TSTP Solution File: SET730+4 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET730+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n032.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 : Fri May 3 03:01:22 EDT 2024
% Result : Theorem 127.40s 17.55s
% Output : CNFRefutation 127.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 22
% Syntax : Number of formulae : 221 ( 25 unt; 0 def)
% Number of atoms : 869 ( 51 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 1060 ( 412 ~; 410 |; 186 &)
% ( 26 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 24 ( 24 usr; 6 con; 0-3 aty)
% Number of variables : 630 ( 18 sgn 360 !; 75 ?)
% 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(f6,axiom,
! [X2] : ~ member(X2,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).
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(f12,axiom,
! [X5,X0,X1] :
( maps(X5,X0,X1)
<=> ( ! [X2,X6,X7] :
( ( member(X7,X1)
& member(X6,X1)
& member(X2,X0) )
=> ( ( apply(X5,X2,X7)
& apply(X5,X2,X6) )
=> X6 = X7 ) )
& ! [X2] :
( member(X2,X0)
=> ? [X4] :
( apply(X5,X2,X4)
& member(X4,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps) ).
fof(f22,axiom,
! [X5,X0,X4] :
( member(X4,image2(X5,X0))
<=> ? [X2] :
( apply(X5,X2,X4)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image2) ).
fof(f23,axiom,
! [X5,X0,X1,X4] :
( member(X4,image3(X5,X0,X1))
<=> ( ? [X2] :
( apply(X5,X2,X4)
& member(X2,X0) )
& member(X4,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image3) ).
fof(f24,axiom,
! [X5,X1,X2] :
( member(X2,inverse_image2(X5,X1))
<=> ? [X4] :
( apply(X5,X2,X4)
& member(X4,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_image2) ).
fof(f25,axiom,
! [X5,X1,X0,X2] :
( member(X2,inverse_image3(X5,X1,X0))
<=> ( ? [X4] :
( apply(X5,X2,X4)
& member(X4,X1) )
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_image3) ).
fof(f29,conjecture,
! [X5,X9,X0,X1,X10] :
( ( ! [X2,X4] :
( ( member(X4,X10)
& member(X2,X0) )
=> ( apply(X9,X2,X4)
<=> apply(X5,X2,X4) ) )
& image2(X5,X0) = X10
& subset(X10,X1)
& maps(X5,X0,X1) )
=> maps(X9,X0,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII21) ).
fof(f30,negated_conjecture,
~ ! [X5,X9,X0,X1,X10] :
( ( ! [X2,X4] :
( ( member(X4,X10)
& member(X2,X0) )
=> ( apply(X9,X2,X4)
<=> apply(X5,X2,X4) ) )
& image2(X5,X0) = X10
& subset(X10,X1)
& maps(X5,X0,X1) )
=> maps(X9,X0,X10) ),
inference(negated_conjecture,[],[f29]) ).
fof(f34,plain,
! [X0] : ~ member(X0,empty_set),
inference(rectify,[],[f6]) ).
fof(f38,plain,
! [X0,X1] :
( member(X0,sum(X1))
<=> ? [X2] :
( member(X0,X2)
& member(X2,X1) ) ),
inference(rectify,[],[f10]) ).
fof(f39,plain,
! [X0,X1] :
( member(X0,product(X1))
<=> ! [X2] :
( member(X2,X1)
=> member(X0,X2) ) ),
inference(rectify,[],[f11]) ).
fof(f40,plain,
! [X0,X1,X2] :
( maps(X0,X1,X2)
<=> ( ! [X3,X4,X5] :
( ( member(X5,X2)
& member(X4,X2)
& member(X3,X1) )
=> ( ( apply(X0,X3,X5)
& apply(X0,X3,X4) )
=> X4 = X5 ) )
& ! [X6] :
( member(X6,X1)
=> ? [X7] :
( apply(X0,X6,X7)
& member(X7,X2) ) ) ) ),
inference(rectify,[],[f12]) ).
fof(f50,plain,
! [X0,X1,X2] :
( member(X2,image2(X0,X1))
<=> ? [X3] :
( apply(X0,X3,X2)
& member(X3,X1) ) ),
inference(rectify,[],[f22]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( member(X3,image3(X0,X1,X2))
<=> ( ? [X4] :
( apply(X0,X4,X3)
& member(X4,X1) )
& member(X3,X2) ) ),
inference(rectify,[],[f23]) ).
fof(f52,plain,
! [X0,X1,X2] :
( member(X2,inverse_image2(X0,X1))
<=> ? [X3] :
( apply(X0,X2,X3)
& member(X3,X1) ) ),
inference(rectify,[],[f24]) ).
fof(f53,plain,
! [X0,X1,X2,X3] :
( member(X3,inverse_image3(X0,X1,X2))
<=> ( ? [X4] :
( apply(X0,X3,X4)
& member(X4,X1) )
& member(X3,X2) ) ),
inference(rectify,[],[f25]) ).
fof(f57,plain,
~ ! [X0,X1,X2,X3,X4] :
( ( ! [X5,X6] :
( ( member(X6,X4)
& member(X5,X2) )
=> ( apply(X1,X5,X6)
<=> apply(X0,X5,X6) ) )
& image2(X0,X2) = X4
& subset(X4,X3)
& maps(X0,X2,X3) )
=> maps(X1,X2,X4) ),
inference(rectify,[],[f30]) ).
fof(f58,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f59,plain,
! [X0,X1] :
( member(X0,product(X1))
<=> ! [X2] :
( member(X0,X2)
| ~ member(X2,X1) ) ),
inference(ennf_transformation,[],[f39]) ).
fof(f60,plain,
! [X0,X1,X2] :
( maps(X0,X1,X2)
<=> ( ! [X3,X4,X5] :
( X4 = X5
| ~ apply(X0,X3,X5)
| ~ apply(X0,X3,X4)
| ~ member(X5,X2)
| ~ member(X4,X2)
| ~ member(X3,X1) )
& ! [X6] :
( ? [X7] :
( apply(X0,X6,X7)
& member(X7,X2) )
| ~ member(X6,X1) ) ) ),
inference(ennf_transformation,[],[f40]) ).
fof(f61,plain,
! [X0,X1,X2] :
( maps(X0,X1,X2)
<=> ( ! [X3,X4,X5] :
( X4 = X5
| ~ apply(X0,X3,X5)
| ~ apply(X0,X3,X4)
| ~ member(X5,X2)
| ~ member(X4,X2)
| ~ member(X3,X1) )
& ! [X6] :
( ? [X7] :
( apply(X0,X6,X7)
& member(X7,X2) )
| ~ member(X6,X1) ) ) ),
inference(flattening,[],[f60]) ).
fof(f66,plain,
? [X0,X1,X2,X3,X4] :
( ~ maps(X1,X2,X4)
& ! [X5,X6] :
( ( apply(X1,X5,X6)
<=> apply(X0,X5,X6) )
| ~ member(X6,X4)
| ~ member(X5,X2) )
& image2(X0,X2) = X4
& subset(X4,X3)
& maps(X0,X2,X3) ),
inference(ennf_transformation,[],[f57]) ).
fof(f67,plain,
? [X0,X1,X2,X3,X4] :
( ~ maps(X1,X2,X4)
& ! [X5,X6] :
( ( apply(X1,X5,X6)
<=> apply(X0,X5,X6) )
| ~ member(X6,X4)
| ~ member(X5,X2) )
& image2(X0,X2) = X4
& subset(X4,X3)
& maps(X0,X2,X3) ),
inference(flattening,[],[f66]) ).
fof(f68,plain,
! [X0,X2,X1] :
( sP0(X0,X2,X1)
<=> ! [X3,X4,X5] :
( X4 = X5
| ~ apply(X0,X3,X5)
| ~ apply(X0,X3,X4)
| ~ member(X5,X2)
| ~ member(X4,X2)
| ~ member(X3,X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f69,plain,
! [X0,X1,X2] :
( maps(X0,X1,X2)
<=> ( sP0(X0,X2,X1)
& ! [X6] :
( ? [X7] :
( apply(X0,X6,X7)
& member(X7,X2) )
| ~ member(X6,X1) ) ) ),
inference(definition_folding,[],[f61,f68]) ).
fof(f70,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,[],[f58]) ).
fof(f71,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,[],[f70]) ).
fof(f72,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK1(X0,X1),X1)
& member(sK1(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f73,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])],[f71,f72]) ).
fof(f84,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,[],[f38]) ).
fof(f85,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,[],[f84]) ).
fof(f86,plain,
! [X0,X1] :
( ? [X3] :
( member(X0,X3)
& member(X3,X1) )
=> ( member(X0,sK2(X0,X1))
& member(sK2(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f87,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])],[f85,f86]) ).
fof(f88,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,[],[f59]) ).
fof(f89,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,[],[f88]) ).
fof(f90,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X0,X2)
& member(X2,X1) )
=> ( ~ member(X0,sK3(X0,X1))
& member(sK3(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f91,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])],[f89,f90]) ).
fof(f92,plain,
! [X0,X2,X1] :
( ( sP0(X0,X2,X1)
| ? [X3,X4,X5] :
( X4 != X5
& apply(X0,X3,X5)
& apply(X0,X3,X4)
& member(X5,X2)
& member(X4,X2)
& member(X3,X1) ) )
& ( ! [X3,X4,X5] :
( X4 = X5
| ~ apply(X0,X3,X5)
| ~ apply(X0,X3,X4)
| ~ member(X5,X2)
| ~ member(X4,X2)
| ~ member(X3,X1) )
| ~ sP0(X0,X2,X1) ) ),
inference(nnf_transformation,[],[f68]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3,X4,X5] :
( X4 != X5
& apply(X0,X3,X5)
& apply(X0,X3,X4)
& member(X5,X1)
& member(X4,X1)
& member(X3,X2) ) )
& ( ! [X6,X7,X8] :
( X7 = X8
| ~ apply(X0,X6,X8)
| ~ apply(X0,X6,X7)
| ~ member(X8,X1)
| ~ member(X7,X1)
| ~ member(X6,X2) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f92]) ).
fof(f94,plain,
! [X0,X1,X2] :
( ? [X3,X4,X5] :
( X4 != X5
& apply(X0,X3,X5)
& apply(X0,X3,X4)
& member(X5,X1)
& member(X4,X1)
& member(X3,X2) )
=> ( sK5(X0,X1,X2) != sK6(X0,X1,X2)
& apply(X0,sK4(X0,X1,X2),sK6(X0,X1,X2))
& apply(X0,sK4(X0,X1,X2),sK5(X0,X1,X2))
& member(sK6(X0,X1,X2),X1)
& member(sK5(X0,X1,X2),X1)
& member(sK4(X0,X1,X2),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f95,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( sK5(X0,X1,X2) != sK6(X0,X1,X2)
& apply(X0,sK4(X0,X1,X2),sK6(X0,X1,X2))
& apply(X0,sK4(X0,X1,X2),sK5(X0,X1,X2))
& member(sK6(X0,X1,X2),X1)
& member(sK5(X0,X1,X2),X1)
& member(sK4(X0,X1,X2),X2) ) )
& ( ! [X6,X7,X8] :
( X7 = X8
| ~ apply(X0,X6,X8)
| ~ apply(X0,X6,X7)
| ~ member(X8,X1)
| ~ member(X7,X1)
| ~ member(X6,X2) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f93,f94]) ).
fof(f96,plain,
! [X0,X1,X2] :
( ( maps(X0,X1,X2)
| ~ sP0(X0,X2,X1)
| ? [X6] :
( ! [X7] :
( ~ apply(X0,X6,X7)
| ~ member(X7,X2) )
& member(X6,X1) ) )
& ( ( sP0(X0,X2,X1)
& ! [X6] :
( ? [X7] :
( apply(X0,X6,X7)
& member(X7,X2) )
| ~ member(X6,X1) ) )
| ~ maps(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f69]) ).
fof(f97,plain,
! [X0,X1,X2] :
( ( maps(X0,X1,X2)
| ~ sP0(X0,X2,X1)
| ? [X6] :
( ! [X7] :
( ~ apply(X0,X6,X7)
| ~ member(X7,X2) )
& member(X6,X1) ) )
& ( ( sP0(X0,X2,X1)
& ! [X6] :
( ? [X7] :
( apply(X0,X6,X7)
& member(X7,X2) )
| ~ member(X6,X1) ) )
| ~ maps(X0,X1,X2) ) ),
inference(flattening,[],[f96]) ).
fof(f98,plain,
! [X0,X1,X2] :
( ( maps(X0,X1,X2)
| ~ sP0(X0,X2,X1)
| ? [X3] :
( ! [X4] :
( ~ apply(X0,X3,X4)
| ~ member(X4,X2) )
& member(X3,X1) ) )
& ( ( sP0(X0,X2,X1)
& ! [X5] :
( ? [X6] :
( apply(X0,X5,X6)
& member(X6,X2) )
| ~ member(X5,X1) ) )
| ~ maps(X0,X1,X2) ) ),
inference(rectify,[],[f97]) ).
fof(f99,plain,
! [X0,X1,X2] :
( ? [X3] :
( ! [X4] :
( ~ apply(X0,X3,X4)
| ~ member(X4,X2) )
& member(X3,X1) )
=> ( ! [X4] :
( ~ apply(X0,sK7(X0,X1,X2),X4)
| ~ member(X4,X2) )
& member(sK7(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f100,plain,
! [X0,X2,X5] :
( ? [X6] :
( apply(X0,X5,X6)
& member(X6,X2) )
=> ( apply(X0,X5,sK8(X0,X2,X5))
& member(sK8(X0,X2,X5),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f101,plain,
! [X0,X1,X2] :
( ( maps(X0,X1,X2)
| ~ sP0(X0,X2,X1)
| ( ! [X4] :
( ~ apply(X0,sK7(X0,X1,X2),X4)
| ~ member(X4,X2) )
& member(sK7(X0,X1,X2),X1) ) )
& ( ( sP0(X0,X2,X1)
& ! [X5] :
( ( apply(X0,X5,sK8(X0,X2,X5))
& member(sK8(X0,X2,X5),X2) )
| ~ member(X5,X1) ) )
| ~ maps(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f98,f100,f99]) ).
fof(f107,plain,
! [X0,X1,X2] :
( ( member(X2,image2(X0,X1))
| ! [X3] :
( ~ apply(X0,X3,X2)
| ~ member(X3,X1) ) )
& ( ? [X3] :
( apply(X0,X3,X2)
& member(X3,X1) )
| ~ member(X2,image2(X0,X1)) ) ),
inference(nnf_transformation,[],[f50]) ).
fof(f108,plain,
! [X0,X1,X2] :
( ( member(X2,image2(X0,X1))
| ! [X3] :
( ~ apply(X0,X3,X2)
| ~ member(X3,X1) ) )
& ( ? [X4] :
( apply(X0,X4,X2)
& member(X4,X1) )
| ~ member(X2,image2(X0,X1)) ) ),
inference(rectify,[],[f107]) ).
fof(f109,plain,
! [X0,X1,X2] :
( ? [X4] :
( apply(X0,X4,X2)
& member(X4,X1) )
=> ( apply(X0,sK10(X0,X1,X2),X2)
& member(sK10(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f110,plain,
! [X0,X1,X2] :
( ( member(X2,image2(X0,X1))
| ! [X3] :
( ~ apply(X0,X3,X2)
| ~ member(X3,X1) ) )
& ( ( apply(X0,sK10(X0,X1,X2),X2)
& member(sK10(X0,X1,X2),X1) )
| ~ member(X2,image2(X0,X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f108,f109]) ).
fof(f111,plain,
! [X0,X1,X2,X3] :
( ( member(X3,image3(X0,X1,X2))
| ! [X4] :
( ~ apply(X0,X4,X3)
| ~ member(X4,X1) )
| ~ member(X3,X2) )
& ( ( ? [X4] :
( apply(X0,X4,X3)
& member(X4,X1) )
& member(X3,X2) )
| ~ member(X3,image3(X0,X1,X2)) ) ),
inference(nnf_transformation,[],[f51]) ).
fof(f112,plain,
! [X0,X1,X2,X3] :
( ( member(X3,image3(X0,X1,X2))
| ! [X4] :
( ~ apply(X0,X4,X3)
| ~ member(X4,X1) )
| ~ member(X3,X2) )
& ( ( ? [X4] :
( apply(X0,X4,X3)
& member(X4,X1) )
& member(X3,X2) )
| ~ member(X3,image3(X0,X1,X2)) ) ),
inference(flattening,[],[f111]) ).
fof(f113,plain,
! [X0,X1,X2,X3] :
( ( member(X3,image3(X0,X1,X2))
| ! [X4] :
( ~ apply(X0,X4,X3)
| ~ member(X4,X1) )
| ~ member(X3,X2) )
& ( ( ? [X5] :
( apply(X0,X5,X3)
& member(X5,X1) )
& member(X3,X2) )
| ~ member(X3,image3(X0,X1,X2)) ) ),
inference(rectify,[],[f112]) ).
fof(f114,plain,
! [X0,X1,X3] :
( ? [X5] :
( apply(X0,X5,X3)
& member(X5,X1) )
=> ( apply(X0,sK11(X0,X1,X3),X3)
& member(sK11(X0,X1,X3),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f115,plain,
! [X0,X1,X2,X3] :
( ( member(X3,image3(X0,X1,X2))
| ! [X4] :
( ~ apply(X0,X4,X3)
| ~ member(X4,X1) )
| ~ member(X3,X2) )
& ( ( apply(X0,sK11(X0,X1,X3),X3)
& member(sK11(X0,X1,X3),X1)
& member(X3,X2) )
| ~ member(X3,image3(X0,X1,X2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f113,f114]) ).
fof(f116,plain,
! [X0,X1,X2] :
( ( member(X2,inverse_image2(X0,X1))
| ! [X3] :
( ~ apply(X0,X2,X3)
| ~ member(X3,X1) ) )
& ( ? [X3] :
( apply(X0,X2,X3)
& member(X3,X1) )
| ~ member(X2,inverse_image2(X0,X1)) ) ),
inference(nnf_transformation,[],[f52]) ).
fof(f117,plain,
! [X0,X1,X2] :
( ( member(X2,inverse_image2(X0,X1))
| ! [X3] :
( ~ apply(X0,X2,X3)
| ~ member(X3,X1) ) )
& ( ? [X4] :
( apply(X0,X2,X4)
& member(X4,X1) )
| ~ member(X2,inverse_image2(X0,X1)) ) ),
inference(rectify,[],[f116]) ).
fof(f118,plain,
! [X0,X1,X2] :
( ? [X4] :
( apply(X0,X2,X4)
& member(X4,X1) )
=> ( apply(X0,X2,sK12(X0,X1,X2))
& member(sK12(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f119,plain,
! [X0,X1,X2] :
( ( member(X2,inverse_image2(X0,X1))
| ! [X3] :
( ~ apply(X0,X2,X3)
| ~ member(X3,X1) ) )
& ( ( apply(X0,X2,sK12(X0,X1,X2))
& member(sK12(X0,X1,X2),X1) )
| ~ member(X2,inverse_image2(X0,X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f117,f118]) ).
fof(f120,plain,
! [X0,X1,X2,X3] :
( ( member(X3,inverse_image3(X0,X1,X2))
| ! [X4] :
( ~ apply(X0,X3,X4)
| ~ member(X4,X1) )
| ~ member(X3,X2) )
& ( ( ? [X4] :
( apply(X0,X3,X4)
& member(X4,X1) )
& member(X3,X2) )
| ~ member(X3,inverse_image3(X0,X1,X2)) ) ),
inference(nnf_transformation,[],[f53]) ).
fof(f121,plain,
! [X0,X1,X2,X3] :
( ( member(X3,inverse_image3(X0,X1,X2))
| ! [X4] :
( ~ apply(X0,X3,X4)
| ~ member(X4,X1) )
| ~ member(X3,X2) )
& ( ( ? [X4] :
( apply(X0,X3,X4)
& member(X4,X1) )
& member(X3,X2) )
| ~ member(X3,inverse_image3(X0,X1,X2)) ) ),
inference(flattening,[],[f120]) ).
fof(f122,plain,
! [X0,X1,X2,X3] :
( ( member(X3,inverse_image3(X0,X1,X2))
| ! [X4] :
( ~ apply(X0,X3,X4)
| ~ member(X4,X1) )
| ~ member(X3,X2) )
& ( ( ? [X5] :
( apply(X0,X3,X5)
& member(X5,X1) )
& member(X3,X2) )
| ~ member(X3,inverse_image3(X0,X1,X2)) ) ),
inference(rectify,[],[f121]) ).
fof(f123,plain,
! [X0,X1,X3] :
( ? [X5] :
( apply(X0,X3,X5)
& member(X5,X1) )
=> ( apply(X0,X3,sK13(X0,X1,X3))
& member(sK13(X0,X1,X3),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f124,plain,
! [X0,X1,X2,X3] :
( ( member(X3,inverse_image3(X0,X1,X2))
| ! [X4] :
( ~ apply(X0,X3,X4)
| ~ member(X4,X1) )
| ~ member(X3,X2) )
& ( ( apply(X0,X3,sK13(X0,X1,X3))
& member(sK13(X0,X1,X3),X1)
& member(X3,X2) )
| ~ member(X3,inverse_image3(X0,X1,X2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f122,f123]) ).
fof(f125,plain,
? [X0,X1,X2,X3,X4] :
( ~ maps(X1,X2,X4)
& ! [X5,X6] :
( ( ( apply(X1,X5,X6)
| ~ apply(X0,X5,X6) )
& ( apply(X0,X5,X6)
| ~ apply(X1,X5,X6) ) )
| ~ member(X6,X4)
| ~ member(X5,X2) )
& image2(X0,X2) = X4
& subset(X4,X3)
& maps(X0,X2,X3) ),
inference(nnf_transformation,[],[f67]) ).
fof(f126,plain,
( ? [X0,X1,X2,X3,X4] :
( ~ maps(X1,X2,X4)
& ! [X5,X6] :
( ( ( apply(X1,X5,X6)
| ~ apply(X0,X5,X6) )
& ( apply(X0,X5,X6)
| ~ apply(X1,X5,X6) ) )
| ~ member(X6,X4)
| ~ member(X5,X2) )
& image2(X0,X2) = X4
& subset(X4,X3)
& maps(X0,X2,X3) )
=> ( ~ maps(sK15,sK16,sK18)
& ! [X6,X5] :
( ( ( apply(sK15,X5,X6)
| ~ apply(sK14,X5,X6) )
& ( apply(sK14,X5,X6)
| ~ apply(sK15,X5,X6) ) )
| ~ member(X6,sK18)
| ~ member(X5,sK16) )
& sK18 = image2(sK14,sK16)
& subset(sK18,sK17)
& maps(sK14,sK16,sK17) ) ),
introduced(choice_axiom,[]) ).
fof(f127,plain,
( ~ maps(sK15,sK16,sK18)
& ! [X5,X6] :
( ( ( apply(sK15,X5,X6)
| ~ apply(sK14,X5,X6) )
& ( apply(sK14,X5,X6)
| ~ apply(sK15,X5,X6) ) )
| ~ member(X6,sK18)
| ~ member(X5,sK16) )
& sK18 = image2(sK14,sK16)
& subset(sK18,sK17)
& maps(sK14,sK16,sK17) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15,sK16,sK17,sK18])],[f125,f126]) ).
fof(f128,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f139,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f34]) ).
fof(f148,plain,
! [X0,X1] :
( member(sK2(X0,X1),X1)
| ~ member(X0,sum(X1)) ),
inference(cnf_transformation,[],[f87]) ).
fof(f152,plain,
! [X0,X1] :
( member(X0,product(X1))
| member(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f91]) ).
fof(f154,plain,
! [X2,X0,X1,X8,X6,X7] :
( X7 = X8
| ~ apply(X0,X6,X8)
| ~ apply(X0,X6,X7)
| ~ member(X8,X1)
| ~ member(X7,X1)
| ~ member(X6,X2)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f95]) ).
fof(f155,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| member(sK4(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f95]) ).
fof(f156,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| member(sK5(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f157,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| member(sK6(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f158,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| apply(X0,sK4(X0,X1,X2),sK5(X0,X1,X2)) ),
inference(cnf_transformation,[],[f95]) ).
fof(f159,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| apply(X0,sK4(X0,X1,X2),sK6(X0,X1,X2)) ),
inference(cnf_transformation,[],[f95]) ).
fof(f160,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| sK5(X0,X1,X2) != sK6(X0,X1,X2) ),
inference(cnf_transformation,[],[f95]) ).
fof(f161,plain,
! [X2,X0,X1,X5] :
( member(sK8(X0,X2,X5),X2)
| ~ member(X5,X1)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f101]) ).
fof(f162,plain,
! [X2,X0,X1,X5] :
( apply(X0,X5,sK8(X0,X2,X5))
| ~ member(X5,X1)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f101]) ).
fof(f163,plain,
! [X2,X0,X1] :
( sP0(X0,X2,X1)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f101]) ).
fof(f164,plain,
! [X2,X0,X1] :
( maps(X0,X1,X2)
| ~ sP0(X0,X2,X1)
| member(sK7(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f101]) ).
fof(f165,plain,
! [X2,X0,X1,X4] :
( maps(X0,X1,X2)
| ~ sP0(X0,X2,X1)
| ~ apply(X0,sK7(X0,X1,X2),X4)
| ~ member(X4,X2) ),
inference(cnf_transformation,[],[f101]) ).
fof(f174,plain,
! [X2,X3,X0,X1] :
( member(X2,image2(X0,X1))
| ~ apply(X0,X3,X2)
| ~ member(X3,X1) ),
inference(cnf_transformation,[],[f110]) ).
fof(f175,plain,
! [X2,X3,X0,X1] :
( member(X3,X2)
| ~ member(X3,image3(X0,X1,X2)) ),
inference(cnf_transformation,[],[f115]) ).
fof(f179,plain,
! [X2,X0,X1] :
( member(sK12(X0,X1,X2),X1)
| ~ member(X2,inverse_image2(X0,X1)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f181,plain,
! [X2,X3,X0,X1] :
( member(X2,inverse_image2(X0,X1))
| ~ apply(X0,X2,X3)
| ~ member(X3,X1) ),
inference(cnf_transformation,[],[f119]) ).
fof(f183,plain,
! [X2,X3,X0,X1] :
( member(sK13(X0,X1,X3),X1)
| ~ member(X3,inverse_image3(X0,X1,X2)) ),
inference(cnf_transformation,[],[f124]) ).
fof(f184,plain,
! [X2,X3,X0,X1] :
( apply(X0,X3,sK13(X0,X1,X3))
| ~ member(X3,inverse_image3(X0,X1,X2)) ),
inference(cnf_transformation,[],[f124]) ).
fof(f185,plain,
! [X2,X3,X0,X1,X4] :
( member(X3,inverse_image3(X0,X1,X2))
| ~ apply(X0,X3,X4)
| ~ member(X4,X1)
| ~ member(X3,X2) ),
inference(cnf_transformation,[],[f124]) ).
fof(f186,plain,
maps(sK14,sK16,sK17),
inference(cnf_transformation,[],[f127]) ).
fof(f187,plain,
subset(sK18,sK17),
inference(cnf_transformation,[],[f127]) ).
fof(f188,plain,
sK18 = image2(sK14,sK16),
inference(cnf_transformation,[],[f127]) ).
fof(f189,plain,
! [X6,X5] :
( apply(sK14,X5,X6)
| ~ apply(sK15,X5,X6)
| ~ member(X6,sK18)
| ~ member(X5,sK16) ),
inference(cnf_transformation,[],[f127]) ).
fof(f190,plain,
! [X6,X5] :
( apply(sK15,X5,X6)
| ~ apply(sK14,X5,X6)
| ~ member(X6,sK18)
| ~ member(X5,sK16) ),
inference(cnf_transformation,[],[f127]) ).
fof(f191,plain,
~ maps(sK15,sK16,sK18),
inference(cnf_transformation,[],[f127]) ).
cnf(c_51,plain,
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f128]) ).
cnf(c_60,plain,
~ member(X0,empty_set),
inference(cnf_transformation,[],[f139]) ).
cnf(c_71,plain,
( ~ member(X0,sum(X1))
| member(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f148]) ).
cnf(c_73,plain,
( member(sK3(X0,X1),X1)
| member(X0,product(X1)) ),
inference(cnf_transformation,[],[f152]) ).
cnf(c_75,plain,
( sK5(X0,X1,X2) != sK6(X0,X1,X2)
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f160]) ).
cnf(c_76,plain,
( apply(X0,sK4(X0,X1,X2),sK6(X0,X1,X2))
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f159]) ).
cnf(c_77,plain,
( apply(X0,sK4(X0,X1,X2),sK5(X0,X1,X2))
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f158]) ).
cnf(c_78,plain,
( member(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f157]) ).
cnf(c_79,plain,
( member(sK5(X0,X1,X2),X1)
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f156]) ).
cnf(c_80,plain,
( member(sK4(X0,X1,X2),X2)
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f155]) ).
cnf(c_81,plain,
( ~ sP0(X0,X1,X2)
| ~ apply(X0,X3,X4)
| ~ apply(X0,X3,X5)
| ~ member(X3,X2)
| ~ member(X4,X1)
| ~ member(X5,X1)
| X4 = X5 ),
inference(cnf_transformation,[],[f154]) ).
cnf(c_82,plain,
( ~ apply(X0,sK7(X0,X1,X2),X3)
| ~ sP0(X0,X2,X1)
| ~ member(X3,X2)
| maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f165]) ).
cnf(c_83,plain,
( ~ sP0(X0,X1,X2)
| member(sK7(X0,X2,X1),X2)
| maps(X0,X2,X1) ),
inference(cnf_transformation,[],[f164]) ).
cnf(c_84,plain,
( ~ maps(X0,X1,X2)
| sP0(X0,X2,X1) ),
inference(cnf_transformation,[],[f163]) ).
cnf(c_85,plain,
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| apply(X0,X3,sK8(X0,X2,X3)) ),
inference(cnf_transformation,[],[f162]) ).
cnf(c_86,plain,
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| member(sK8(X0,X2,X3),X2) ),
inference(cnf_transformation,[],[f161]) ).
cnf(c_93,plain,
( ~ apply(X0,X1,X2)
| ~ member(X1,X3)
| member(X2,image2(X0,X3)) ),
inference(cnf_transformation,[],[f174]) ).
cnf(c_99,plain,
( ~ member(X0,image3(X1,X2,X3))
| member(X0,X3) ),
inference(cnf_transformation,[],[f175]) ).
cnf(c_100,plain,
( ~ apply(X0,X1,X2)
| ~ member(X2,X3)
| member(X1,inverse_image2(X0,X3)) ),
inference(cnf_transformation,[],[f181]) ).
cnf(c_102,plain,
( ~ member(X0,inverse_image2(X1,X2))
| member(sK12(X1,X2,X0),X2) ),
inference(cnf_transformation,[],[f179]) ).
cnf(c_103,plain,
( ~ apply(X0,X1,X2)
| ~ member(X1,X3)
| ~ member(X2,X4)
| member(X1,inverse_image3(X0,X4,X3)) ),
inference(cnf_transformation,[],[f185]) ).
cnf(c_104,plain,
( ~ member(X0,inverse_image3(X1,X2,X3))
| apply(X1,X0,sK13(X1,X2,X0)) ),
inference(cnf_transformation,[],[f184]) ).
cnf(c_105,plain,
( ~ member(X0,inverse_image3(X1,X2,X3))
| member(sK13(X1,X2,X0),X2) ),
inference(cnf_transformation,[],[f183]) ).
cnf(c_107,negated_conjecture,
~ maps(sK15,sK16,sK18),
inference(cnf_transformation,[],[f191]) ).
cnf(c_108,negated_conjecture,
( ~ apply(sK14,X0,X1)
| ~ member(X0,sK16)
| ~ member(X1,sK18)
| apply(sK15,X0,X1) ),
inference(cnf_transformation,[],[f190]) ).
cnf(c_109,negated_conjecture,
( ~ apply(sK15,X0,X1)
| ~ member(X0,sK16)
| ~ member(X1,sK18)
| apply(sK14,X0,X1) ),
inference(cnf_transformation,[],[f189]) ).
cnf(c_110,negated_conjecture,
image2(sK14,sK16) = sK18,
inference(cnf_transformation,[],[f188]) ).
cnf(c_111,negated_conjecture,
subset(sK18,sK17),
inference(cnf_transformation,[],[f187]) ).
cnf(c_112,negated_conjecture,
maps(sK14,sK16,sK17),
inference(cnf_transformation,[],[f186]) ).
cnf(c_1199,plain,
( X0 != sK14
| X1 != sK16
| X2 != sK17
| ~ member(X3,X1)
| member(sK8(X0,X2,X3),X2) ),
inference(resolution_lifted,[status(thm)],[c_86,c_112]) ).
cnf(c_1200,plain,
( ~ member(X0,sK16)
| member(sK8(sK14,sK17,X0),sK17) ),
inference(unflattening,[status(thm)],[c_1199]) ).
cnf(c_3107,plain,
sP0(sK14,sK17,sK16),
inference(superposition,[status(thm)],[c_112,c_84]) ).
cnf(c_3181,plain,
( sK5(sK15,sK18,sK16) != sK6(sK15,sK18,sK16)
| sP0(sK15,sK18,sK16) ),
inference(instantiation,[status(thm)],[c_75]) ).
cnf(c_3182,plain,
( member(sK4(sK15,sK18,sK16),sK16)
| sP0(sK15,sK18,sK16) ),
inference(instantiation,[status(thm)],[c_80]) ).
cnf(c_3183,plain,
( member(sK5(sK15,sK18,sK16),sK18)
| sP0(sK15,sK18,sK16) ),
inference(instantiation,[status(thm)],[c_79]) ).
cnf(c_3184,plain,
( member(sK6(sK15,sK18,sK16),sK18)
| sP0(sK15,sK18,sK16) ),
inference(instantiation,[status(thm)],[c_78]) ).
cnf(c_8531,plain,
( ~ maps(sK14,sK16,sK17)
| ~ member(X0,sK16)
| member(sK8(sK14,sK17,X0),sK17) ),
inference(instantiation,[status(thm)],[c_86]) ).
cnf(c_8534,plain,
( ~ maps(sK14,sK16,sK17)
| ~ member(X0,sK16)
| apply(sK14,X0,sK8(sK14,sK17,X0)) ),
inference(instantiation,[status(thm)],[c_85]) ).
cnf(c_9443,plain,
( ~ member(X0,sK16)
| apply(sK14,X0,sK8(sK14,sK17,X0)) ),
inference(superposition,[status(thm)],[c_112,c_85]) ).
cnf(c_10220,plain,
( ~ member(X0,X1)
| ~ member(X0,sK16)
| member(sK8(sK14,sK17,X0),image2(sK14,X1)) ),
inference(superposition,[status(thm)],[c_9443,c_93]) ).
cnf(c_10221,plain,
( ~ member(sK8(sK14,sK17,X0),sK18)
| ~ member(X0,sK16)
| apply(sK15,X0,sK8(sK14,sK17,X0)) ),
inference(superposition,[status(thm)],[c_9443,c_108]) ).
cnf(c_10383,plain,
( ~ subset(sK18,X0)
| ~ member(X1,sK18)
| member(X1,X0) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_10481,plain,
( ~ member(X0,sK16)
| member(sK8(sK14,sK17,X0),sK18) ),
inference(superposition,[status(thm)],[c_110,c_10220]) ).
cnf(c_10716,plain,
( ~ member(X0,sK16)
| apply(sK14,X0,sK8(sK14,sK17,X0)) ),
inference(resolution,[status(thm)],[c_85,c_112]) ).
cnf(c_10755,plain,
( ~ member(sK8(sK14,sK17,X0),sK18)
| ~ member(X0,sK16)
| apply(sK15,X0,sK8(sK14,sK17,X0)) ),
inference(resolution,[status(thm)],[c_10716,c_108]) ).
cnf(c_10846,plain,
( ~ member(X0,sK16)
| apply(sK15,X0,sK8(sK14,sK17,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_10755,c_10221,c_10481]) ).
cnf(c_12777,plain,
( ~ member(X0,sK16)
| apply(sK14,X0,sK8(sK14,sK17,X0)) ),
inference(superposition,[status(thm)],[c_112,c_85]) ).
cnf(c_12897,plain,
( ~ member(X0,X1)
| ~ member(X0,sK16)
| member(sK8(sK14,sK17,X0),image2(sK14,X1)) ),
inference(superposition,[status(thm)],[c_12777,c_93]) ).
cnf(c_12898,plain,
( ~ member(sK8(sK14,sK17,X0),sK18)
| ~ member(X0,sK16)
| apply(sK15,X0,sK8(sK14,sK17,X0)) ),
inference(superposition,[status(thm)],[c_12777,c_108]) ).
cnf(c_12899,plain,
( ~ member(X0,sK16)
| apply(sK15,X0,sK8(sK14,sK17,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_12898,c_10846]) ).
cnf(c_13010,plain,
( ~ member(X0,sK16)
| member(sK8(sK14,sK17,X0),sK18) ),
inference(superposition,[status(thm)],[c_110,c_12897]) ).
cnf(c_13041,plain,
( ~ member(sK8(sK14,sK17,sK7(sK15,X0,X1)),X1)
| ~ member(sK7(sK15,X0,X1),sK16)
| ~ sP0(sK15,X1,X0)
| maps(sK15,X0,X1) ),
inference(superposition,[status(thm)],[c_12899,c_82]) ).
cnf(c_13305,plain,
( ~ apply(sK14,X0,X1)
| ~ apply(sK14,X0,X2)
| ~ member(X0,sK16)
| ~ member(X1,sK17)
| ~ member(X2,sK17)
| X1 = X2 ),
inference(superposition,[status(thm)],[c_3107,c_81]) ).
cnf(c_13912,plain,
( ~ member(sK7(sK15,X0,sK18),sK16)
| ~ sP0(sK15,sK18,X0)
| maps(sK15,X0,sK18) ),
inference(superposition,[status(thm)],[c_13010,c_13041]) ).
cnf(c_13970,plain,
( ~ sP0(sK15,sK18,sK16)
| maps(sK15,sK16,sK18) ),
inference(superposition,[status(thm)],[c_83,c_13912]) ).
cnf(c_13971,plain,
~ sP0(sK15,sK18,sK16),
inference(forward_subsumption_resolution,[status(thm)],[c_13970,c_107]) ).
cnf(c_13982,plain,
( ~ member(sK8(sK14,sK17,X0),sK17)
| ~ apply(sK14,X0,X1)
| ~ member(X0,sK16)
| ~ member(X1,sK17)
| sK8(sK14,sK17,X0) = X1 ),
inference(superposition,[status(thm)],[c_12777,c_13305]) ).
cnf(c_17953,plain,
( ~ member(sK4(sK15,sK18,sK16),sK16)
| ~ maps(sK14,sK16,sK17)
| member(sK8(sK14,sK17,sK4(sK15,sK18,sK16)),sK17) ),
inference(instantiation,[status(thm)],[c_8531]) ).
cnf(c_17954,plain,
( ~ member(sK4(sK15,sK18,sK16),sK16)
| ~ maps(sK14,sK16,sK17)
| apply(sK14,sK4(sK15,sK18,sK16),sK8(sK14,sK17,sK4(sK15,sK18,sK16))) ),
inference(instantiation,[status(thm)],[c_8534]) ).
cnf(c_33875,plain,
( ~ member(X0,sK18)
| ~ subset(sK18,sK17)
| member(X0,sK17) ),
inference(instantiation,[status(thm)],[c_10383]) ).
cnf(c_35055,plain,
( ~ member(sK5(sK15,sK18,sK16),sK18)
| ~ subset(sK18,sK17)
| member(sK5(sK15,sK18,sK16),sK17) ),
inference(instantiation,[status(thm)],[c_33875]) ).
cnf(c_35638,plain,
( ~ member(sK6(sK15,sK18,sK16),sK18)
| ~ subset(sK18,sK17)
| member(sK6(sK15,sK18,sK16),sK17) ),
inference(instantiation,[status(thm)],[c_33875]) ).
cnf(c_51785,plain,
~ member(X0,inverse_image2(X1,empty_set)),
inference(superposition,[status(thm)],[c_102,c_60]) ).
cnf(c_51850,plain,
member(X0,product(inverse_image2(X1,empty_set))),
inference(superposition,[status(thm)],[c_73,c_51785]) ).
cnf(c_52173,plain,
( ~ member(X0,sK16)
| apply(sK14,X0,sK8(sK14,sK17,X0)) ),
inference(superposition,[status(thm)],[c_112,c_85]) ).
cnf(c_52265,plain,
( ~ member(X0,X1)
| ~ member(X0,sK16)
| member(sK8(sK14,sK17,X0),image2(sK14,X1)) ),
inference(superposition,[status(thm)],[c_52173,c_93]) ).
cnf(c_52266,plain,
( ~ member(sK8(sK14,sK17,X0),sK18)
| ~ member(X0,sK16)
| apply(sK15,X0,sK8(sK14,sK17,X0)) ),
inference(superposition,[status(thm)],[c_52173,c_108]) ).
cnf(c_52267,plain,
( ~ member(X0,sK16)
| apply(sK15,X0,sK8(sK14,sK17,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_52266,c_10846]) ).
cnf(c_52271,plain,
( ~ member(sK8(sK14,sK17,X0),X1)
| ~ member(X0,sK16)
| member(X0,inverse_image2(sK15,X1)) ),
inference(superposition,[status(thm)],[c_52267,c_100]) ).
cnf(c_52372,plain,
( ~ member(X0,sK16)
| member(sK8(sK14,sK17,X0),sK18) ),
inference(superposition,[status(thm)],[c_110,c_52265]) ).
cnf(c_52414,plain,
( ~ member(sK8(sK14,sK17,X0),X1)
| ~ member(X0,X2)
| ~ member(X0,sK16)
| member(X0,inverse_image3(sK15,X1,X2)) ),
inference(superposition,[status(thm)],[c_52267,c_103]) ).
cnf(c_52537,plain,
( ~ member(X0,sK16)
| member(X0,inverse_image2(sK15,product(inverse_image2(X1,empty_set)))) ),
inference(superposition,[status(thm)],[c_51850,c_52271]) ).
cnf(c_52733,plain,
( ~ member(X0,X1)
| ~ member(X0,sK16)
| member(X0,inverse_image3(sK15,sK18,X1)) ),
inference(superposition,[status(thm)],[c_52372,c_52414]) ).
cnf(c_52765,plain,
( ~ member(X0,X1)
| ~ member(X0,sK16)
| member(sK13(sK15,sK18,X0),sK18) ),
inference(superposition,[status(thm)],[c_52733,c_105]) ).
cnf(c_64447,plain,
( ~ member(X0,sK16)
| member(sK13(sK15,sK18,X0),sK18) ),
inference(superposition,[status(thm)],[c_52537,c_52765]) ).
cnf(c_111983,plain,
( ~ member(X0,sum(image3(X1,X2,X3)))
| member(sK2(X0,image3(X1,X2,X3)),X3) ),
inference(superposition,[status(thm)],[c_71,c_99]) ).
cnf(c_111993,plain,
~ member(X0,sum(image3(X1,X2,empty_set))),
inference(superposition,[status(thm)],[c_111983,c_60]) ).
cnf(c_112022,plain,
member(X0,product(sum(image3(X1,X2,empty_set)))),
inference(superposition,[status(thm)],[c_73,c_111993]) ).
cnf(c_112968,plain,
( ~ member(X0,sK16)
| apply(sK14,X0,sK8(sK14,sK17,X0)) ),
inference(superposition,[status(thm)],[c_112,c_85]) ).
cnf(c_113048,plain,
( ~ member(X0,X1)
| ~ member(X0,sK16)
| member(sK8(sK14,sK17,X0),image2(sK14,X1)) ),
inference(superposition,[status(thm)],[c_112968,c_93]) ).
cnf(c_113049,plain,
( ~ member(sK8(sK14,sK17,X0),sK18)
| ~ member(X0,sK16)
| apply(sK15,X0,sK8(sK14,sK17,X0)) ),
inference(superposition,[status(thm)],[c_112968,c_108]) ).
cnf(c_113050,plain,
( ~ member(X0,sK16)
| apply(sK15,X0,sK8(sK14,sK17,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_113049,c_10846]) ).
cnf(c_113150,plain,
( ~ member(X0,sK16)
| member(sK8(sK14,sK17,X0),sK18) ),
inference(superposition,[status(thm)],[c_110,c_113048]) ).
cnf(c_113174,plain,
( ~ member(sK8(sK14,sK17,X0),X1)
| ~ member(X0,X2)
| ~ member(X0,sK16)
| member(X0,inverse_image3(sK15,X1,X2)) ),
inference(superposition,[status(thm)],[c_113050,c_103]) ).
cnf(c_113678,plain,
( ~ member(X0,X1)
| ~ member(X0,sK16)
| member(X0,inverse_image3(sK15,sK18,X1)) ),
inference(superposition,[status(thm)],[c_113150,c_113174]) ).
cnf(c_113712,plain,
( ~ member(X0,X1)
| ~ member(X0,sK16)
| apply(sK15,X0,sK13(sK15,sK18,X0)) ),
inference(superposition,[status(thm)],[c_113678,c_104]) ).
cnf(c_114026,plain,
( ~ member(X0,sK16)
| apply(sK15,X0,sK13(sK15,sK18,X0)) ),
inference(superposition,[status(thm)],[c_112022,c_113712]) ).
cnf(c_276424,plain,
( ~ member(sK13(sK15,sK18,X0),sK18)
| ~ member(X0,sK16)
| apply(sK14,X0,sK13(sK15,sK18,X0)) ),
inference(superposition,[status(thm)],[c_114026,c_109]) ).
cnf(c_276438,plain,
( ~ member(X0,sK16)
| apply(sK14,X0,sK13(sK15,sK18,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_276424,c_64447,c_276424]) ).
cnf(c_276691,plain,
( ~ subset(sK18,X0)
| ~ member(X1,sK16)
| member(sK13(sK15,sK18,X1),X0) ),
inference(superposition,[status(thm)],[c_64447,c_51]) ).
cnf(c_277146,plain,
( ~ member(sK6(sK15,X0,X1),sK18)
| ~ member(sK4(sK15,X0,X1),sK16)
| apply(sK14,sK4(sK15,X0,X1),sK6(sK15,X0,X1))
| sP0(sK15,X0,X1) ),
inference(superposition,[status(thm)],[c_76,c_109]) ).
cnf(c_277150,plain,
( ~ member(sK5(sK15,X0,X1),sK18)
| ~ member(sK4(sK15,X0,X1),sK16)
| apply(sK14,sK4(sK15,X0,X1),sK5(sK15,X0,X1))
| sP0(sK15,X0,X1) ),
inference(superposition,[status(thm)],[c_77,c_109]) ).
cnf(c_277610,plain,
( ~ member(X0,sK16)
| apply(sK14,X0,sK8(sK14,sK17,X0)) ),
inference(superposition,[status(thm)],[c_112,c_85]) ).
cnf(c_277724,plain,
( ~ member(X0,X1)
| ~ member(X0,sK16)
| member(sK8(sK14,sK17,X0),image2(sK14,X1)) ),
inference(superposition,[status(thm)],[c_277610,c_93]) ).
cnf(c_277725,plain,
( ~ member(sK8(sK14,sK17,X0),sK18)
| ~ member(X0,sK16)
| apply(sK15,X0,sK8(sK14,sK17,X0)) ),
inference(superposition,[status(thm)],[c_277610,c_108]) ).
cnf(c_277726,plain,
( ~ member(X0,sK16)
| apply(sK15,X0,sK8(sK14,sK17,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_277725,c_10846]) ).
cnf(c_277821,plain,
( ~ member(X0,sK16)
| member(sK8(sK14,sK17,X0),sK18) ),
inference(superposition,[status(thm)],[c_110,c_277724]) ).
cnf(c_277889,plain,
( ~ member(sK8(sK14,sK17,sK7(sK15,X0,X1)),X1)
| ~ member(sK7(sK15,X0,X1),sK16)
| ~ sP0(sK15,X1,X0)
| maps(sK15,X0,X1) ),
inference(superposition,[status(thm)],[c_277726,c_82]) ).
cnf(c_278199,plain,
( ~ apply(sK14,X0,X1)
| ~ apply(sK14,X0,X2)
| ~ member(X0,sK16)
| ~ member(X1,sK17)
| ~ member(X2,sK17)
| X1 = X2 ),
inference(superposition,[status(thm)],[c_3107,c_81]) ).
cnf(c_278860,plain,
( ~ member(sK7(sK15,X0,sK18),sK16)
| ~ sP0(sK15,sK18,X0)
| maps(sK15,X0,sK18) ),
inference(superposition,[status(thm)],[c_277821,c_277889]) ).
cnf(c_278881,plain,
( ~ sP0(sK15,sK18,sK16)
| maps(sK15,sK16,sK18) ),
inference(superposition,[status(thm)],[c_83,c_278860]) ).
cnf(c_278882,plain,
~ sP0(sK15,sK18,sK16),
inference(forward_subsumption_resolution,[status(thm)],[c_278881,c_107]) ).
cnf(c_278971,plain,
( ~ member(sK8(sK14,sK17,X0),sK17)
| ~ apply(sK14,X0,X1)
| ~ member(X0,sK16)
| ~ member(X1,sK17)
| sK8(sK14,sK17,X0) = X1 ),
inference(superposition,[status(thm)],[c_277610,c_278199]) ).
cnf(c_278974,plain,
( ~ apply(sK14,sK4(sK15,X0,X1),X2)
| ~ member(sK6(sK15,X0,X1),sK18)
| ~ member(sK6(sK15,X0,X1),sK17)
| ~ member(sK4(sK15,X0,X1),sK16)
| ~ member(X2,sK17)
| sK6(sK15,X0,X1) = X2
| sP0(sK15,X0,X1) ),
inference(superposition,[status(thm)],[c_277146,c_278199]) ).
cnf(c_278975,plain,
( ~ apply(sK14,sK4(sK15,X0,X1),X2)
| ~ member(sK5(sK15,X0,X1),sK18)
| ~ member(sK5(sK15,X0,X1),sK17)
| ~ member(sK4(sK15,X0,X1),sK16)
| ~ member(X2,sK17)
| sK5(sK15,X0,X1) = X2
| sP0(sK15,X0,X1) ),
inference(superposition,[status(thm)],[c_277150,c_278199]) ).
cnf(c_279065,plain,
( ~ apply(sK14,X0,X1)
| ~ member(X0,sK16)
| ~ member(X1,sK17)
| sK8(sK14,sK17,X0) = X1 ),
inference(global_subsumption_just,[status(thm)],[c_278971,c_1200,c_13982]) ).
cnf(c_279084,plain,
( ~ member(sK13(sK15,sK18,X0),sK17)
| ~ member(X0,sK16)
| sK8(sK14,sK17,X0) = sK13(sK15,sK18,X0) ),
inference(superposition,[status(thm)],[c_276438,c_279065]) ).
cnf(c_279093,plain,
( ~ member(X0,sK16)
| ~ subset(sK18,sK17)
| sK8(sK14,sK17,X0) = sK13(sK15,sK18,X0) ),
inference(superposition,[status(thm)],[c_276691,c_279084]) ).
cnf(c_279094,plain,
( ~ member(X0,sK16)
| sK8(sK14,sK17,X0) = sK13(sK15,sK18,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_279093,c_111]) ).
cnf(c_279103,plain,
( sK8(sK14,sK17,sK4(X0,X1,sK16)) = sK13(sK15,sK18,sK4(X0,X1,sK16))
| sP0(X0,X1,sK16) ),
inference(superposition,[status(thm)],[c_80,c_279094]) ).
cnf(c_279388,plain,
sK8(sK14,sK17,sK4(sK15,sK18,sK16)) = sK13(sK15,sK18,sK4(sK15,sK18,sK16)),
inference(superposition,[status(thm)],[c_279103,c_278882]) ).
cnf(c_279398,plain,
( ~ member(sK4(sK15,sK18,sK16),sK16)
| apply(sK14,sK4(sK15,sK18,sK16),sK8(sK14,sK17,sK4(sK15,sK18,sK16))) ),
inference(superposition,[status(thm)],[c_279388,c_276438]) ).
cnf(c_279407,plain,
apply(sK14,sK4(sK15,sK18,sK16),sK8(sK14,sK17,sK4(sK15,sK18,sK16))),
inference(global_subsumption_just,[status(thm)],[c_279398,c_112,c_3182,c_13971,c_17954]) ).
cnf(c_288079,plain,
( ~ member(sK8(sK14,sK17,sK4(sK15,sK18,sK16)),sK17)
| ~ member(sK6(sK15,sK18,sK16),sK18)
| ~ member(sK6(sK15,sK18,sK16),sK17)
| ~ member(sK4(sK15,sK18,sK16),sK16)
| sK8(sK14,sK17,sK4(sK15,sK18,sK16)) = sK6(sK15,sK18,sK16)
| sP0(sK15,sK18,sK16) ),
inference(superposition,[status(thm)],[c_279407,c_278974]) ).
cnf(c_288084,plain,
( ~ member(sK8(sK14,sK17,sK4(sK15,sK18,sK16)),sK17)
| ~ member(sK6(sK15,sK18,sK16),sK18)
| ~ member(sK6(sK15,sK18,sK16),sK17)
| ~ member(sK4(sK15,sK18,sK16),sK16)
| sK8(sK14,sK17,sK4(sK15,sK18,sK16)) = sK6(sK15,sK18,sK16) ),
inference(forward_subsumption_resolution,[status(thm)],[c_288079,c_278882]) ).
cnf(c_288102,plain,
( ~ member(sK8(sK14,sK17,sK4(sK15,sK18,sK16)),sK17)
| ~ member(sK5(sK15,sK18,sK16),sK18)
| ~ member(sK5(sK15,sK18,sK16),sK17)
| ~ member(sK4(sK15,sK18,sK16),sK16)
| sK8(sK14,sK17,sK4(sK15,sK18,sK16)) = sK5(sK15,sK18,sK16)
| sP0(sK15,sK18,sK16) ),
inference(superposition,[status(thm)],[c_279407,c_278975]) ).
cnf(c_288107,plain,
( ~ member(sK8(sK14,sK17,sK4(sK15,sK18,sK16)),sK17)
| ~ member(sK5(sK15,sK18,sK16),sK18)
| ~ member(sK5(sK15,sK18,sK16),sK17)
| ~ member(sK4(sK15,sK18,sK16),sK16)
| sK8(sK14,sK17,sK4(sK15,sK18,sK16)) = sK5(sK15,sK18,sK16) ),
inference(forward_subsumption_resolution,[status(thm)],[c_288102,c_278882]) ).
cnf(c_288111,plain,
sK8(sK14,sK17,sK4(sK15,sK18,sK16)) = sK6(sK15,sK18,sK16),
inference(global_subsumption_just,[status(thm)],[c_288084,c_111,c_112,c_3184,c_3182,c_13971,c_17953,c_35638,c_288084]) ).
cnf(c_288279,plain,
sK8(sK14,sK17,sK4(sK15,sK18,sK16)) = sK5(sK15,sK18,sK16),
inference(global_subsumption_just,[status(thm)],[c_288107,c_111,c_112,c_3183,c_3182,c_13971,c_17953,c_35055,c_288107]) ).
cnf(c_288281,plain,
sK5(sK15,sK18,sK16) = sK6(sK15,sK18,sK16),
inference(demodulation,[status(thm)],[c_288111,c_288279]) ).
cnf(c_288282,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_288281,c_13971,c_3181]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.07 % Problem : SET730+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.06/0.07 % Command : run_iprover %s %d THM
% 0.07/0.26 % Computer : n032.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Thu May 2 20:40:08 EDT 2024
% 0.07/0.26 % CPUTime :
% 0.12/0.33 Running first-order theorem proving
% 0.12/0.33 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
% 127.40/17.55 % SZS status Started for theBenchmark.p
% 127.40/17.55 % SZS status Theorem for theBenchmark.p
% 127.40/17.55
% 127.40/17.55 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 127.40/17.55
% 127.40/17.55 ------ iProver source info
% 127.40/17.55
% 127.40/17.55 git: date: 2024-05-02 19:28:25 +0000
% 127.40/17.55 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 127.40/17.55 git: non_committed_changes: false
% 127.40/17.55
% 127.40/17.55 ------ Parsing...
% 127.40/17.55 ------ Clausification by vclausify_rel & Parsing by iProver...
% 127.40/17.55
% 127.40/17.55 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 127.40/17.55
% 127.40/17.55 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 127.40/17.55
% 127.40/17.55 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 127.40/17.55 ------ Proving...
% 127.40/17.55 ------ Problem Properties
% 127.40/17.55
% 127.40/17.55
% 127.40/17.55 clauses 64
% 127.40/17.55 conjectures 6
% 127.40/17.55 EPR 9
% 127.40/17.55 Horn 53
% 127.40/17.55 unary 8
% 127.40/17.55 binary 32
% 127.40/17.55 lits 161
% 127.40/17.55 lits eq 6
% 127.40/17.55 fd_pure 0
% 127.40/17.55 fd_pseudo 0
% 127.40/17.55 fd_cond 0
% 127.40/17.55 fd_pseudo_cond 3
% 127.40/17.55 AC symbols 0
% 127.40/17.55
% 127.40/17.55 ------ Input Options Time Limit: Unbounded
% 127.40/17.55
% 127.40/17.55
% 127.40/17.55 ------
% 127.40/17.55 Current options:
% 127.40/17.55 ------
% 127.40/17.55
% 127.40/17.55
% 127.40/17.55
% 127.40/17.55
% 127.40/17.55 ------ Proving...
% 127.40/17.55
% 127.40/17.55
% 127.40/17.55 % SZS status Theorem for theBenchmark.p
% 127.40/17.55
% 127.40/17.55 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 127.40/17.55
% 127.40/17.56
%------------------------------------------------------------------------------