TSTP Solution File: SET955+1 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET955+1 : TPTP v8.2.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 14:36:41 EDT 2024
% Result : Theorem 3.89s 1.12s
% Output : CNFRefutation 3.89s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named definition)
% 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] :
( cartesian_product2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& 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,[],[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] :
( cartesian_product2(X0,X1) != cartesian_product2(X2,X3)
& ! [X4,X5] :
( in(ordered_pair(X4,X5),cartesian_product2(X0,X1))
<=> in(ordered_pair(X4,X5),cartesian_product2(X2,X3)) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f13,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) = X2
| ? [X3] :
( ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) )
| ~ in(X3,X2) )
& ( ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) ) )
& ( ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) )
| ~ in(X3,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) = X2
| ? [X3] :
( ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) )
| ~ in(X3,X2) )
& ( ? [X6,X7] :
( ordered_pair(X6,X7) = X3
& in(X7,X1)
& in(X6,X0) )
| in(X3,X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ordered_pair(X9,X10) != X8
| ~ in(X10,X1)
| ~ in(X9,X0) ) )
& ( ? [X11,X12] :
( ordered_pair(X11,X12) = X8
& in(X12,X1)
& in(X11,X0) )
| ~ in(X8,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(rectify,[],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) )
| ~ in(X3,X2) )
& ( ? [X6,X7] :
( ordered_pair(X6,X7) = X3
& in(X7,X1)
& in(X6,X0) )
| in(X3,X2) ) )
=> ( ( ! [X5,X4] :
( ordered_pair(X4,X5) != sK0(X0,X1,X2)
| ~ in(X5,X1)
| ~ in(X4,X0) )
| ~ in(sK0(X0,X1,X2),X2) )
& ( ? [X7,X6] :
( ordered_pair(X6,X7) = sK0(X0,X1,X2)
& in(X7,X1)
& in(X6,X0) )
| in(sK0(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ? [X7,X6] :
( ordered_pair(X6,X7) = sK0(X0,X1,X2)
& in(X7,X1)
& in(X6,X0) )
=> ( 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) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
! [X0,X1,X8] :
( ? [X11,X12] :
( ordered_pair(X11,X12) = X8
& in(X12,X1)
& in(X11,X0) )
=> ( ordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)) = X8
& in(sK4(X0,X1,X8),X1)
& in(sK3(X0,X1,X8),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) = X2
| ( ( ! [X4,X5] :
( ordered_pair(X4,X5) != sK0(X0,X1,X2)
| ~ in(X5,X1)
| ~ in(X4,X0) )
| ~ 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) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ordered_pair(X9,X10) != X8
| ~ in(X10,X1)
| ~ in(X9,X0) ) )
& ( ( ordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)) = X8
& in(sK4(X0,X1,X8),X1)
& in(sK3(X0,X1,X8),X0) )
| ~ in(X8,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f15,f18,f17,f16]) ).
fof(f24,plain,
? [X0,X1,X2,X3] :
( cartesian_product2(X0,X1) != cartesian_product2(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)) ) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f25,plain,
( ? [X0,X1,X2,X3] :
( cartesian_product2(X0,X1) != cartesian_product2(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(sK7,sK8) != cartesian_product2(sK9,sK10)
& ! [X5,X4] :
( ( 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)) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f26,plain,
( cartesian_product2(sK7,sK8) != cartesian_product2(sK9,sK10)
& ! [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)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10])],[f24,f25]) ).
fof(f27,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f28,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) )
=> ( ( ~ in(sK11(X0,X1),X1)
| ~ in(sK11(X0,X1),X0) )
& ( in(sK11(X0,X1),X1)
| in(sK11(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK11(X0,X1),X1)
| ~ in(sK11(X0,X1),X0) )
& ( in(sK11(X0,X1),X1)
| in(sK11(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f27,f28]) ).
fof(f31,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f32,plain,
! [X2,X0,X1,X8] :
( in(sK3(X0,X1,X8),X0)
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f19]) ).
fof(f33,plain,
! [X2,X0,X1,X8] :
( in(sK4(X0,X1,X8),X1)
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f19]) ).
fof(f34,plain,
! [X2,X0,X1,X8] :
( ordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)) = X8
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f19]) ).
fof(f35,plain,
! [X2,X10,X0,X1,X8,X9] :
( in(X8,X2)
| ordered_pair(X9,X10) != X8
| ~ in(X10,X1)
| ~ in(X9,X0)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f19]) ).
fof(f40,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f4]) ).
fof(f44,plain,
! [X4,X5] :
( in(ordered_pair(X4,X5),cartesian_product2(sK9,sK10))
| ~ in(ordered_pair(X4,X5),cartesian_product2(sK7,sK8)) ),
inference(cnf_transformation,[],[f26]) ).
fof(f45,plain,
! [X4,X5] :
( in(ordered_pair(X4,X5),cartesian_product2(sK7,sK8))
| ~ in(ordered_pair(X4,X5),cartesian_product2(sK9,sK10)) ),
inference(cnf_transformation,[],[f26]) ).
fof(f46,plain,
cartesian_product2(sK7,sK8) != cartesian_product2(sK9,sK10),
inference(cnf_transformation,[],[f26]) ).
fof(f47,plain,
! [X0,X1] :
( X0 = X1
| in(sK11(X0,X1),X1)
| in(sK11(X0,X1),X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f48,plain,
! [X0,X1] :
( X0 = X1
| ~ in(sK11(X0,X1),X1)
| ~ in(sK11(X0,X1),X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f51,plain,
! [X2,X10,X0,X1,X8,X9] :
( in(X8,X2)
| unordered_pair(unordered_pair(X9,X10),singleton(X9)) != X8
| ~ in(X10,X1)
| ~ in(X9,X0)
| cartesian_product2(X0,X1) != X2 ),
inference(definition_unfolding,[],[f35,f40]) ).
fof(f52,plain,
! [X2,X0,X1,X8] :
( unordered_pair(unordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)),singleton(sK3(X0,X1,X8))) = X8
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(definition_unfolding,[],[f34,f40]) ).
fof(f54,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,[],[f45,f40,f40]) ).
fof(f55,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,[],[f44,f40,f40]) ).
fof(f56,plain,
! [X2,X10,X0,X1,X9] :
( in(unordered_pair(unordered_pair(X9,X10),singleton(X9)),X2)
| ~ in(X10,X1)
| ~ in(X9,X0)
| cartesian_product2(X0,X1) != X2 ),
inference(equality_resolution,[],[f51]) ).
fof(f57,plain,
! [X10,X0,X1,X9] :
( in(unordered_pair(unordered_pair(X9,X10),singleton(X9)),cartesian_product2(X0,X1))
| ~ in(X10,X1)
| ~ in(X9,X0) ),
inference(equality_resolution,[],[f56]) ).
fof(f58,plain,
! [X0,X1,X8] :
( unordered_pair(unordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)),singleton(sK3(X0,X1,X8))) = X8
| ~ in(X8,cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f52]) ).
fof(f59,plain,
! [X0,X1,X8] :
( in(sK4(X0,X1,X8),X1)
| ~ in(X8,cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f33]) ).
fof(f60,plain,
! [X0,X1,X8] :
( in(sK3(X0,X1,X8),X0)
| ~ in(X8,cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f32]) ).
cnf(c_50,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f31]) ).
cnf(c_55,plain,
( ~ in(X0,X1)
| ~ in(X2,X3)
| in(unordered_pair(unordered_pair(X0,X2),singleton(X0)),cartesian_product2(X1,X3)) ),
inference(cnf_transformation,[],[f57]) ).
cnf(c_56,plain,
( ~ in(X0,cartesian_product2(X1,X2))
| unordered_pair(unordered_pair(sK3(X1,X2,X0),sK4(X1,X2,X0)),singleton(sK3(X1,X2,X0))) = X0 ),
inference(cnf_transformation,[],[f58]) ).
cnf(c_57,plain,
( ~ in(X0,cartesian_product2(X1,X2))
| in(sK4(X1,X2,X0),X2) ),
inference(cnf_transformation,[],[f59]) ).
cnf(c_58,plain,
( ~ in(X0,cartesian_product2(X1,X2))
| in(sK3(X1,X2,X0),X1) ),
inference(cnf_transformation,[],[f60]) ).
cnf(c_62,negated_conjecture,
cartesian_product2(sK7,sK8) != cartesian_product2(sK9,sK10),
inference(cnf_transformation,[],[f46]) ).
cnf(c_63,negated_conjecture,
( ~ 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,[],[f54]) ).
cnf(c_64,negated_conjecture,
( ~ 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,[],[f55]) ).
cnf(c_65,plain,
( ~ in(sK11(X0,X1),X0)
| ~ in(sK11(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f48]) ).
cnf(c_66,plain,
( X0 = X1
| in(sK11(X0,X1),X0)
| in(sK11(X0,X1),X1) ),
inference(cnf_transformation,[],[f47]) ).
cnf(c_80,plain,
( 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(prop_impl_just,[status(thm)],[c_63]) ).
cnf(c_81,plain,
( ~ 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(renaming,[status(thm)],[c_80]) ).
cnf(c_82,plain,
( ~ 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(prop_impl_just,[status(thm)],[c_64]) ).
cnf(c_88,plain,
( ~ in(X0,cartesian_product2(X1,X2))
| unordered_pair(unordered_pair(sK3(X1,X2,X0),sK4(X1,X2,X0)),singleton(sK3(X1,X2,X0))) = X0 ),
inference(prop_impl_just,[status(thm)],[c_56]) ).
cnf(c_237,plain,
( ~ in(X0,X1)
| ~ in(X2,X3)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X2)),cartesian_product2(X1,X3)) ),
inference(demodulation,[status(thm)],[c_55,c_50]) ).
cnf(c_259,plain,
( ~ 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_82,c_50]) ).
cnf(c_266,plain,
( ~ 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_81,c_50]) ).
cnf(c_273,plain,
( ~ in(X0,cartesian_product2(X1,X2))
| unordered_pair(singleton(sK3(X1,X2,X0)),unordered_pair(sK3(X1,X2,X0),sK4(X1,X2,X0))) = X0 ),
inference(demodulation,[status(thm)],[c_88,c_50]) ).
cnf(c_330,plain,
cartesian_product2(sK7,sK8) = sP0_iProver_def,
definition ).
cnf(c_331,plain,
cartesian_product2(sK9,sK10) = sP1_iProver_def,
definition ).
cnf(c_332,negated_conjecture,
sP0_iProver_def != sP1_iProver_def,
inference(demodulation,[status(thm)],[c_62,c_331,c_330]) ).
cnf(c_333,plain,
X0 = X0,
theory(equality) ).
cnf(c_335,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_747,plain,
( ~ in(X0,sK9)
| ~ in(X1,sK10)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sP1_iProver_def) ),
inference(superposition,[status(thm)],[c_331,c_237]) ).
cnf(c_893,plain,
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sP0_iProver_def)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sP1_iProver_def) ),
inference(light_normalisation,[status(thm)],[c_259,c_330,c_331]) ).
cnf(c_959,plain,
( ~ in(X0,sP0_iProver_def)
| unordered_pair(singleton(sK3(sK7,sK8,X0)),unordered_pair(sK3(sK7,sK8,X0),sK4(sK7,sK8,X0))) = X0 ),
inference(superposition,[status(thm)],[c_330,c_273]) ).
cnf(c_960,plain,
( ~ in(X0,sP1_iProver_def)
| unordered_pair(singleton(sK3(sK9,sK10,X0)),unordered_pair(sK3(sK9,sK10,X0),sK4(sK9,sK10,X0))) = X0 ),
inference(superposition,[status(thm)],[c_331,c_273]) ).
cnf(c_1000,plain,
( sP0_iProver_def != X0
| sP1_iProver_def != X0
| sP0_iProver_def = sP1_iProver_def ),
inference(instantiation,[status(thm)],[c_335]) ).
cnf(c_1061,plain,
( sP0_iProver_def != sP0_iProver_def
| sP1_iProver_def != sP0_iProver_def
| sP0_iProver_def = sP1_iProver_def ),
inference(instantiation,[status(thm)],[c_1000]) ).
cnf(c_1062,plain,
sP0_iProver_def = sP0_iProver_def,
inference(instantiation,[status(thm)],[c_333]) ).
cnf(c_1349,plain,
( sP1_iProver_def = sP0_iProver_def
| in(sK11(sP1_iProver_def,sP0_iProver_def),sP0_iProver_def)
| in(sK11(sP1_iProver_def,sP0_iProver_def),sP1_iProver_def) ),
inference(instantiation,[status(thm)],[c_66]) ).
cnf(c_1350,plain,
( ~ in(sK11(sP1_iProver_def,sP0_iProver_def),sP0_iProver_def)
| ~ in(sK11(sP1_iProver_def,sP0_iProver_def),sP1_iProver_def)
| sP1_iProver_def = sP0_iProver_def ),
inference(instantiation,[status(thm)],[c_65]) ).
cnf(c_1517,plain,
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sP1_iProver_def)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sP0_iProver_def) ),
inference(light_normalisation,[status(thm)],[c_266,c_330,c_331]) ).
cnf(c_1525,plain,
( ~ in(X0,sK9)
| ~ in(X1,sK10)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sP0_iProver_def) ),
inference(superposition,[status(thm)],[c_747,c_1517]) ).
cnf(c_2175,plain,
( unordered_pair(singleton(sK3(sK7,sK8,sK11(X0,sP0_iProver_def))),unordered_pair(sK3(sK7,sK8,sK11(X0,sP0_iProver_def)),sK4(sK7,sK8,sK11(X0,sP0_iProver_def)))) = sK11(X0,sP0_iProver_def)
| X0 = sP0_iProver_def
| in(sK11(X0,sP0_iProver_def),X0) ),
inference(superposition,[status(thm)],[c_66,c_959]) ).
cnf(c_2485,plain,
( unordered_pair(singleton(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def))),unordered_pair(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)),sK4(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)))) = sK11(sP1_iProver_def,sP0_iProver_def)
| unordered_pair(singleton(sK3(sK9,sK10,sK11(sP1_iProver_def,sP0_iProver_def))),unordered_pair(sK3(sK9,sK10,sK11(sP1_iProver_def,sP0_iProver_def)),sK4(sK9,sK10,sK11(sP1_iProver_def,sP0_iProver_def)))) = sK11(sP1_iProver_def,sP0_iProver_def)
| sP0_iProver_def = sP1_iProver_def ),
inference(superposition,[status(thm)],[c_2175,c_960]) ).
cnf(c_2489,plain,
( unordered_pair(singleton(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def))),unordered_pair(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)),sK4(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)))) = sK11(sP1_iProver_def,sP0_iProver_def)
| unordered_pair(singleton(sK3(sK9,sK10,sK11(sP1_iProver_def,sP0_iProver_def))),unordered_pair(sK3(sK9,sK10,sK11(sP1_iProver_def,sP0_iProver_def)),sK4(sK9,sK10,sK11(sP1_iProver_def,sP0_iProver_def)))) = sK11(sP1_iProver_def,sP0_iProver_def) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2485,c_332]) ).
cnf(c_2588,plain,
( ~ in(sK3(sK9,sK10,sK11(sP1_iProver_def,sP0_iProver_def)),sK9)
| ~ in(sK4(sK9,sK10,sK11(sP1_iProver_def,sP0_iProver_def)),sK10)
| unordered_pair(singleton(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def))),unordered_pair(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)),sK4(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)))) = sK11(sP1_iProver_def,sP0_iProver_def)
| in(sK11(sP1_iProver_def,sP0_iProver_def),sP0_iProver_def) ),
inference(superposition,[status(thm)],[c_2489,c_1525]) ).
cnf(c_2596,plain,
( ~ in(sK3(sK9,sK10,sK11(sP1_iProver_def,sP0_iProver_def)),sK9)
| ~ in(sK4(sK9,sK10,sK11(sP1_iProver_def,sP0_iProver_def)),sK10)
| unordered_pair(singleton(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def))),unordered_pair(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)),sK4(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)))) = sK11(sP1_iProver_def,sP0_iProver_def)
| in(sK11(sP1_iProver_def,sP0_iProver_def),sP1_iProver_def) ),
inference(superposition,[status(thm)],[c_2489,c_747]) ).
cnf(c_4464,plain,
( unordered_pair(singleton(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def))),unordered_pair(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)),sK4(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)))) = sK11(sP1_iProver_def,sP0_iProver_def)
| ~ in(sK4(sK9,sK10,sK11(sP1_iProver_def,sP0_iProver_def)),sK10)
| ~ in(sK3(sK9,sK10,sK11(sP1_iProver_def,sP0_iProver_def)),sK9) ),
inference(global_subsumption_just,[status(thm)],[c_2588,c_332,c_1061,c_1062,c_1350,c_2596,c_2588]) ).
cnf(c_4465,plain,
( ~ in(sK3(sK9,sK10,sK11(sP1_iProver_def,sP0_iProver_def)),sK9)
| ~ in(sK4(sK9,sK10,sK11(sP1_iProver_def,sP0_iProver_def)),sK10)
| unordered_pair(singleton(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def))),unordered_pair(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)),sK4(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)))) = sK11(sP1_iProver_def,sP0_iProver_def) ),
inference(renaming,[status(thm)],[c_4464]) ).
cnf(c_4472,plain,
( ~ in(sK3(sK9,sK10,sK11(sP1_iProver_def,sP0_iProver_def)),sK9)
| ~ in(sK11(sP1_iProver_def,sP0_iProver_def),cartesian_product2(sK9,sK10))
| unordered_pair(singleton(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def))),unordered_pair(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)),sK4(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)))) = sK11(sP1_iProver_def,sP0_iProver_def) ),
inference(superposition,[status(thm)],[c_57,c_4465]) ).
cnf(c_4473,plain,
( ~ in(sK3(sK9,sK10,sK11(sP1_iProver_def,sP0_iProver_def)),sK9)
| ~ in(sK11(sP1_iProver_def,sP0_iProver_def),sP1_iProver_def)
| unordered_pair(singleton(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def))),unordered_pair(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)),sK4(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)))) = sK11(sP1_iProver_def,sP0_iProver_def) ),
inference(light_normalisation,[status(thm)],[c_4472,c_331]) ).
cnf(c_5616,plain,
( ~ in(sK11(sP1_iProver_def,sP0_iProver_def),cartesian_product2(sK9,sK10))
| ~ in(sK11(sP1_iProver_def,sP0_iProver_def),sP1_iProver_def)
| unordered_pair(singleton(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def))),unordered_pair(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)),sK4(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)))) = sK11(sP1_iProver_def,sP0_iProver_def) ),
inference(superposition,[status(thm)],[c_58,c_4473]) ).
cnf(c_5617,plain,
( ~ in(sK11(sP1_iProver_def,sP0_iProver_def),sP1_iProver_def)
| unordered_pair(singleton(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def))),unordered_pair(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)),sK4(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)))) = sK11(sP1_iProver_def,sP0_iProver_def) ),
inference(light_normalisation,[status(thm)],[c_5616,c_331]) ).
cnf(c_5627,plain,
( unordered_pair(singleton(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def))),unordered_pair(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)),sK4(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)))) = sK11(sP1_iProver_def,sP0_iProver_def)
| sP0_iProver_def = sP1_iProver_def ),
inference(superposition,[status(thm)],[c_2175,c_5617]) ).
cnf(c_5628,plain,
unordered_pair(singleton(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def))),unordered_pair(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)),sK4(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)))) = sK11(sP1_iProver_def,sP0_iProver_def),
inference(forward_subsumption_resolution,[status(thm)],[c_5627,c_332]) ).
cnf(c_5656,plain,
( ~ in(sK11(sP1_iProver_def,sP0_iProver_def),sP1_iProver_def)
| in(unordered_pair(singleton(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def))),unordered_pair(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)),sK4(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)))),sP0_iProver_def) ),
inference(superposition,[status(thm)],[c_5628,c_1517]) ).
cnf(c_5661,plain,
( ~ in(sK11(sP1_iProver_def,sP0_iProver_def),sP0_iProver_def)
| in(unordered_pair(singleton(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def))),unordered_pair(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)),sK4(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)))),sP1_iProver_def) ),
inference(superposition,[status(thm)],[c_5628,c_893]) ).
cnf(c_5701,plain,
( ~ in(sK11(sP1_iProver_def,sP0_iProver_def),sP0_iProver_def)
| in(sK11(sP1_iProver_def,sP0_iProver_def),sP1_iProver_def) ),
inference(light_normalisation,[status(thm)],[c_5661,c_5628]) ).
cnf(c_5704,plain,
( ~ in(sK11(sP1_iProver_def,sP0_iProver_def),sP1_iProver_def)
| in(sK11(sP1_iProver_def,sP0_iProver_def),sP0_iProver_def) ),
inference(light_normalisation,[status(thm)],[c_5656,c_5628]) ).
cnf(c_5894,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_5701,c_5704,c_1349,c_1350,c_1062,c_1061,c_332]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET955+1 : TPTP v8.2.0. Bugfixed v4.0.0.
% 0.00/0.11 % Command : run_iprover %s %d THM
% 0.10/0.31 % Computer : n021.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Sun Jun 23 15:59:39 EDT 2024
% 0.16/0.31 % CPUTime :
% 0.16/0.42 Running first-order theorem proving
% 0.16/0.43 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.89/1.12 % SZS status Started for theBenchmark.p
% 3.89/1.12 % SZS status Theorem for theBenchmark.p
% 3.89/1.12
% 3.89/1.12 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.89/1.12
% 3.89/1.12 ------ iProver source info
% 3.89/1.12
% 3.89/1.12 git: date: 2024-06-12 09:56:46 +0000
% 3.89/1.12 git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 3.89/1.12 git: non_committed_changes: false
% 3.89/1.12
% 3.89/1.12 ------ Parsing...
% 3.89/1.12 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.89/1.12
% 3.89/1.12 ------ Preprocessing... sup_sim: 7 sf_s rm: 1 0s sf_e pe_s pe_e
% 3.89/1.12
% 3.89/1.12 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.89/1.12
% 3.89/1.12 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.89/1.12 ------ Proving...
% 3.89/1.12 ------ Problem Properties
% 3.89/1.12
% 3.89/1.12
% 3.89/1.12 clauses 20
% 3.89/1.12 conjectures 1
% 3.89/1.12 EPR 4
% 3.89/1.12 Horn 16
% 3.89/1.12 unary 7
% 3.89/1.12 binary 6
% 3.89/1.12 lits 42
% 3.89/1.12 lits eq 13
% 3.89/1.12 fd_pure 0
% 3.89/1.12 fd_pseudo 0
% 3.89/1.12 fd_cond 0
% 3.89/1.12 fd_pseudo_cond 6
% 3.89/1.12 AC symbols 0
% 3.89/1.12
% 3.89/1.12 ------ Schedule dynamic 5 is on
% 3.89/1.12
% 3.89/1.12 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.89/1.12
% 3.89/1.12
% 3.89/1.12 ------
% 3.89/1.12 Current options:
% 3.89/1.12 ------
% 3.89/1.12
% 3.89/1.12
% 3.89/1.12
% 3.89/1.12
% 3.89/1.12 ------ Proving...
% 3.89/1.12
% 3.89/1.12
% 3.89/1.12 % SZS status Theorem for theBenchmark.p
% 3.89/1.12
% 3.89/1.12 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.89/1.12
% 3.89/1.12
%------------------------------------------------------------------------------