%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET955+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n026.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 02:49:11 PM UTC 2026
% Result : Theorem 1.12s 1.74s
% Output : CNFRefutation 1.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 9
% Syntax : Number of formulae : 87 ( 14 unt; 2 def)
% Number of atoms : 498 ( 91 equ)
% Maximal formula atoms : 18 ( 5 avg)
% Number of connectives : 303 ( 125 ~; 138 |; 30 &)
% ( 6 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-3 aty)
% Number of variables : 202 ( 0 sgn 180 !; 22 ?; 59 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
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/sandbox/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(f4,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f8,conjecture,
! [X0,X1,X2,X3] :
( ! [X4,X5] :
( in(ordered_pair(X4,X5),cartesian_product2(X0,X1))
<=> in(ordered_pair(X4,X5),cartesian_product2(X2,X3)) )
=> cartesian_product2(X0,X1) = cartesian_product2(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t108_zfmisc_1) ).
fof(f9,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ! [X4,X5] :
( in(ordered_pair(X4,X5),cartesian_product2(X0,X1))
<=> in(ordered_pair(X4,X5),cartesian_product2(X2,X3)) )
=> cartesian_product2(X0,X1) = cartesian_product2(X2,X3) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(f12,plain,
? [X0,X1,X2,X3] :
( ! [X4,X5] :
( in(ordered_pair(X4,X5),cartesian_product2(X0,X1))
<=> in(ordered_pair(X4,X5),cartesian_product2(X2,X3)) )
& cartesian_product2(X0,X1) != cartesian_product2(X2,X3) ),
inference(ennf_transformation,[],[f9]) ).
fof(f13,plain,
! [X0,X1] :
( ? [X2] :
( in(X2,X0)
<~> in(X2,X1) )
| X0 = X1 ),
inference(ennf_transformation,[],[f10]) ).
fof(f14,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(f15,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,[],[f14]) ).
fof(f16,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))],[f15]) ).
fof(f19,plain,
? [X0,X1,X2,X3] :
( ! [X4,X5] :
( ( ~ in(ordered_pair(X4,X5),cartesian_product2(X0,X1))
| in(ordered_pair(X4,X5),cartesian_product2(X2,X3)) )
& ( ~ in(ordered_pair(X4,X5),cartesian_product2(X2,X3))
| in(ordered_pair(X4,X5),cartesian_product2(X0,X1)) ) )
& cartesian_product2(X0,X1) != cartesian_product2(X2,X3) ),
inference(nnf_transformation,[],[f12]) ).
fof(f20,plain,
( ! [X4,X5] :
( ( ~ in(ordered_pair(X4,X5),cartesian_product2(sK7,sK8))
| in(ordered_pair(X4,X5),cartesian_product2(sK9,sK10)) )
& ( ~ in(ordered_pair(X4,X5),cartesian_product2(sK9,sK10))
| in(ordered_pair(X4,X5),cartesian_product2(sK7,sK8)) ) )
& cartesian_product2(sK7,sK8) != cartesian_product2(sK9,sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10]),skolemize(X0,sK7),skolemize(X1,sK8),skolemize(X2,sK9),skolemize(X3,sK10)],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ? [X2] :
( ( in(X2,X0)
| in(X2,X1) )
& ( ~ in(X2,X0)
| ~ in(X2,X1) ) )
| X0 = X1 ),
inference(nnf_transformation,[],[f13]) ).
fof(f22,plain,
! [X0,X1] :
( ( ( in(sK11(X0,X1),X0)
| in(sK11(X0,X1),X1) )
& ( ~ in(sK11(X0,X1),X0)
| ~ in(sK11(X0,X1),X1) ) )
| X0 = X1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X2,sK11(X0,X1))],[f21]) ).
fof(f24,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f25,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,[],[f16]) ).
fof(f26,plain,
! [X2,X0,X1,X8] :
( cartesian_product2(X0,X1) != X2
| ~ in(X8,X2)
| in(sK4(X0,X1,X8),X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f27,plain,
! [X2,X0,X1,X8] :
( cartesian_product2(X0,X1) != X2
| ~ in(X8,X2)
| in(sK3(X0,X1,X8),X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f28,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,[],[f16]) ).
fof(f33,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f4]) ).
fof(f37,plain,
! [X4,X5] :
( ~ in(ordered_pair(X4,X5),cartesian_product2(sK7,sK8))
| in(ordered_pair(X4,X5),cartesian_product2(sK9,sK10)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f38,plain,
! [X4,X5] :
( ~ in(ordered_pair(X4,X5),cartesian_product2(sK9,sK10))
| in(ordered_pair(X4,X5),cartesian_product2(sK7,sK8)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f39,plain,
cartesian_product2(sK7,sK8) != cartesian_product2(sK9,sK10),
inference(cnf_transformation,[],[f20]) ).
fof(f40,plain,
! [X0,X1] :
( in(sK11(X0,X1),X0)
| in(sK11(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f41,plain,
! [X0,X1] :
( ~ in(sK11(X0,X1),X0)
| ~ in(sK11(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f44,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,[],[f28,f33]) ).
fof(f45,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,[],[f25,f33]) ).
fof(f47,plain,
! [X4,X5] :
( ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),cartesian_product2(sK9,sK10))
| in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),cartesian_product2(sK7,sK8)) ),
inference(definition_unfolding,[],[f38,f33,f33]) ).
fof(f48,plain,
! [X4,X5] :
( ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),cartesian_product2(sK7,sK8))
| in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),cartesian_product2(sK9,sK10)) ),
inference(definition_unfolding,[],[f37,f33,f33]) ).
fof(f49,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,[],[f44]) ).
fof(f50,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,[],[f49]) ).
fof(f51,plain,
! [X0,X1,X8] :
( ~ in(X8,cartesian_product2(X0,X1))
| in(sK3(X0,X1,X8),X0) ),
inference(equality_resolution,[],[f27]) ).
fof(f52,plain,
! [X0,X1,X8] :
( ~ in(X8,cartesian_product2(X0,X1))
| in(sK4(X0,X1,X8),X1) ),
inference(equality_resolution,[],[f26]) ).
fof(f53,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,[],[f45]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f24]) ).
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,[],[f50]) ).
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,[],[f51]) ).
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,[],[f52]) ).
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,[],[f53]) ).
tcf(c_62,negated_conjecture,
cartesian_product2(sK7,sK8) != cartesian_product2(sK9,sK10),
inference(cnf_transformation,[],[f39]) ).
tcf(c_63,negated_conjecture,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(sK7,sK8))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(sK9,sK10)) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_64,negated_conjecture,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(sK9,sK10))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(sK7,sK8)) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(sK11(X0,X1),X1)
| ~ in(sK11(X0,X1),X0) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,X1),X1)
| in(sK11(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(sK9,sK10))
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(sK7,sK8)) ),
inference(prop_impl_just,[status(thm)],[c_63]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(sK7,sK8))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(sK9,sK10)) ),
inference(renaming,[status(thm)],[c_80]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(sK9,sK10))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(sK7,sK8)) ),
inference(prop_impl_just,[status(thm)],[c_64]) ).
tcf(c_92,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(prop_impl_just,[status(thm)],[c_58]) ).
tcf(c_237,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(demodulation,[status(thm)],[c_55,c_50]) ).
tcf(c_259,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(sK9,sK10))
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(sK7,sK8)) ),
inference(demodulation,[status(thm)],[c_82,c_50]) ).
tcf(c_266,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(sK7,sK8))
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(sK9,sK10)) ),
inference(demodulation,[status(thm)],[c_81,c_50]) ).
tcf(c_273,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(singleton(sK3(X1,X2,X0)),unordered_pair(sK3(X1,X2,X0),sK4(X1,X2,X0))) = X0 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(demodulation,[status(thm)],[c_92,c_50]) ).
tcf(c_330,definition,
iPr_def_10 = cartesian_product2(sK7,sK8),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_331,definition,
iPr_def_11 = cartesian_product2(sK9,sK10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_332,negated_conjecture,
iPr_def_10 != iPr_def_11,
inference(demodulation,[status(thm)],[c_62,c_331,c_330]) ).
tcf(c_333,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_335,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_747,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),iPr_def_11)
| ~ in(X1,sK10)
| ~ in(X0,sK9) ),
inference(superposition,[status(thm)],[c_331,c_237]) ).
tcf(c_893,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),iPr_def_11)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_259,c_330,c_331]) ).
tcf(c_959,plain,
! [X0: $i] :
( ( unordered_pair(singleton(sK3(sK7,sK8,X0)),unordered_pair(sK3(sK7,sK8,X0),sK4(sK7,sK8,X0))) = X0 )
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_330,c_273]) ).
tcf(c_960,plain,
! [X0: $i] :
( ( unordered_pair(singleton(sK3(sK9,sK10,X0)),unordered_pair(sK3(sK9,sK10,X0),sK4(sK9,sK10,X0))) = X0 )
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_331,c_273]) ).
tcf(c_1000,plain,
! [X0: $i] :
( ( iPr_def_10 = iPr_def_11 )
| ( iPr_def_11 != X0 )
| ( iPr_def_10 != X0 ) ),
inference(instantiation,[status(thm)],[c_335]) ).
tcf(c_1061,plain,
( ( iPr_def_10 = iPr_def_11 )
| ( iPr_def_11 != iPr_def_10 )
| ( iPr_def_10 != iPr_def_10 ) ),
inference(instantiation,[status(thm)],[c_1000]) ).
tcf(c_1062,plain,
iPr_def_10 = iPr_def_10,
inference(instantiation,[status(thm)],[c_333]) ).
tcf(c_1350,plain,
( in(sK11(iPr_def_11,iPr_def_10),iPr_def_11)
| in(sK11(iPr_def_11,iPr_def_10),iPr_def_10)
| ( iPr_def_11 = iPr_def_10 ) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_1351,plain,
( ( iPr_def_11 = iPr_def_10 )
| ~ in(sK11(iPr_def_11,iPr_def_10),iPr_def_11)
| ~ in(sK11(iPr_def_11,iPr_def_10),iPr_def_10) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_1506,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),iPr_def_10)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_266,c_330,c_331]) ).
tcf(c_1514,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),iPr_def_10)
| ~ in(X1,sK10)
| ~ in(X0,sK9) ),
inference(superposition,[status(thm)],[c_747,c_1506]) ).
tcf(c_2176,plain,
! [X0: $i] :
( in(sK11(X0,iPr_def_10),X0)
| ( X0 = iPr_def_10 )
| ( unordered_pair(singleton(sK3(sK7,sK8,sK11(X0,iPr_def_10))),unordered_pair(sK3(sK7,sK8,sK11(X0,iPr_def_10)),sK4(sK7,sK8,sK11(X0,iPr_def_10)))) = sK11(X0,iPr_def_10) ) ),
inference(superposition,[status(thm)],[c_66,c_959]) ).
tcf(c_2460,plain,
( ( iPr_def_10 = iPr_def_11 )
| ( unordered_pair(singleton(sK3(sK9,sK10,sK11(iPr_def_11,iPr_def_10))),unordered_pair(sK3(sK9,sK10,sK11(iPr_def_11,iPr_def_10)),sK4(sK9,sK10,sK11(iPr_def_11,iPr_def_10)))) = sK11(iPr_def_11,iPr_def_10) )
| ( unordered_pair(singleton(sK3(sK7,sK8,sK11(iPr_def_11,iPr_def_10))),unordered_pair(sK3(sK7,sK8,sK11(iPr_def_11,iPr_def_10)),sK4(sK7,sK8,sK11(iPr_def_11,iPr_def_10)))) = sK11(iPr_def_11,iPr_def_10) ) ),
inference(superposition,[status(thm)],[c_2176,c_960]) ).
tcf(c_2464,plain,
( ( unordered_pair(singleton(sK3(sK9,sK10,sK11(iPr_def_11,iPr_def_10))),unordered_pair(sK3(sK9,sK10,sK11(iPr_def_11,iPr_def_10)),sK4(sK9,sK10,sK11(iPr_def_11,iPr_def_10)))) = sK11(iPr_def_11,iPr_def_10) )
| ( unordered_pair(singleton(sK3(sK7,sK8,sK11(iPr_def_11,iPr_def_10))),unordered_pair(sK3(sK7,sK8,sK11(iPr_def_11,iPr_def_10)),sK4(sK7,sK8,sK11(iPr_def_11,iPr_def_10)))) = sK11(iPr_def_11,iPr_def_10) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2460,c_332]) ).
tcf(c_2556,plain,
( in(sK11(iPr_def_11,iPr_def_10),iPr_def_10)
| ( unordered_pair(singleton(sK3(sK7,sK8,sK11(iPr_def_11,iPr_def_10))),unordered_pair(sK3(sK7,sK8,sK11(iPr_def_11,iPr_def_10)),sK4(sK7,sK8,sK11(iPr_def_11,iPr_def_10)))) = sK11(iPr_def_11,iPr_def_10) )
| ~ in(sK4(sK9,sK10,sK11(iPr_def_11,iPr_def_10)),sK10)
| ~ in(sK3(sK9,sK10,sK11(iPr_def_11,iPr_def_10)),sK9) ),
inference(superposition,[status(thm)],[c_2464,c_1514]) ).
tcf(c_2564,plain,
( in(sK11(iPr_def_11,iPr_def_10),iPr_def_11)
| ( unordered_pair(singleton(sK3(sK7,sK8,sK11(iPr_def_11,iPr_def_10))),unordered_pair(sK3(sK7,sK8,sK11(iPr_def_11,iPr_def_10)),sK4(sK7,sK8,sK11(iPr_def_11,iPr_def_10)))) = sK11(iPr_def_11,iPr_def_10) )
| ~ in(sK4(sK9,sK10,sK11(iPr_def_11,iPr_def_10)),sK10)
| ~ in(sK3(sK9,sK10,sK11(iPr_def_11,iPr_def_10)),sK9) ),
inference(superposition,[status(thm)],[c_2464,c_747]) ).
tcf(c_4462,plain,
( ~ in(sK3(sK9,sK10,sK11(iPr_def_11,iPr_def_10)),sK9)
| ~ in(sK4(sK9,sK10,sK11(iPr_def_11,iPr_def_10)),sK10)
| ( unordered_pair(singleton(sK3(sK7,sK8,sK11(iPr_def_11,iPr_def_10))),unordered_pair(sK3(sK7,sK8,sK11(iPr_def_11,iPr_def_10)),sK4(sK7,sK8,sK11(iPr_def_11,iPr_def_10)))) = sK11(iPr_def_11,iPr_def_10) ) ),
inference(global_subsumption_just,[status(thm)],[c_2556,c_332,c_1061,c_1062,c_1351,c_2564,c_2556]) ).
tcf(c_4463,plain,
( ( unordered_pair(singleton(sK3(sK7,sK8,sK11(iPr_def_11,iPr_def_10))),unordered_pair(sK3(sK7,sK8,sK11(iPr_def_11,iPr_def_10)),sK4(sK7,sK8,sK11(iPr_def_11,iPr_def_10)))) = sK11(iPr_def_11,iPr_def_10) )
| ~ in(sK4(sK9,sK10,sK11(iPr_def_11,iPr_def_10)),sK10)
| ~ in(sK3(sK9,sK10,sK11(iPr_def_11,iPr_def_10)),sK9) ),
inference(renaming,[status(thm)],[c_4462]) ).
tcf(c_4470,plain,
( ( unordered_pair(singleton(sK3(sK7,sK8,sK11(iPr_def_11,iPr_def_10))),unordered_pair(sK3(sK7,sK8,sK11(iPr_def_11,iPr_def_10)),sK4(sK7,sK8,sK11(iPr_def_11,iPr_def_10)))) = sK11(iPr_def_11,iPr_def_10) )
| ~ in(sK11(iPr_def_11,iPr_def_10),cartesian_product2(sK9,sK10))
| ~ in(sK3(sK9,sK10,sK11(iPr_def_11,iPr_def_10)),sK9) ),
inference(superposition,[status(thm)],[c_57,c_4463]) ).
tcf(c_4471,plain,
( ( unordered_pair(singleton(sK3(sK7,sK8,sK11(iPr_def_11,iPr_def_10))),unordered_pair(sK3(sK7,sK8,sK11(iPr_def_11,iPr_def_10)),sK4(sK7,sK8,sK11(iPr_def_11,iPr_def_10)))) = sK11(iPr_def_11,iPr_def_10) )
| ~ in(sK11(iPr_def_11,iPr_def_10),iPr_def_11)
| ~ in(sK3(sK9,sK10,sK11(iPr_def_11,iPr_def_10)),sK9) ),
inference(light_normalisation,[status(thm)],[c_4470,c_331]) ).
tcf(c_5601,plain,
( ( unordered_pair(singleton(sK3(sK7,sK8,sK11(iPr_def_11,iPr_def_10))),unordered_pair(sK3(sK7,sK8,sK11(iPr_def_11,iPr_def_10)),sK4(sK7,sK8,sK11(iPr_def_11,iPr_def_10)))) = sK11(iPr_def_11,iPr_def_10) )
| ~ in(sK11(iPr_def_11,iPr_def_10),iPr_def_11)
| ~ in(sK11(iPr_def_11,iPr_def_10),cartesian_product2(sK9,sK10)) ),
inference(superposition,[status(thm)],[c_56,c_4471]) ).
tcf(c_5602,plain,
( ( unordered_pair(singleton(sK3(sK7,sK8,sK11(iPr_def_11,iPr_def_10))),unordered_pair(sK3(sK7,sK8,sK11(iPr_def_11,iPr_def_10)),sK4(sK7,sK8,sK11(iPr_def_11,iPr_def_10)))) = sK11(iPr_def_11,iPr_def_10) )
| ~ in(sK11(iPr_def_11,iPr_def_10),iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_5601,c_331]) ).
tcf(c_5612,plain,
( ( iPr_def_10 = iPr_def_11 )
| ( unordered_pair(singleton(sK3(sK7,sK8,sK11(iPr_def_11,iPr_def_10))),unordered_pair(sK3(sK7,sK8,sK11(iPr_def_11,iPr_def_10)),sK4(sK7,sK8,sK11(iPr_def_11,iPr_def_10)))) = sK11(iPr_def_11,iPr_def_10) ) ),
inference(superposition,[status(thm)],[c_2176,c_5602]) ).
tcf(c_5613,plain,
unordered_pair(singleton(sK3(sK7,sK8,sK11(iPr_def_11,iPr_def_10))),unordered_pair(sK3(sK7,sK8,sK11(iPr_def_11,iPr_def_10)),sK4(sK7,sK8,sK11(iPr_def_11,iPr_def_10)))) = sK11(iPr_def_11,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_5612,c_332]) ).
tcf(c_5641,plain,
( in(unordered_pair(singleton(sK3(sK7,sK8,sK11(iPr_def_11,iPr_def_10))),unordered_pair(sK3(sK7,sK8,sK11(iPr_def_11,iPr_def_10)),sK4(sK7,sK8,sK11(iPr_def_11,iPr_def_10)))),iPr_def_10)
| ~ in(sK11(iPr_def_11,iPr_def_10),iPr_def_11) ),
inference(superposition,[status(thm)],[c_5613,c_1506]) ).
tcf(c_5646,plain,
( in(unordered_pair(singleton(sK3(sK7,sK8,sK11(iPr_def_11,iPr_def_10))),unordered_pair(sK3(sK7,sK8,sK11(iPr_def_11,iPr_def_10)),sK4(sK7,sK8,sK11(iPr_def_11,iPr_def_10)))),iPr_def_11)
| ~ in(sK11(iPr_def_11,iPr_def_10),iPr_def_10) ),
inference(superposition,[status(thm)],[c_5613,c_893]) ).
tcf(c_5686,plain,
( in(sK11(iPr_def_11,iPr_def_10),iPr_def_11)
| ~ in(sK11(iPr_def_11,iPr_def_10),iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_5646,c_5613]) ).
tcf(c_5689,plain,
( in(sK11(iPr_def_11,iPr_def_10),iPr_def_10)
| ~ in(sK11(iPr_def_11,iPr_def_10),iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_5641,c_5613]) ).
tcf(c_5848,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_5686,c_5689,c_1350,c_1351,c_1062,c_1061,c_332]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET955+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n026.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 12:29:53 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 1.12/1.74 % SZS status Started for theBenchmark.p
% 1.12/1.74 % SZS status Theorem for theBenchmark.p
% 1.12/1.74
% 1.12/1.74 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.12/1.74
% 1.12/1.74 % ------ iProver source info
% 1.12/1.74
% 1.12/1.74 % git: date: 2026-07-19 20:42:38 +0200
% 1.12/1.74 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.12/1.74 % git: non_committed_changes: false
% 1.12/1.74
% 1.12/1.74 % ------ Parsing...
% 1.12/1.74 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.12/1.74
% 1.12/1.74 % ------ Preprocessing... sup_sim: 7 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.12/1.74
% 1.12/1.74 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.12/1.74
% 1.12/1.74 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.12/1.74 % ------ Proving...
% 1.12/1.74 % ------ Problem Properties
% 1.12/1.74
% 1.12/1.74 %
% 1.12/1.74 % clauses 20
% 1.12/1.74 % conjectures 1
% 1.12/1.74 % EPR 4
% 1.12/1.74 % Horn 16
% 1.12/1.74 % unary 7
% 1.12/1.74 % binary 6
% 1.12/1.74 % lits 42
% 1.12/1.74 % lits eq 13
% 1.12/1.74 % fd_pure 0
% 1.12/1.74 % fd_pseudo 0
% 1.12/1.74 % fd_cond 0
% 1.12/1.74 % fd_pseudo_cond 6
% 1.12/1.74 % AC symbols 0
% 1.12/1.74
% 1.12/1.74 % ------ Schedule dynamic 5 is on
% 1.12/1.74
% 1.12/1.74 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.12/1.74
% 1.12/1.74
% 1.12/1.74 % ------
% 1.12/1.74 % Current options:
% 1.12/1.74 % ------
% 1.12/1.74
% 1.12/1.74
% 1.12/1.74 %
% 1.12/1.74
% 1.12/1.74 % ------ Proving...
% 1.12/1.74 %
% 1.12/1.74
% 1.12/1.74 % SZS status Theorem for theBenchmark.p
% 1.12/1.74
% 1.12/1.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.12/1.75
% 1.12/1.75
%------------------------------------------------------------------------------