TSTP Solution File: SET772+4 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET772+4 : TPTP v8.2.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n029.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 14:35:41 EDT 2024
% Result : Theorem 81.37s 11.77s
% Output : CNFRefutation 81.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 24
% Syntax : Number of formulae : 195 ( 17 unt; 0 def)
% Number of atoms : 821 ( 33 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 943 ( 317 ~; 334 |; 212 &)
% ( 30 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 24 ( 24 usr; 4 con; 0-3 aty)
% Number of variables : 602 ( 13 sgn 389 !; 78 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
fof(f3,axiom,
! [X2,X0] :
( member(X2,power_set(X0))
<=> subset(X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_set) ).
fof(f4,axiom,
! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection) ).
fof(f5,axiom,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).
fof(f6,axiom,
! [X2] : ~ member(X2,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).
fof(f7,axiom,
! [X1,X0,X3] :
( member(X1,difference(X3,X0))
<=> ( ~ member(X1,X0)
& member(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference) ).
fof(f8,axiom,
! [X2,X0] :
( member(X2,singleton(X0))
<=> X0 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
fof(f9,axiom,
! [X2,X0,X1] :
( member(X2,unordered_pair(X0,X1))
<=> ( X1 = X2
| X0 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair) ).
fof(f10,axiom,
! [X2,X0] :
( member(X2,sum(X0))
<=> ? [X4] :
( member(X2,X4)
& member(X4,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum) ).
fof(f11,axiom,
! [X2,X0] :
( member(X2,product(X0))
<=> ! [X4] :
( member(X4,X0)
=> member(X2,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product) ).
fof(f13,axiom,
! [X0,X3] :
( partition(X0,X3)
<=> ( ! [X2,X4] :
( ( member(X4,X0)
& member(X2,X0) )
=> ( ? [X5] :
( member(X5,X4)
& member(X5,X2) )
=> X2 = X4 ) )
& ! [X2] :
( member(X2,X3)
=> ? [X4] :
( member(X2,X4)
& member(X4,X0) ) )
& ! [X2] :
( member(X2,X0)
=> subset(X2,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partition) ).
fof(f14,axiom,
! [X0,X6] :
( equivalence(X6,X0)
<=> ( ! [X2,X4,X5] :
( ( member(X5,X0)
& member(X4,X0)
& member(X2,X0) )
=> ( ( apply(X6,X4,X5)
& apply(X6,X2,X4) )
=> apply(X6,X2,X5) ) )
& ! [X2,X4] :
( ( member(X4,X0)
& member(X2,X0) )
=> ( apply(X6,X2,X4)
=> apply(X6,X4,X2) ) )
& ! [X2] :
( member(X2,X0)
=> apply(X6,X2,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence) ).
fof(f15,axiom,
! [X6,X3,X0,X2] :
( member(X2,equivalence_class(X0,X3,X6))
<=> ( apply(X6,X0,X2)
& member(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_class) ).
fof(f17,conjecture,
! [X0,X3,X6] :
( partition(X0,X3)
=> ( ! [X2,X4] :
( ( member(X4,X3)
& member(X2,X3) )
=> ( apply(X6,X2,X4)
<=> ? [X5] :
( member(X4,X5)
& member(X2,X5)
& member(X5,X0) ) ) )
=> equivalence(X6,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIII08) ).
fof(f18,negated_conjecture,
~ ! [X0,X3,X6] :
( partition(X0,X3)
=> ( ! [X2,X4] :
( ( member(X4,X3)
& member(X2,X3) )
=> ( apply(X6,X2,X4)
<=> ? [X5] :
( member(X4,X5)
& member(X2,X5)
& member(X5,X0) ) ) )
=> equivalence(X6,X3) ) ),
inference(negated_conjecture,[],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( member(X0,power_set(X1))
<=> subset(X0,X1) ),
inference(rectify,[],[f3]) ).
fof(f20,plain,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
<=> ( member(X0,X2)
& member(X0,X1) ) ),
inference(rectify,[],[f4]) ).
fof(f21,plain,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
<=> ( member(X0,X2)
| member(X0,X1) ) ),
inference(rectify,[],[f5]) ).
fof(f22,plain,
! [X0] : ~ member(X0,empty_set),
inference(rectify,[],[f6]) ).
fof(f23,plain,
! [X0,X1,X2] :
( member(X0,difference(X2,X1))
<=> ( ~ member(X0,X1)
& member(X0,X2) ) ),
inference(rectify,[],[f7]) ).
fof(f24,plain,
! [X0,X1] :
( member(X0,singleton(X1))
<=> X0 = X1 ),
inference(rectify,[],[f8]) ).
fof(f25,plain,
! [X0,X1,X2] :
( member(X0,unordered_pair(X1,X2))
<=> ( X0 = X2
| X0 = X1 ) ),
inference(rectify,[],[f9]) ).
fof(f26,plain,
! [X0,X1] :
( member(X0,sum(X1))
<=> ? [X2] :
( member(X0,X2)
& member(X2,X1) ) ),
inference(rectify,[],[f10]) ).
fof(f27,plain,
! [X0,X1] :
( member(X0,product(X1))
<=> ! [X2] :
( member(X2,X1)
=> member(X0,X2) ) ),
inference(rectify,[],[f11]) ).
fof(f28,plain,
! [X0,X1] :
( partition(X0,X1)
<=> ( ! [X2,X3] :
( ( member(X3,X0)
& member(X2,X0) )
=> ( ? [X4] :
( member(X4,X3)
& member(X4,X2) )
=> X2 = X3 ) )
& ! [X5] :
( member(X5,X1)
=> ? [X6] :
( member(X5,X6)
& member(X6,X0) ) )
& ! [X7] :
( member(X7,X0)
=> subset(X7,X1) ) ) ),
inference(rectify,[],[f13]) ).
fof(f29,plain,
! [X0,X1] :
( equivalence(X1,X0)
<=> ( ! [X2,X3,X4] :
( ( member(X4,X0)
& member(X3,X0)
& member(X2,X0) )
=> ( ( apply(X1,X3,X4)
& apply(X1,X2,X3) )
=> apply(X1,X2,X4) ) )
& ! [X5,X6] :
( ( member(X6,X0)
& member(X5,X0) )
=> ( apply(X1,X5,X6)
=> apply(X1,X6,X5) ) )
& ! [X7] :
( member(X7,X0)
=> apply(X1,X7,X7) ) ) ),
inference(rectify,[],[f14]) ).
fof(f30,plain,
! [X0,X1,X2,X3] :
( member(X3,equivalence_class(X2,X1,X0))
<=> ( apply(X0,X2,X3)
& member(X3,X1) ) ),
inference(rectify,[],[f15]) ).
fof(f32,plain,
~ ! [X0,X1,X2] :
( partition(X0,X1)
=> ( ! [X3,X4] :
( ( member(X4,X1)
& member(X3,X1) )
=> ( apply(X2,X3,X4)
<=> ? [X5] :
( member(X4,X5)
& member(X3,X5)
& member(X5,X0) ) ) )
=> equivalence(X2,X1) ) ),
inference(rectify,[],[f18]) ).
fof(f33,plain,
! [X0,X1] :
( ( ! [X2,X3,X4] :
( ( member(X4,X0)
& member(X3,X0)
& member(X2,X0) )
=> ( ( apply(X1,X3,X4)
& apply(X1,X2,X3) )
=> apply(X1,X2,X4) ) )
& ! [X5,X6] :
( ( member(X6,X0)
& member(X5,X0) )
=> ( apply(X1,X5,X6)
=> apply(X1,X6,X5) ) )
& ! [X7] :
( member(X7,X0)
=> apply(X1,X7,X7) ) )
=> equivalence(X1,X0) ),
inference(unused_predicate_definition_removal,[],[f29]) ).
fof(f34,plain,
! [X0,X1] :
( partition(X0,X1)
=> ( ! [X2,X3] :
( ( member(X3,X0)
& member(X2,X0) )
=> ( ? [X4] :
( member(X4,X3)
& member(X4,X2) )
=> X2 = X3 ) )
& ! [X5] :
( member(X5,X1)
=> ? [X6] :
( member(X5,X6)
& member(X6,X0) ) )
& ! [X7] :
( member(X7,X0)
=> subset(X7,X1) ) ) ),
inference(unused_predicate_definition_removal,[],[f28]) ).
fof(f35,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f36,plain,
! [X0,X1] :
( member(X0,product(X1))
<=> ! [X2] :
( member(X0,X2)
| ~ member(X2,X1) ) ),
inference(ennf_transformation,[],[f27]) ).
fof(f37,plain,
! [X0,X1] :
( ( ! [X2,X3] :
( X2 = X3
| ! [X4] :
( ~ member(X4,X3)
| ~ member(X4,X2) )
| ~ member(X3,X0)
| ~ member(X2,X0) )
& ! [X5] :
( ? [X6] :
( member(X5,X6)
& member(X6,X0) )
| ~ member(X5,X1) )
& ! [X7] :
( subset(X7,X1)
| ~ member(X7,X0) ) )
| ~ partition(X0,X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f38,plain,
! [X0,X1] :
( ( ! [X2,X3] :
( X2 = X3
| ! [X4] :
( ~ member(X4,X3)
| ~ member(X4,X2) )
| ~ member(X3,X0)
| ~ member(X2,X0) )
& ! [X5] :
( ? [X6] :
( member(X5,X6)
& member(X6,X0) )
| ~ member(X5,X1) )
& ! [X7] :
( subset(X7,X1)
| ~ member(X7,X0) ) )
| ~ partition(X0,X1) ),
inference(flattening,[],[f37]) ).
fof(f39,plain,
! [X0,X1] :
( equivalence(X1,X0)
| ? [X2,X3,X4] :
( ~ apply(X1,X2,X4)
& apply(X1,X3,X4)
& apply(X1,X2,X3)
& member(X4,X0)
& member(X3,X0)
& member(X2,X0) )
| ? [X5,X6] :
( ~ apply(X1,X6,X5)
& apply(X1,X5,X6)
& member(X6,X0)
& member(X5,X0) )
| ? [X7] :
( ~ apply(X1,X7,X7)
& member(X7,X0) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f40,plain,
! [X0,X1] :
( equivalence(X1,X0)
| ? [X2,X3,X4] :
( ~ apply(X1,X2,X4)
& apply(X1,X3,X4)
& apply(X1,X2,X3)
& member(X4,X0)
& member(X3,X0)
& member(X2,X0) )
| ? [X5,X6] :
( ~ apply(X1,X6,X5)
& apply(X1,X5,X6)
& member(X6,X0)
& member(X5,X0) )
| ? [X7] :
( ~ apply(X1,X7,X7)
& member(X7,X0) ) ),
inference(flattening,[],[f39]) ).
fof(f41,plain,
? [X0,X1,X2] :
( ~ equivalence(X2,X1)
& ! [X3,X4] :
( ( apply(X2,X3,X4)
<=> ? [X5] :
( member(X4,X5)
& member(X3,X5)
& member(X5,X0) ) )
| ~ member(X4,X1)
| ~ member(X3,X1) )
& partition(X0,X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f42,plain,
? [X0,X1,X2] :
( ~ equivalence(X2,X1)
& ! [X3,X4] :
( ( apply(X2,X3,X4)
<=> ? [X5] :
( member(X4,X5)
& member(X3,X5)
& member(X5,X0) ) )
| ~ member(X4,X1)
| ~ member(X3,X1) )
& partition(X0,X1) ),
inference(flattening,[],[f41]) ).
fof(f43,plain,
! [X1,X0] :
( ? [X2,X3,X4] :
( ~ apply(X1,X2,X4)
& apply(X1,X3,X4)
& apply(X1,X2,X3)
& member(X4,X0)
& member(X3,X0)
& member(X2,X0) )
| ~ sP0(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f44,plain,
! [X0,X1] :
( equivalence(X1,X0)
| sP0(X1,X0)
| ? [X5,X6] :
( ~ apply(X1,X6,X5)
& apply(X1,X5,X6)
& member(X6,X0)
& member(X5,X0) )
| ? [X7] :
( ~ apply(X1,X7,X7)
& member(X7,X0) ) ),
inference(definition_folding,[],[f40,f43]) ).
fof(f45,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f35]) ).
fof(f46,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f45]) ).
fof(f47,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK1(X0,X1),X1)
& member(sK1(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f48,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK1(X0,X1),X1)
& member(sK1(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f46,f47]) ).
fof(f49,plain,
! [X0,X1] :
( ( member(X0,power_set(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ member(X0,power_set(X1)) ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) )
& ( ( member(X0,X2)
& member(X0,X1) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(nnf_transformation,[],[f20]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) )
& ( ( member(X0,X2)
& member(X0,X1) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(flattening,[],[f50]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ( member(X0,union(X1,X2))
| ( ~ member(X0,X2)
& ~ member(X0,X1) ) )
& ( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ( member(X0,union(X1,X2))
| ( ~ member(X0,X2)
& ~ member(X0,X1) ) )
& ( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ) ),
inference(flattening,[],[f52]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ( member(X0,difference(X2,X1))
| member(X0,X1)
| ~ member(X0,X2) )
& ( ( ~ member(X0,X1)
& member(X0,X2) )
| ~ member(X0,difference(X2,X1)) ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ( member(X0,difference(X2,X1))
| member(X0,X1)
| ~ member(X0,X2) )
& ( ( ~ member(X0,X1)
& member(X0,X2) )
| ~ member(X0,difference(X2,X1)) ) ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
! [X0,X1] :
( ( member(X0,singleton(X1))
| X0 != X1 )
& ( X0 = X1
| ~ member(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f24]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ( X0 != X2
& X0 != X1 ) )
& ( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(nnf_transformation,[],[f25]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ( X0 != X2
& X0 != X1 ) )
& ( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(flattening,[],[f57]) ).
fof(f59,plain,
! [X0,X1] :
( ( member(X0,sum(X1))
| ! [X2] :
( ~ member(X0,X2)
| ~ member(X2,X1) ) )
& ( ? [X2] :
( member(X0,X2)
& member(X2,X1) )
| ~ member(X0,sum(X1)) ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f60,plain,
! [X0,X1] :
( ( member(X0,sum(X1))
| ! [X2] :
( ~ member(X0,X2)
| ~ member(X2,X1) ) )
& ( ? [X3] :
( member(X0,X3)
& member(X3,X1) )
| ~ member(X0,sum(X1)) ) ),
inference(rectify,[],[f59]) ).
fof(f61,plain,
! [X0,X1] :
( ? [X3] :
( member(X0,X3)
& member(X3,X1) )
=> ( member(X0,sK2(X0,X1))
& member(sK2(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f62,plain,
! [X0,X1] :
( ( member(X0,sum(X1))
| ! [X2] :
( ~ member(X0,X2)
| ~ member(X2,X1) ) )
& ( ( member(X0,sK2(X0,X1))
& member(sK2(X0,X1),X1) )
| ~ member(X0,sum(X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f60,f61]) ).
fof(f63,plain,
! [X0,X1] :
( ( member(X0,product(X1))
| ? [X2] :
( ~ member(X0,X2)
& member(X2,X1) ) )
& ( ! [X2] :
( member(X0,X2)
| ~ member(X2,X1) )
| ~ member(X0,product(X1)) ) ),
inference(nnf_transformation,[],[f36]) ).
fof(f64,plain,
! [X0,X1] :
( ( member(X0,product(X1))
| ? [X2] :
( ~ member(X0,X2)
& member(X2,X1) ) )
& ( ! [X3] :
( member(X0,X3)
| ~ member(X3,X1) )
| ~ member(X0,product(X1)) ) ),
inference(rectify,[],[f63]) ).
fof(f65,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X0,X2)
& member(X2,X1) )
=> ( ~ member(X0,sK3(X0,X1))
& member(sK3(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f66,plain,
! [X0,X1] :
( ( member(X0,product(X1))
| ( ~ member(X0,sK3(X0,X1))
& member(sK3(X0,X1),X1) ) )
& ( ! [X3] :
( member(X0,X3)
| ~ member(X3,X1) )
| ~ member(X0,product(X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f64,f65]) ).
fof(f67,plain,
! [X0,X5] :
( ? [X6] :
( member(X5,X6)
& member(X6,X0) )
=> ( member(X5,sK4(X0,X5))
& member(sK4(X0,X5),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f68,plain,
! [X0,X1] :
( ( ! [X2,X3] :
( X2 = X3
| ! [X4] :
( ~ member(X4,X3)
| ~ member(X4,X2) )
| ~ member(X3,X0)
| ~ member(X2,X0) )
& ! [X5] :
( ( member(X5,sK4(X0,X5))
& member(sK4(X0,X5),X0) )
| ~ member(X5,X1) )
& ! [X7] :
( subset(X7,X1)
| ~ member(X7,X0) ) )
| ~ partition(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f38,f67]) ).
fof(f69,plain,
! [X1,X0] :
( ? [X2,X3,X4] :
( ~ apply(X1,X2,X4)
& apply(X1,X3,X4)
& apply(X1,X2,X3)
& member(X4,X0)
& member(X3,X0)
& member(X2,X0) )
| ~ sP0(X1,X0) ),
inference(nnf_transformation,[],[f43]) ).
fof(f70,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( ~ apply(X0,X2,X4)
& apply(X0,X3,X4)
& apply(X0,X2,X3)
& member(X4,X1)
& member(X3,X1)
& member(X2,X1) )
| ~ sP0(X0,X1) ),
inference(rectify,[],[f69]) ).
fof(f71,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( ~ apply(X0,X2,X4)
& apply(X0,X3,X4)
& apply(X0,X2,X3)
& member(X4,X1)
& member(X3,X1)
& member(X2,X1) )
=> ( ~ apply(X0,sK5(X0,X1),sK7(X0,X1))
& apply(X0,sK6(X0,X1),sK7(X0,X1))
& apply(X0,sK5(X0,X1),sK6(X0,X1))
& member(sK7(X0,X1),X1)
& member(sK6(X0,X1),X1)
& member(sK5(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f72,plain,
! [X0,X1] :
( ( ~ apply(X0,sK5(X0,X1),sK7(X0,X1))
& apply(X0,sK6(X0,X1),sK7(X0,X1))
& apply(X0,sK5(X0,X1),sK6(X0,X1))
& member(sK7(X0,X1),X1)
& member(sK6(X0,X1),X1)
& member(sK5(X0,X1),X1) )
| ~ sP0(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f70,f71]) ).
fof(f73,plain,
! [X0,X1] :
( equivalence(X1,X0)
| sP0(X1,X0)
| ? [X2,X3] :
( ~ apply(X1,X3,X2)
& apply(X1,X2,X3)
& member(X3,X0)
& member(X2,X0) )
| ? [X4] :
( ~ apply(X1,X4,X4)
& member(X4,X0) ) ),
inference(rectify,[],[f44]) ).
fof(f74,plain,
! [X0,X1] :
( ? [X2,X3] :
( ~ apply(X1,X3,X2)
& apply(X1,X2,X3)
& member(X3,X0)
& member(X2,X0) )
=> ( ~ apply(X1,sK9(X0,X1),sK8(X0,X1))
& apply(X1,sK8(X0,X1),sK9(X0,X1))
& member(sK9(X0,X1),X0)
& member(sK8(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f75,plain,
! [X0,X1] :
( ? [X4] :
( ~ apply(X1,X4,X4)
& member(X4,X0) )
=> ( ~ apply(X1,sK10(X0,X1),sK10(X0,X1))
& member(sK10(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f76,plain,
! [X0,X1] :
( equivalence(X1,X0)
| sP0(X1,X0)
| ( ~ apply(X1,sK9(X0,X1),sK8(X0,X1))
& apply(X1,sK8(X0,X1),sK9(X0,X1))
& member(sK9(X0,X1),X0)
& member(sK8(X0,X1),X0) )
| ( ~ apply(X1,sK10(X0,X1),sK10(X0,X1))
& member(sK10(X0,X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f73,f75,f74]) ).
fof(f77,plain,
! [X0,X1,X2,X3] :
( ( member(X3,equivalence_class(X2,X1,X0))
| ~ apply(X0,X2,X3)
| ~ member(X3,X1) )
& ( ( apply(X0,X2,X3)
& member(X3,X1) )
| ~ member(X3,equivalence_class(X2,X1,X0)) ) ),
inference(nnf_transformation,[],[f30]) ).
fof(f78,plain,
! [X0,X1,X2,X3] :
( ( member(X3,equivalence_class(X2,X1,X0))
| ~ apply(X0,X2,X3)
| ~ member(X3,X1) )
& ( ( apply(X0,X2,X3)
& member(X3,X1) )
| ~ member(X3,equivalence_class(X2,X1,X0)) ) ),
inference(flattening,[],[f77]) ).
fof(f79,plain,
? [X0,X1,X2] :
( ~ equivalence(X2,X1)
& ! [X3,X4] :
( ( ( apply(X2,X3,X4)
| ! [X5] :
( ~ member(X4,X5)
| ~ member(X3,X5)
| ~ member(X5,X0) ) )
& ( ? [X5] :
( member(X4,X5)
& member(X3,X5)
& member(X5,X0) )
| ~ apply(X2,X3,X4) ) )
| ~ member(X4,X1)
| ~ member(X3,X1) )
& partition(X0,X1) ),
inference(nnf_transformation,[],[f42]) ).
fof(f80,plain,
? [X0,X1,X2] :
( ~ equivalence(X2,X1)
& ! [X3,X4] :
( ( ( apply(X2,X3,X4)
| ! [X5] :
( ~ member(X4,X5)
| ~ member(X3,X5)
| ~ member(X5,X0) ) )
& ( ? [X6] :
( member(X4,X6)
& member(X3,X6)
& member(X6,X0) )
| ~ apply(X2,X3,X4) ) )
| ~ member(X4,X1)
| ~ member(X3,X1) )
& partition(X0,X1) ),
inference(rectify,[],[f79]) ).
fof(f81,plain,
( ? [X0,X1,X2] :
( ~ equivalence(X2,X1)
& ! [X3,X4] :
( ( ( apply(X2,X3,X4)
| ! [X5] :
( ~ member(X4,X5)
| ~ member(X3,X5)
| ~ member(X5,X0) ) )
& ( ? [X6] :
( member(X4,X6)
& member(X3,X6)
& member(X6,X0) )
| ~ apply(X2,X3,X4) ) )
| ~ member(X4,X1)
| ~ member(X3,X1) )
& partition(X0,X1) )
=> ( ~ equivalence(sK13,sK12)
& ! [X4,X3] :
( ( ( apply(sK13,X3,X4)
| ! [X5] :
( ~ member(X4,X5)
| ~ member(X3,X5)
| ~ member(X5,sK11) ) )
& ( ? [X6] :
( member(X4,X6)
& member(X3,X6)
& member(X6,sK11) )
| ~ apply(sK13,X3,X4) ) )
| ~ member(X4,sK12)
| ~ member(X3,sK12) )
& partition(sK11,sK12) ) ),
introduced(choice_axiom,[]) ).
fof(f82,plain,
! [X3,X4] :
( ? [X6] :
( member(X4,X6)
& member(X3,X6)
& member(X6,sK11) )
=> ( member(X4,sK14(X3,X4))
& member(X3,sK14(X3,X4))
& member(sK14(X3,X4),sK11) ) ),
introduced(choice_axiom,[]) ).
fof(f83,plain,
( ~ equivalence(sK13,sK12)
& ! [X3,X4] :
( ( ( apply(sK13,X3,X4)
| ! [X5] :
( ~ member(X4,X5)
| ~ member(X3,X5)
| ~ member(X5,sK11) ) )
& ( ( member(X4,sK14(X3,X4))
& member(X3,sK14(X3,X4))
& member(sK14(X3,X4),sK11) )
| ~ apply(sK13,X3,X4) ) )
| ~ member(X4,sK12)
| ~ member(X3,sK12) )
& partition(sK11,sK12) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13,sK14])],[f80,f82,f81]) ).
fof(f84,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f85,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f86,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f87,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f49]) ).
fof(f88,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f49]) ).
fof(f89,plain,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f51]) ).
fof(f90,plain,
! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f51]) ).
fof(f91,plain,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f92,plain,
! [X2,X0,X1] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f53]) ).
fof(f93,plain,
! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f94,plain,
! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f53]) ).
fof(f95,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f22]) ).
fof(f96,plain,
! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,difference(X2,X1)) ),
inference(cnf_transformation,[],[f55]) ).
fof(f97,plain,
! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,difference(X2,X1)) ),
inference(cnf_transformation,[],[f55]) ).
fof(f98,plain,
! [X2,X0,X1] :
( member(X0,difference(X2,X1))
| member(X0,X1)
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f55]) ).
fof(f99,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f56]) ).
fof(f100,plain,
! [X0,X1] :
( member(X0,singleton(X1))
| X0 != X1 ),
inference(cnf_transformation,[],[f56]) ).
fof(f101,plain,
! [X2,X0,X1] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f58]) ).
fof(f102,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| X0 != X1 ),
inference(cnf_transformation,[],[f58]) ).
fof(f103,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| X0 != X2 ),
inference(cnf_transformation,[],[f58]) ).
fof(f104,plain,
! [X0,X1] :
( member(sK2(X0,X1),X1)
| ~ member(X0,sum(X1)) ),
inference(cnf_transformation,[],[f62]) ).
fof(f105,plain,
! [X0,X1] :
( member(X0,sK2(X0,X1))
| ~ member(X0,sum(X1)) ),
inference(cnf_transformation,[],[f62]) ).
fof(f106,plain,
! [X2,X0,X1] :
( member(X0,sum(X1))
| ~ member(X0,X2)
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f107,plain,
! [X3,X0,X1] :
( member(X0,X3)
| ~ member(X3,X1)
| ~ member(X0,product(X1)) ),
inference(cnf_transformation,[],[f66]) ).
fof(f108,plain,
! [X0,X1] :
( member(X0,product(X1))
| member(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f109,plain,
! [X0,X1] :
( member(X0,product(X1))
| ~ member(X0,sK3(X0,X1)) ),
inference(cnf_transformation,[],[f66]) ).
fof(f110,plain,
! [X0,X1,X7] :
( subset(X7,X1)
| ~ member(X7,X0)
| ~ partition(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f111,plain,
! [X0,X1,X5] :
( member(sK4(X0,X5),X0)
| ~ member(X5,X1)
| ~ partition(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f112,plain,
! [X0,X1,X5] :
( member(X5,sK4(X0,X5))
| ~ member(X5,X1)
| ~ partition(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f113,plain,
! [X2,X3,X0,X1,X4] :
( X2 = X3
| ~ member(X4,X3)
| ~ member(X4,X2)
| ~ member(X3,X0)
| ~ member(X2,X0)
| ~ partition(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f114,plain,
! [X0,X1] :
( member(sK5(X0,X1),X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f115,plain,
! [X0,X1] :
( member(sK6(X0,X1),X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f116,plain,
! [X0,X1] :
( member(sK7(X0,X1),X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f117,plain,
! [X0,X1] :
( apply(X0,sK5(X0,X1),sK6(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f118,plain,
! [X0,X1] :
( apply(X0,sK6(X0,X1),sK7(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f119,plain,
! [X0,X1] :
( ~ apply(X0,sK5(X0,X1),sK7(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f120,plain,
! [X0,X1] :
( equivalence(X1,X0)
| sP0(X1,X0)
| member(sK8(X0,X1),X0)
| member(sK10(X0,X1),X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f121,plain,
! [X0,X1] :
( equivalence(X1,X0)
| sP0(X1,X0)
| member(sK8(X0,X1),X0)
| ~ apply(X1,sK10(X0,X1),sK10(X0,X1)) ),
inference(cnf_transformation,[],[f76]) ).
fof(f122,plain,
! [X0,X1] :
( equivalence(X1,X0)
| sP0(X1,X0)
| member(sK9(X0,X1),X0)
| member(sK10(X0,X1),X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f123,plain,
! [X0,X1] :
( equivalence(X1,X0)
| sP0(X1,X0)
| member(sK9(X0,X1),X0)
| ~ apply(X1,sK10(X0,X1),sK10(X0,X1)) ),
inference(cnf_transformation,[],[f76]) ).
fof(f124,plain,
! [X0,X1] :
( equivalence(X1,X0)
| sP0(X1,X0)
| apply(X1,sK8(X0,X1),sK9(X0,X1))
| member(sK10(X0,X1),X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f125,plain,
! [X0,X1] :
( equivalence(X1,X0)
| sP0(X1,X0)
| apply(X1,sK8(X0,X1),sK9(X0,X1))
| ~ apply(X1,sK10(X0,X1),sK10(X0,X1)) ),
inference(cnf_transformation,[],[f76]) ).
fof(f126,plain,
! [X0,X1] :
( equivalence(X1,X0)
| sP0(X1,X0)
| ~ apply(X1,sK9(X0,X1),sK8(X0,X1))
| member(sK10(X0,X1),X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f127,plain,
! [X0,X1] :
( equivalence(X1,X0)
| sP0(X1,X0)
| ~ apply(X1,sK9(X0,X1),sK8(X0,X1))
| ~ apply(X1,sK10(X0,X1),sK10(X0,X1)) ),
inference(cnf_transformation,[],[f76]) ).
fof(f128,plain,
! [X2,X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,equivalence_class(X2,X1,X0)) ),
inference(cnf_transformation,[],[f78]) ).
fof(f129,plain,
! [X2,X3,X0,X1] :
( apply(X0,X2,X3)
| ~ member(X3,equivalence_class(X2,X1,X0)) ),
inference(cnf_transformation,[],[f78]) ).
fof(f130,plain,
! [X2,X3,X0,X1] :
( member(X3,equivalence_class(X2,X1,X0))
| ~ apply(X0,X2,X3)
| ~ member(X3,X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f131,plain,
partition(sK11,sK12),
inference(cnf_transformation,[],[f83]) ).
fof(f132,plain,
! [X3,X4] :
( member(sK14(X3,X4),sK11)
| ~ apply(sK13,X3,X4)
| ~ member(X4,sK12)
| ~ member(X3,sK12) ),
inference(cnf_transformation,[],[f83]) ).
fof(f133,plain,
! [X3,X4] :
( member(X3,sK14(X3,X4))
| ~ apply(sK13,X3,X4)
| ~ member(X4,sK12)
| ~ member(X3,sK12) ),
inference(cnf_transformation,[],[f83]) ).
fof(f134,plain,
! [X3,X4] :
( member(X4,sK14(X3,X4))
| ~ apply(sK13,X3,X4)
| ~ member(X4,sK12)
| ~ member(X3,sK12) ),
inference(cnf_transformation,[],[f83]) ).
fof(f135,plain,
! [X3,X4,X5] :
( apply(sK13,X3,X4)
| ~ member(X4,X5)
| ~ member(X3,X5)
| ~ member(X5,sK11)
| ~ member(X4,sK12)
| ~ member(X3,sK12) ),
inference(cnf_transformation,[],[f83]) ).
fof(f136,plain,
~ equivalence(sK13,sK12),
inference(cnf_transformation,[],[f83]) ).
fof(f137,plain,
! [X1] : member(X1,singleton(X1)),
inference(equality_resolution,[],[f100]) ).
fof(f138,plain,
! [X2,X1] : member(X2,unordered_pair(X1,X2)),
inference(equality_resolution,[],[f103]) ).
fof(f139,plain,
! [X2,X1] : member(X1,unordered_pair(X1,X2)),
inference(equality_resolution,[],[f102]) ).
cnf(c_49,plain,
( ~ member(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f86]) ).
cnf(c_50,plain,
( member(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f85]) ).
cnf(c_51,plain,
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f84]) ).
cnf(c_52,plain,
( ~ subset(X0,X1)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f88]) ).
cnf(c_53,plain,
( ~ member(X0,power_set(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f87]) ).
cnf(c_54,plain,
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f91]) ).
cnf(c_55,plain,
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[],[f90]) ).
cnf(c_56,plain,
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f89]) ).
cnf(c_57,plain,
( ~ member(X0,X1)
| member(X0,union(X2,X1)) ),
inference(cnf_transformation,[],[f94]) ).
cnf(c_58,plain,
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f93]) ).
cnf(c_59,plain,
( ~ member(X0,union(X1,X2))
| member(X0,X1)
| member(X0,X2) ),
inference(cnf_transformation,[],[f92]) ).
cnf(c_60,plain,
~ member(X0,empty_set),
inference(cnf_transformation,[],[f95]) ).
cnf(c_61,plain,
( ~ member(X0,X1)
| member(X0,difference(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[],[f98]) ).
cnf(c_62,plain,
( ~ member(X0,difference(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f97]) ).
cnf(c_63,plain,
( ~ member(X0,difference(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f96]) ).
cnf(c_64,plain,
member(X0,singleton(X0)),
inference(cnf_transformation,[],[f137]) ).
cnf(c_65,plain,
( ~ member(X0,singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f99]) ).
cnf(c_66,plain,
member(X0,unordered_pair(X1,X0)),
inference(cnf_transformation,[],[f138]) ).
cnf(c_67,plain,
member(X0,unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f139]) ).
cnf(c_68,plain,
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
inference(cnf_transformation,[],[f101]) ).
cnf(c_69,plain,
( ~ member(X0,X1)
| ~ member(X1,X2)
| member(X0,sum(X2)) ),
inference(cnf_transformation,[],[f106]) ).
cnf(c_70,plain,
( ~ member(X0,sum(X1))
| member(X0,sK2(X0,X1)) ),
inference(cnf_transformation,[],[f105]) ).
cnf(c_71,plain,
( ~ member(X0,sum(X1))
| member(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f104]) ).
cnf(c_72,plain,
( ~ member(X0,sK3(X0,X1))
| member(X0,product(X1)) ),
inference(cnf_transformation,[],[f109]) ).
cnf(c_73,plain,
( member(sK3(X0,X1),X1)
| member(X0,product(X1)) ),
inference(cnf_transformation,[],[f108]) ).
cnf(c_74,plain,
( ~ member(X0,product(X1))
| ~ member(X2,X1)
| member(X0,X2) ),
inference(cnf_transformation,[],[f107]) ).
cnf(c_75,plain,
( ~ member(X0,X1)
| ~ member(X2,X1)
| ~ member(X3,X0)
| ~ member(X3,X2)
| ~ partition(X1,X4)
| X0 = X2 ),
inference(cnf_transformation,[],[f113]) ).
cnf(c_76,plain,
( ~ member(X0,X1)
| ~ partition(X2,X1)
| member(X0,sK4(X2,X0)) ),
inference(cnf_transformation,[],[f112]) ).
cnf(c_77,plain,
( ~ member(X0,X1)
| ~ partition(X2,X1)
| member(sK4(X2,X0),X2) ),
inference(cnf_transformation,[],[f111]) ).
cnf(c_78,plain,
( ~ member(X0,X1)
| ~ partition(X1,X2)
| subset(X0,X2) ),
inference(cnf_transformation,[],[f110]) ).
cnf(c_79,plain,
( ~ apply(X0,sK5(X0,X1),sK7(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f119]) ).
cnf(c_80,plain,
( ~ sP0(X0,X1)
| apply(X0,sK6(X0,X1),sK7(X0,X1)) ),
inference(cnf_transformation,[],[f118]) ).
cnf(c_81,plain,
( ~ sP0(X0,X1)
| apply(X0,sK5(X0,X1),sK6(X0,X1)) ),
inference(cnf_transformation,[],[f117]) ).
cnf(c_82,plain,
( ~ sP0(X0,X1)
| member(sK7(X0,X1),X1) ),
inference(cnf_transformation,[],[f116]) ).
cnf(c_83,plain,
( ~ sP0(X0,X1)
| member(sK6(X0,X1),X1) ),
inference(cnf_transformation,[],[f115]) ).
cnf(c_84,plain,
( ~ sP0(X0,X1)
| member(sK5(X0,X1),X1) ),
inference(cnf_transformation,[],[f114]) ).
cnf(c_85,plain,
( ~ apply(X0,sK9(X1,X0),sK8(X1,X0))
| ~ apply(X0,sK10(X1,X0),sK10(X1,X0))
| sP0(X0,X1)
| equivalence(X0,X1) ),
inference(cnf_transformation,[],[f127]) ).
cnf(c_86,plain,
( ~ apply(X0,sK9(X1,X0),sK8(X1,X0))
| member(sK10(X1,X0),X1)
| sP0(X0,X1)
| equivalence(X0,X1) ),
inference(cnf_transformation,[],[f126]) ).
cnf(c_87,plain,
( ~ apply(X0,sK10(X1,X0),sK10(X1,X0))
| apply(X0,sK8(X1,X0),sK9(X1,X0))
| sP0(X0,X1)
| equivalence(X0,X1) ),
inference(cnf_transformation,[],[f125]) ).
cnf(c_88,plain,
( apply(X0,sK8(X1,X0),sK9(X1,X0))
| member(sK10(X1,X0),X1)
| sP0(X0,X1)
| equivalence(X0,X1) ),
inference(cnf_transformation,[],[f124]) ).
cnf(c_89,plain,
( ~ apply(X0,sK10(X1,X0),sK10(X1,X0))
| member(sK9(X1,X0),X1)
| sP0(X0,X1)
| equivalence(X0,X1) ),
inference(cnf_transformation,[],[f123]) ).
cnf(c_90,plain,
( member(sK9(X0,X1),X0)
| member(sK10(X0,X1),X0)
| sP0(X1,X0)
| equivalence(X1,X0) ),
inference(cnf_transformation,[],[f122]) ).
cnf(c_91,plain,
( ~ apply(X0,sK10(X1,X0),sK10(X1,X0))
| member(sK8(X1,X0),X1)
| sP0(X0,X1)
| equivalence(X0,X1) ),
inference(cnf_transformation,[],[f121]) ).
cnf(c_92,plain,
( member(sK8(X0,X1),X0)
| member(sK10(X0,X1),X0)
| sP0(X1,X0)
| equivalence(X1,X0) ),
inference(cnf_transformation,[],[f120]) ).
cnf(c_93,plain,
( ~ apply(X0,X1,X2)
| ~ member(X2,X3)
| member(X2,equivalence_class(X1,X3,X0)) ),
inference(cnf_transformation,[],[f130]) ).
cnf(c_94,plain,
( ~ member(X0,equivalence_class(X1,X2,X3))
| apply(X3,X1,X0) ),
inference(cnf_transformation,[],[f129]) ).
cnf(c_95,plain,
( ~ member(X0,equivalence_class(X1,X2,X3))
| member(X0,X2) ),
inference(cnf_transformation,[],[f128]) ).
cnf(c_96,negated_conjecture,
~ equivalence(sK13,sK12),
inference(cnf_transformation,[],[f136]) ).
cnf(c_97,negated_conjecture,
( ~ member(X0,X1)
| ~ member(X2,X1)
| ~ member(X0,sK12)
| ~ member(X1,sK11)
| ~ member(X2,sK12)
| apply(sK13,X0,X2) ),
inference(cnf_transformation,[],[f135]) ).
cnf(c_98,negated_conjecture,
( ~ apply(sK13,X0,X1)
| ~ member(X0,sK12)
| ~ member(X1,sK12)
| member(X1,sK14(X0,X1)) ),
inference(cnf_transformation,[],[f134]) ).
cnf(c_99,negated_conjecture,
( ~ apply(sK13,X0,X1)
| ~ member(X0,sK12)
| ~ member(X1,sK12)
| member(X0,sK14(X0,X1)) ),
inference(cnf_transformation,[],[f133]) ).
cnf(c_100,negated_conjecture,
( ~ apply(sK13,X0,X1)
| ~ member(X0,sK12)
| ~ member(X1,sK12)
| member(sK14(X0,X1),sK11) ),
inference(cnf_transformation,[],[f132]) ).
cnf(c_101,negated_conjecture,
partition(sK11,sK12),
inference(cnf_transformation,[],[f131]) ).
cnf(c_428,negated_conjecture,
partition(sK11,sK12),
inference(demodulation,[status(thm)],[c_101]) ).
cnf(c_429,negated_conjecture,
( ~ apply(sK13,X0,X1)
| ~ member(X0,sK12)
| ~ member(X1,sK12)
| member(sK14(X0,X1),sK11) ),
inference(demodulation,[status(thm)],[c_100]) ).
cnf(c_430,negated_conjecture,
( ~ apply(sK13,X0,X1)
| ~ member(X0,sK12)
| ~ member(X1,sK12)
| member(X0,sK14(X0,X1)) ),
inference(demodulation,[status(thm)],[c_99]) ).
cnf(c_431,negated_conjecture,
( ~ apply(sK13,X0,X1)
| ~ member(X0,sK12)
| ~ member(X1,sK12)
| member(X1,sK14(X0,X1)) ),
inference(demodulation,[status(thm)],[c_98]) ).
cnf(c_432,negated_conjecture,
( ~ member(X0,X1)
| ~ member(X2,X1)
| ~ member(X0,sK12)
| ~ member(X1,sK11)
| ~ member(X2,sK12)
| apply(sK13,X0,X2) ),
inference(demodulation,[status(thm)],[c_97]) ).
cnf(c_433,negated_conjecture,
~ equivalence(sK13,sK12),
inference(demodulation,[status(thm)],[c_96]) ).
cnf(c_60924,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_428,c_429,c_430,c_431,c_432,c_433,c_95,c_94,c_93,c_92,c_91,c_90,c_89,c_88,c_87,c_86,c_85,c_84,c_83,c_82,c_81,c_80,c_79,c_78,c_77,c_76,c_75,c_74,c_73,c_72,c_71,c_70,c_69,c_68,c_67,c_66,c_65,c_64,c_63,c_62,c_61,c_60,c_59,c_58,c_57,c_56,c_55,c_54,c_53,c_52,c_51,c_50,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET772+4 : TPTP v8.2.0. Released v2.2.0.
% 0.07/0.12 % Command : run_iprover %s %d THM
% 0.13/0.33 % Computer : n029.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sun Jun 23 14:32:09 EDT 2024
% 0.13/0.33 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 81.37/11.77 % SZS status Started for theBenchmark.p
% 81.37/11.77 % SZS status Theorem for theBenchmark.p
% 81.37/11.77
% 81.37/11.77 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 81.37/11.77
% 81.37/11.77 ------ iProver source info
% 81.37/11.77
% 81.37/11.77 git: date: 2024-06-12 09:56:46 +0000
% 81.37/11.77 git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 81.37/11.77 git: non_committed_changes: false
% 81.37/11.77
% 81.37/11.77 ------ Parsing...
% 81.37/11.77 ------ Clausification by vclausify_rel & Parsing by iProver...
% 81.37/11.77
% 81.37/11.77 ------ Preprocessing...
% 81.37/11.77
% 81.37/11.77 ------ Preprocessing...
% 81.37/11.77
% 81.37/11.77 ------ Preprocessing...
% 81.37/11.77 ------ Proving...
% 81.37/11.77 ------ Problem Properties
% 81.37/11.77
% 81.37/11.77
% 81.37/11.77 clauses 53
% 81.37/11.77 conjectures 6
% 81.37/11.77 EPR 7
% 81.37/11.77 Horn 40
% 81.37/11.77 unary 6
% 81.37/11.77 binary 23
% 81.37/11.77 lits 141
% 81.37/11.77 lits eq 4
% 81.37/11.77 fd_pure 0
% 81.37/11.77 fd_pseudo 0
% 81.37/11.77 fd_cond 0
% 81.37/11.77 fd_pseudo_cond 3
% 81.37/11.77 AC symbols 0
% 81.37/11.77
% 81.37/11.77 ------ Input Options Time Limit: Unbounded
% 81.37/11.77
% 81.37/11.77
% 81.37/11.77 ------
% 81.37/11.77 Current options:
% 81.37/11.77 ------
% 81.37/11.77
% 81.37/11.77
% 81.37/11.77
% 81.37/11.77
% 81.37/11.77 ------ Proving...
% 81.37/11.77
% 81.37/11.77
% 81.37/11.77 % SZS status Theorem for theBenchmark.p
% 81.37/11.77
% 81.37/11.77 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 81.37/11.77
% 81.37/11.77
%------------------------------------------------------------------------------