%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU166+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n007.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 02:55:43 PM UTC 2026
% Result : Theorem 46.57s 8.34s
% Output : CNFRefutation 46.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 5
% Syntax : Number of formulae : 75 ( 13 unt; 0 def)
% Number of atoms : 246 ( 48 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 290 ( 119 ~; 131 |; 33 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 179 ( 1 sgn 162 !; 17 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,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(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
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(f9,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f10,conjecture,
! [X0,X1,X2] :
( subset(X0,X1)
=> ( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
& subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_zfmisc_1) ).
fof(f11,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(X0,X1)
=> ( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
& subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f12,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f9]) ).
fof(f14,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f15,plain,
? [X0,X1,X2] :
( subset(X0,X1)
& ( ~ subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
| ~ subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f16,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,[],[f3]) ).
fof(f17,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,[],[f16]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) != X2
| ! [X8] :
( ( ~ in(X8,X2)
| ( ordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)) = X8
& in(sK4(X0,X1,X8),X1)
& in(sK3(X0,X1,X8),X0) ) )
& ( ! [X9,X10] :
( ordered_pair(X9,X10) != X8
| ~ in(X10,X1)
| ~ in(X9,X0) )
| in(X8,X2) ) ) )
& ( ( ( in(sK0(X0,X1,X2),X2)
| ( sK0(X0,X1,X2) = ordered_pair(sK1(X0,X1,X2),sK2(X0,X1,X2))
& in(sK2(X0,X1,X2),X1)
& in(sK1(X0,X1,X2),X0) ) )
& ( ~ in(sK0(X0,X1,X2),X2)
| ! [X4,X5] :
( ordered_pair(X4,X5) != sK0(X0,X1,X2)
| ~ in(X5,X1)
| ~ in(X4,X0) ) ) )
| X2 = cartesian_product2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X3,sK0(X0,X1,X2)),skolemize(X6,sK1(X0,X1,X2)),skolemize(X7,sK2(X0,X1,X2)),skolemize(X11,sK3(X0,X1,X8)),skolemize(X12,sK4(X0,X1,X8))],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f20,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK5(X0,X1),X0)
& ~ in(sK5(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f20]) ).
fof(f24,plain,
( subset(sK8,sK9)
& ( ~ subset(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))
| ~ subset(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10]),skolemize(X0,sK8),skolemize(X1,sK9),skolemize(X2,sK10)],[f15]) ).
fof(f27,plain,
! [X2,X0,X1,X8] :
( cartesian_product2(X0,X1) != X2
| ~ in(X8,X2)
| ordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)) = X8 ),
inference(cnf_transformation,[],[f18]) ).
fof(f28,plain,
! [X2,X0,X1,X8] :
( cartesian_product2(X0,X1) != X2
| ~ in(X8,X2)
| in(sK4(X0,X1,X8),X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f29,plain,
! [X2,X0,X1,X8] :
( cartesian_product2(X0,X1) != X2
| ~ in(X8,X2)
| in(sK3(X0,X1,X8),X0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f30,plain,
! [X2,X10,X0,X1,X8,X9] :
( cartesian_product2(X0,X1) != X2
| ordered_pair(X9,X10) != X8
| ~ in(X10,X1)
| ~ in(X9,X0)
| in(X8,X2) ),
inference(cnf_transformation,[],[f18]) ).
fof(f35,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f36,plain,
! [X0,X1] :
( in(sK5(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f37,plain,
! [X0,X1] :
( ~ in(sK5(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f38,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f5]) ).
fof(f42,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f12]) ).
fof(f43,plain,
subset(sK8,sK9),
inference(cnf_transformation,[],[f24]) ).
fof(f44,plain,
( ~ subset(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))
| ~ subset(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f47,plain,
! [X2,X10,X0,X1,X8,X9] :
( cartesian_product2(X0,X1) != X2
| unordered_pair(unordered_pair(X9,X10),singleton(X9)) != X8
| ~ in(X10,X1)
| ~ in(X9,X0)
| in(X8,X2) ),
inference(definition_unfolding,[],[f30,f38]) ).
fof(f48,plain,
! [X2,X0,X1,X8] :
( cartesian_product2(X0,X1) != X2
| ~ in(X8,X2)
| unordered_pair(unordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)),singleton(sK3(X0,X1,X8))) = X8 ),
inference(definition_unfolding,[],[f27,f38]) ).
fof(f50,plain,
! [X2,X10,X0,X1,X9] :
( cartesian_product2(X0,X1) != X2
| ~ in(X10,X1)
| ~ in(X9,X0)
| in(unordered_pair(unordered_pair(X9,X10),singleton(X9)),X2) ),
inference(equality_resolution,[],[f47]) ).
fof(f51,plain,
! [X10,X0,X1,X9] :
( ~ in(X10,X1)
| ~ in(X9,X0)
| in(unordered_pair(unordered_pair(X9,X10),singleton(X9)),cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f50]) ).
fof(f52,plain,
! [X0,X1,X8] :
( ~ in(X8,cartesian_product2(X0,X1))
| in(sK3(X0,X1,X8),X0) ),
inference(equality_resolution,[],[f29]) ).
fof(f53,plain,
! [X0,X1,X8] :
( ~ in(X8,cartesian_product2(X0,X1))
| in(sK4(X0,X1,X8),X1) ),
inference(equality_resolution,[],[f28]) ).
fof(f54,plain,
! [X0,X1,X8] :
( ~ in(X8,cartesian_product2(X0,X1))
| unordered_pair(unordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)),singleton(sK3(X0,X1,X8))) = X8 ),
inference(equality_resolution,[],[f48]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X2),singleton(X0)),cartesian_product2(X1,X3))
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X1,X2,X0),X1)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(X1,X2,X0),X2)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK3(X1,X2,X0),sK4(X1,X2,X0)),singleton(sK3(X1,X2,X0))) = X0 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK5(X0,X1),X1) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK5(X0,X1),X0) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_65,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f42]) ).
tcf(c_66,negated_conjecture,
( ~ subset(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))
| ~ subset(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_67,negated_conjecture,
subset(sK8,sK9),
inference(cnf_transformation,[],[f43]) ).
tcf(c_68,plain,
subset(sK10,sK10),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_538,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X1,X2,X0),X3)
| ~ subset(X1,X3)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_56,c_61]) ).
tcf(c_546,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK4(X1,X2,X0),X3)
| ~ subset(X2,X3)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_57,c_61]) ).
tcf(c_593,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(cartesian_product2(X0,X1),X2)
| ( unordered_pair(unordered_pair(sK3(X0,X1,sK5(cartesian_product2(X0,X1),X2)),sK4(X0,X1,sK5(cartesian_product2(X0,X1),X2))),singleton(sK3(X0,X1,sK5(cartesian_product2(X0,X1),X2)))) = sK5(cartesian_product2(X0,X1),X2) ) ),
inference(superposition,[status(thm)],[c_60,c_58]) ).
tcf(c_1460,plain,
( ( unordered_pair(unordered_pair(sK3(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))),sK4(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)))),singleton(sK3(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))))) = sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)) )
| ~ subset(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)) ),
inference(superposition,[status(thm)],[c_593,c_66]) ).
tcf(c_1468,plain,
( ( unordered_pair(unordered_pair(sK3(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))),sK4(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)))),singleton(sK3(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))))) = sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)) )
| ( unordered_pair(unordered_pair(sK3(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))),sK4(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)))),singleton(sK3(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))))) = sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)) ) ),
inference(superposition,[status(thm)],[c_593,c_1460]) ).
tcf(c_1472,plain,
! [X0: $i,X1: $i] :
( in(sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)),cartesian_product2(X0,X1))
| ( unordered_pair(unordered_pair(sK3(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))),sK4(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)))),singleton(sK3(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))))) = sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)) )
| ~ in(sK4(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))),X1)
| ~ in(sK3(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))),X0) ),
inference(superposition,[status(thm)],[c_1468,c_55]) ).
tcf(c_1554,plain,
! [X0: $i,X1: $i] :
( in(sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)),cartesian_product2(X1,X0))
| ( unordered_pair(unordered_pair(sK3(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))),sK4(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)))),singleton(sK3(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))))) = sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)) )
| ~ subset(sK8,X1)
| ~ in(sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)),cartesian_product2(sK8,sK10))
| ~ in(sK4(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))),X0) ),
inference(superposition,[status(thm)],[c_538,c_1472]) ).
tcf(c_1584,plain,
! [X0: $i] :
( in(sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)),cartesian_product2(X0,sK10))
| ( unordered_pair(unordered_pair(sK3(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))),sK4(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)))),singleton(sK3(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))))) = sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)) )
| ~ subset(sK8,X0)
| ~ in(sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)),cartesian_product2(sK8,sK10)) ),
inference(superposition,[status(thm)],[c_57,c_1554]) ).
tcf(c_1633,plain,
! [X0: $i] :
( subset(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))
| in(sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)),cartesian_product2(X0,sK10))
| ( unordered_pair(unordered_pair(sK3(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))),sK4(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)))),singleton(sK3(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))))) = sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)) )
| ~ subset(sK8,X0) ),
inference(superposition,[status(thm)],[c_60,c_1584]) ).
tcf(c_1715,plain,
( subset(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))
| ( unordered_pair(unordered_pair(sK3(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))),sK4(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)))),singleton(sK3(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))))) = sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)) )
| ~ subset(sK8,sK9) ),
inference(superposition,[status(thm)],[c_1633,c_59]) ).
tcf(c_1722,plain,
( subset(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))
| ( unordered_pair(unordered_pair(sK3(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))),sK4(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)))),singleton(sK3(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))))) = sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)) ) ),
inference(global_subsumption_just,[status(thm)],[c_1715,c_67,c_1715]) ).
tcf(c_1755,plain,
( ( unordered_pair(unordered_pair(sK3(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))),sK4(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)))),singleton(sK3(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))))) = sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)) )
| ~ subset(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)) ),
inference(superposition,[status(thm)],[c_1722,c_66]) ).
tcf(c_1763,plain,
unordered_pair(unordered_pair(sK3(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))),sK4(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)))),singleton(sK3(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))))) = sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)),
inference(superposition,[status(thm)],[c_593,c_1755]) ).
tcf(c_1767,plain,
! [X0: $i,X1: $i] :
( in(sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)),cartesian_product2(X0,X1))
| ~ in(sK4(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))),X1)
| ~ in(sK3(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))),X0) ),
inference(superposition,[status(thm)],[c_1763,c_55]) ).
tcf(c_1858,plain,
! [X0: $i] :
( in(sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)),cartesian_product2(sK10,X0))
| ~ in(sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)),cartesian_product2(sK10,sK8))
| ~ in(sK4(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))),X0) ),
inference(superposition,[status(thm)],[c_56,c_1767]) ).
tcf(c_1911,plain,
! [X0: $i] :
( in(sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)),cartesian_product2(sK10,X0))
| ~ subset(sK8,X0)
| ~ in(sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)),cartesian_product2(sK10,sK8)) ),
inference(superposition,[status(thm)],[c_546,c_1858]) ).
tcf(c_1942,plain,
! [X0: $i] :
( subset(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))
| in(sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)),cartesian_product2(sK10,X0))
| ~ subset(sK8,X0) ),
inference(superposition,[status(thm)],[c_60,c_1911]) ).
tcf(c_1986,plain,
( subset(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))
| ~ subset(sK8,sK9) ),
inference(superposition,[status(thm)],[c_1942,c_59]) ).
tcf(c_1993,plain,
subset(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)),
inference(global_subsumption_just,[status(thm)],[c_1986,c_67,c_1986]) ).
tcf(c_2020,plain,
unordered_pair(unordered_pair(sK3(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))),sK4(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)))),singleton(sK3(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))))) = sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)),
inference(superposition,[status(thm)],[c_1993,c_1460]) ).
tcf(c_2025,plain,
! [X0: $i,X1: $i] :
( in(sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)),cartesian_product2(X0,X1))
| ~ in(sK4(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))),X1)
| ~ in(sK3(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))),X0) ),
inference(superposition,[status(thm)],[c_2020,c_55]) ).
tcf(c_2114,plain,
! [X0: $i] :
( in(sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)),cartesian_product2(sK8,X0))
| ~ in(sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)),cartesian_product2(sK8,sK10))
| ~ in(sK4(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))),X0) ),
inference(superposition,[status(thm)],[c_56,c_2025]) ).
tcf(c_2115,plain,
! [X0: $i,X1: $i] :
( in(sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)),cartesian_product2(X1,X0))
| ~ subset(sK8,X1)
| ~ in(sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)),cartesian_product2(sK8,sK10))
| ~ in(sK4(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))),X0) ),
inference(superposition,[status(thm)],[c_538,c_2025]) ).
tcf(c_2136,plain,
! [X0: $i] :
( in(sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)),cartesian_product2(sK8,X0))
| ~ subset(sK10,X0)
| ~ in(sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)),cartesian_product2(sK8,sK10)) ),
inference(superposition,[status(thm)],[c_546,c_2114]) ).
tcf(c_2140,plain,
! [X0: $i] :
( in(sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)),cartesian_product2(X0,sK10))
| ~ subset(sK8,X0)
| ~ in(sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)),cartesian_product2(sK8,sK10)) ),
inference(superposition,[status(thm)],[c_57,c_2115]) ).
tcf(c_2167,plain,
! [X0: $i] :
( subset(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))
| in(sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)),cartesian_product2(sK8,X0))
| ~ subset(sK10,X0) ),
inference(superposition,[status(thm)],[c_60,c_2136]) ).
tcf(c_2171,plain,
( subset(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))
| in(sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)),cartesian_product2(sK8,sK10))
| ~ subset(sK10,sK10) ),
inference(instantiation,[status(thm)],[c_2167]) ).
tcf(c_2183,plain,
! [X0: $i] :
( in(sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)),cartesian_product2(X0,sK10))
| ~ subset(sK8,X0) ),
inference(global_subsumption_just,[status(thm)],[c_2140,c_67,c_68,c_66,c_1986,c_2140,c_2171]) ).
tcf(c_2189,plain,
( subset(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))
| ~ subset(sK8,sK9) ),
inference(superposition,[status(thm)],[c_2183,c_59]) ).
tcf(c_2195,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2189,c_1986,c_66,c_67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU166+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 12:59:22 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 46.57/8.34 % SZS status Started for theBenchmark.p
% 46.57/8.34 % SZS status Theorem for theBenchmark.p
% 46.57/8.34
% 46.57/8.34 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 46.57/8.34
% 46.57/8.34 % ------ iProver source info
% 46.57/8.34
% 46.57/8.34 % git: date: 2026-07-19 20:42:38 +0200
% 46.57/8.34 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 46.57/8.34 % git: non_committed_changes: false
% 46.57/8.34
% 46.57/8.34 % ------ Parsing...
% 46.57/8.34 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 46.57/8.34
% 46.57/8.34 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 46.57/8.34
% 46.57/8.34 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 46.57/8.34
% 46.57/8.34 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 46.57/8.34 % ------ Proving...
% 46.57/8.34 % ------ Problem Properties
% 46.57/8.34
% 46.57/8.34 %
% 46.57/8.34 % clauses 19
% 46.57/8.34 % conjectures 2
% 46.57/8.34 % EPR 6
% 46.57/8.34 % Horn 15
% 46.57/8.34 % unary 6
% 46.57/8.34 % binary 7
% 46.57/8.34 % lits 40
% 46.57/8.34 % lits eq 8
% 46.57/8.34 % fd_pure 0
% 46.57/8.34 % fd_pseudo 0
% 46.57/8.34 % fd_cond 0
% 46.57/8.34 % fd_pseudo_cond 4
% 46.57/8.34 % AC symbols 0
% 46.57/8.34
% 46.57/8.34 % ------ Input Options Time Limit: Unbounded
% 46.57/8.34
% 46.57/8.34
% 46.57/8.34 % ------
% 46.57/8.34 % Current options:
% 46.57/8.34 % ------
% 46.57/8.34
% 46.57/8.34
% 46.57/8.34 %
% 46.57/8.34
% 46.57/8.34 % ------ Proving...
% 46.57/8.34 %
% 46.57/8.34
% 46.57/8.34 % SZS status Theorem for theBenchmark.p
% 46.57/8.34
% 46.57/8.34 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 46.57/8.34
% 46.57/8.34
%------------------------------------------------------------------------------