 20.38/4.80 %
% 20.38/4.80
% 20.38/4.80 % SZS status Theorem for theBenchmark.p
% 20.38/4.80
% 20.38/4.80 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 15.90/4.80
% 15.90/4.80
%------------------------------------------------------------------------------