TSTP Solution File: SET712+4 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET712+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n014.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 03:01:19 EDT 2024
% Result : Theorem 42.78s 6.68s
% Output : CNFRefutation 42.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 114 ( 7 unt; 0 def)
% Number of atoms : 488 ( 46 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 600 ( 226 ~; 230 |; 100 &)
% ( 16 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 389 ( 0 sgn 241 !; 36 ?)
% Comments :
%------------------------------------------------------------------------------
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(f17,axiom,
! [X5,X0,X1] :
( injective(X5,X0,X1)
<=> ! [X12,X13,X4] :
( ( member(X4,X1)
& member(X13,X0)
& member(X12,X0) )
=> ( ( apply(X5,X13,X4)
& apply(X5,X12,X4) )
=> X12 = X13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',injective) ).
fof(f18,axiom,
! [X5,X0,X1] :
( surjective(X5,X0,X1)
<=> ! [X4] :
( member(X4,X1)
=> ? [X3] :
( apply(X5,X3,X4)
& member(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',surjective) ).
fof(f19,axiom,
! [X5,X0,X1] :
( one_to_one(X5,X0,X1)
<=> ( surjective(X5,X0,X1)
& injective(X5,X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one) ).
fof(f21,axiom,
! [X5,X0,X1,X2,X4] :
( ( member(X4,X1)
& member(X2,X0) )
=> ( apply(X5,X2,X4)
<=> apply(inverse_function(X5,X0,X1),X4,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_function) ).
fof(f29,conjecture,
! [X5,X0,X1] :
( ( one_to_one(X5,X0,X1)
& maps(X5,X0,X1) )
=> maps(inverse_function(X5,X0,X1),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII03) ).
fof(f30,negated_conjecture,
~ ! [X5,X0,X1] :
( ( one_to_one(X5,X0,X1)
& maps(X5,X0,X1) )
=> maps(inverse_function(X5,X0,X1),X1,X0) ),
inference(negated_conjecture,[],[f29]) ).
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(f45,plain,
! [X0,X1,X2] :
( injective(X0,X1,X2)
<=> ! [X3,X4,X5] :
( ( member(X5,X2)
& member(X4,X1)
& member(X3,X1) )
=> ( ( apply(X0,X4,X5)
& apply(X0,X3,X5) )
=> X3 = X4 ) ) ),
inference(rectify,[],[f17]) ).
fof(f46,plain,
! [X0,X1,X2] :
( surjective(X0,X1,X2)
<=> ! [X3] :
( member(X3,X2)
=> ? [X4] :
( apply(X0,X4,X3)
& member(X4,X1) ) ) ),
inference(rectify,[],[f18]) ).
fof(f47,plain,
! [X0,X1,X2] :
( one_to_one(X0,X1,X2)
<=> ( surjective(X0,X1,X2)
& injective(X0,X1,X2) ) ),
inference(rectify,[],[f19]) ).
fof(f49,plain,
! [X0,X1,X2,X3,X4] :
( ( member(X4,X2)
& member(X3,X1) )
=> ( apply(X0,X3,X4)
<=> apply(inverse_function(X0,X1,X2),X4,X3) ) ),
inference(rectify,[],[f21]) ).
fof(f57,plain,
~ ! [X0,X1,X2] :
( ( one_to_one(X0,X1,X2)
& maps(X0,X1,X2) )
=> maps(inverse_function(X0,X1,X2),X2,X1) ),
inference(rectify,[],[f30]) ).
fof(f58,plain,
! [X0,X1,X2] :
( one_to_one(X0,X1,X2)
=> ( surjective(X0,X1,X2)
& injective(X0,X1,X2) ) ),
inference(unused_predicate_definition_removal,[],[f47]) ).
fof(f59,plain,
! [X0,X1,X2] :
( surjective(X0,X1,X2)
=> ! [X3] :
( member(X3,X2)
=> ? [X4] :
( apply(X0,X4,X3)
& member(X4,X1) ) ) ),
inference(unused_predicate_definition_removal,[],[f46]) ).
fof(f60,plain,
! [X0,X1,X2] :
( injective(X0,X1,X2)
=> ! [X3,X4,X5] :
( ( member(X5,X2)
& member(X4,X1)
& member(X3,X1) )
=> ( ( apply(X0,X4,X5)
& apply(X0,X3,X5) )
=> X3 = X4 ) ) ),
inference(unused_predicate_definition_removal,[],[f45]) ).
fof(f63,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(f64,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,[],[f63]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ! [X3,X4,X5] :
( X3 = X4
| ~ apply(X0,X4,X5)
| ~ apply(X0,X3,X5)
| ~ member(X5,X2)
| ~ member(X4,X1)
| ~ member(X3,X1) )
| ~ injective(X0,X1,X2) ),
inference(ennf_transformation,[],[f60]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ! [X3,X4,X5] :
( X3 = X4
| ~ apply(X0,X4,X5)
| ~ apply(X0,X3,X5)
| ~ member(X5,X2)
| ~ member(X4,X1)
| ~ member(X3,X1) )
| ~ injective(X0,X1,X2) ),
inference(flattening,[],[f67]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ! [X3] :
( ? [X4] :
( apply(X0,X4,X3)
& member(X4,X1) )
| ~ member(X3,X2) )
| ~ surjective(X0,X1,X2) ),
inference(ennf_transformation,[],[f59]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ( surjective(X0,X1,X2)
& injective(X0,X1,X2) )
| ~ one_to_one(X0,X1,X2) ),
inference(ennf_transformation,[],[f58]) ).
fof(f71,plain,
! [X0,X1,X2,X3,X4] :
( ( apply(X0,X3,X4)
<=> apply(inverse_function(X0,X1,X2),X4,X3) )
| ~ member(X4,X2)
| ~ member(X3,X1) ),
inference(ennf_transformation,[],[f49]) ).
fof(f72,plain,
! [X0,X1,X2,X3,X4] :
( ( apply(X0,X3,X4)
<=> apply(inverse_function(X0,X1,X2),X4,X3) )
| ~ member(X4,X2)
| ~ member(X3,X1) ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
? [X0,X1,X2] :
( ~ maps(inverse_function(X0,X1,X2),X2,X1)
& one_to_one(X0,X1,X2)
& maps(X0,X1,X2) ),
inference(ennf_transformation,[],[f57]) ).
fof(f74,plain,
? [X0,X1,X2] :
( ~ maps(inverse_function(X0,X1,X2),X2,X1)
& one_to_one(X0,X1,X2)
& maps(X0,X1,X2) ),
inference(flattening,[],[f73]) ).
fof(f75,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(f76,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,[],[f64,f75]) ).
fof(f99,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,[],[f75]) ).
fof(f100,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,[],[f99]) ).
fof(f101,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(f102,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])],[f100,f101]) ).
fof(f103,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,[],[f76]) ).
fof(f104,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,[],[f103]) ).
fof(f105,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,[],[f104]) ).
fof(f106,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(f107,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(f108,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])],[f105,f107,f106]) ).
fof(f113,plain,
! [X0,X1,X3] :
( ? [X4] :
( apply(X0,X4,X3)
& member(X4,X1) )
=> ( apply(X0,sK10(X0,X1,X3),X3)
& member(sK10(X0,X1,X3),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f114,plain,
! [X0,X1,X2] :
( ! [X3] :
( ( apply(X0,sK10(X0,X1,X3),X3)
& member(sK10(X0,X1,X3),X1) )
| ~ member(X3,X2) )
| ~ surjective(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f69,f113]) ).
fof(f115,plain,
! [X0,X1,X2,X3,X4] :
( ( ( apply(X0,X3,X4)
| ~ apply(inverse_function(X0,X1,X2),X4,X3) )
& ( apply(inverse_function(X0,X1,X2),X4,X3)
| ~ apply(X0,X3,X4) ) )
| ~ member(X4,X2)
| ~ member(X3,X1) ),
inference(nnf_transformation,[],[f72]) ).
fof(f134,plain,
( ? [X0,X1,X2] :
( ~ maps(inverse_function(X0,X1,X2),X2,X1)
& one_to_one(X0,X1,X2)
& maps(X0,X1,X2) )
=> ( ~ maps(inverse_function(sK15,sK16,sK17),sK17,sK16)
& one_to_one(sK15,sK16,sK17)
& maps(sK15,sK16,sK17) ) ),
introduced(choice_axiom,[]) ).
fof(f135,plain,
( ~ maps(inverse_function(sK15,sK16,sK17),sK17,sK16)
& one_to_one(sK15,sK16,sK17)
& maps(sK15,sK16,sK17) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16,sK17])],[f74,f134]) ).
fof(f163,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| member(sK4(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f102]) ).
fof(f164,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| member(sK5(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f165,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| member(sK6(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f166,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| apply(X0,sK4(X0,X1,X2),sK5(X0,X1,X2)) ),
inference(cnf_transformation,[],[f102]) ).
fof(f167,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| apply(X0,sK4(X0,X1,X2),sK6(X0,X1,X2)) ),
inference(cnf_transformation,[],[f102]) ).
fof(f168,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| sK5(X0,X1,X2) != sK6(X0,X1,X2) ),
inference(cnf_transformation,[],[f102]) ).
fof(f172,plain,
! [X2,X0,X1] :
( maps(X0,X1,X2)
| ~ sP0(X0,X2,X1)
| member(sK7(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f108]) ).
fof(f173,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,[],[f108]) ).
fof(f178,plain,
! [X2,X3,X0,X1,X4,X5] :
( X3 = X4
| ~ apply(X0,X4,X5)
| ~ apply(X0,X3,X5)
| ~ member(X5,X2)
| ~ member(X4,X1)
| ~ member(X3,X1)
| ~ injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f68]) ).
fof(f179,plain,
! [X2,X3,X0,X1] :
( member(sK10(X0,X1,X3),X1)
| ~ member(X3,X2)
| ~ surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f114]) ).
fof(f180,plain,
! [X2,X3,X0,X1] :
( apply(X0,sK10(X0,X1,X3),X3)
| ~ member(X3,X2)
| ~ surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f114]) ).
fof(f181,plain,
! [X2,X0,X1] :
( injective(X0,X1,X2)
| ~ one_to_one(X0,X1,X2) ),
inference(cnf_transformation,[],[f70]) ).
fof(f182,plain,
! [X2,X0,X1] :
( surjective(X0,X1,X2)
| ~ one_to_one(X0,X1,X2) ),
inference(cnf_transformation,[],[f70]) ).
fof(f183,plain,
! [X2,X3,X0,X1,X4] :
( apply(inverse_function(X0,X1,X2),X4,X3)
| ~ apply(X0,X3,X4)
| ~ member(X4,X2)
| ~ member(X3,X1) ),
inference(cnf_transformation,[],[f115]) ).
fof(f184,plain,
! [X2,X3,X0,X1,X4] :
( apply(X0,X3,X4)
| ~ apply(inverse_function(X0,X1,X2),X4,X3)
| ~ member(X4,X2)
| ~ member(X3,X1) ),
inference(cnf_transformation,[],[f115]) ).
fof(f200,plain,
one_to_one(sK15,sK16,sK17),
inference(cnf_transformation,[],[f135]) ).
fof(f201,plain,
~ maps(inverse_function(sK15,sK16,sK17),sK17,sK16),
inference(cnf_transformation,[],[f135]) ).
cnf(c_75,plain,
( sK5(X0,X1,X2) != sK6(X0,X1,X2)
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f168]) ).
cnf(c_76,plain,
( apply(X0,sK4(X0,X1,X2),sK6(X0,X1,X2))
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f167]) ).
cnf(c_77,plain,
( apply(X0,sK4(X0,X1,X2),sK5(X0,X1,X2))
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f166]) ).
cnf(c_78,plain,
( member(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f165]) ).
cnf(c_79,plain,
( member(sK5(X0,X1,X2),X1)
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f164]) ).
cnf(c_80,plain,
( member(sK4(X0,X1,X2),X2)
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f163]) ).
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,[],[f173]) ).
cnf(c_83,plain,
( ~ sP0(X0,X1,X2)
| member(sK7(X0,X2,X1),X2)
| maps(X0,X2,X1) ),
inference(cnf_transformation,[],[f172]) ).
cnf(c_91,plain,
( ~ apply(X0,X1,X2)
| ~ apply(X0,X3,X2)
| ~ injective(X0,X4,X5)
| ~ member(X1,X4)
| ~ member(X2,X5)
| ~ member(X3,X4)
| X1 = X3 ),
inference(cnf_transformation,[],[f178]) ).
cnf(c_92,plain,
( ~ surjective(X0,X1,X2)
| ~ member(X3,X2)
| apply(X0,sK10(X0,X1,X3),X3) ),
inference(cnf_transformation,[],[f180]) ).
cnf(c_93,plain,
( ~ surjective(X0,X1,X2)
| ~ member(X3,X2)
| member(sK10(X0,X1,X3),X1) ),
inference(cnf_transformation,[],[f179]) ).
cnf(c_94,plain,
( ~ one_to_one(X0,X1,X2)
| surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f182]) ).
cnf(c_95,plain,
( ~ one_to_one(X0,X1,X2)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f181]) ).
cnf(c_96,plain,
( ~ apply(inverse_function(X0,X1,X2),X3,X4)
| ~ member(X3,X2)
| ~ member(X4,X1)
| apply(X0,X4,X3) ),
inference(cnf_transformation,[],[f184]) ).
cnf(c_97,plain,
( ~ apply(X0,X1,X2)
| ~ member(X1,X3)
| ~ member(X2,X4)
| apply(inverse_function(X0,X3,X4),X2,X1) ),
inference(cnf_transformation,[],[f183]) ).
cnf(c_112,negated_conjecture,
~ maps(inverse_function(sK15,sK16,sK17),sK17,sK16),
inference(cnf_transformation,[],[f201]) ).
cnf(c_113,negated_conjecture,
one_to_one(sK15,sK16,sK17),
inference(cnf_transformation,[],[f200]) ).
cnf(c_238,plain,
( surjective(X0,X1,X2)
| ~ one_to_one(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_94]) ).
cnf(c_239,plain,
( ~ one_to_one(X0,X1,X2)
| surjective(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_238]) ).
cnf(c_242,plain,
( ~ one_to_one(X0,X1,X2)
| injective(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_95]) ).
cnf(c_1085,plain,
( X0 != sK15
| X1 != sK16
| X2 != sK17
| injective(X0,X1,X2) ),
inference(resolution_lifted,[status(thm)],[c_242,c_113]) ).
cnf(c_1086,plain,
injective(sK15,sK16,sK17),
inference(unflattening,[status(thm)],[c_1085]) ).
cnf(c_1090,plain,
( X0 != sK15
| X1 != sK16
| X2 != sK17
| surjective(X0,X1,X2) ),
inference(resolution_lifted,[status(thm)],[c_239,c_113]) ).
cnf(c_1091,plain,
surjective(sK15,sK16,sK17),
inference(unflattening,[status(thm)],[c_1090]) ).
cnf(c_1097,plain,
( X0 != sK15
| X1 != sK16
| X2 != sK17
| ~ member(X3,X2)
| member(sK10(X0,X1,X3),X1) ),
inference(resolution_lifted,[status(thm)],[c_93,c_1091]) ).
cnf(c_1098,plain,
( ~ member(X0,sK17)
| member(sK10(sK15,sK16,X0),sK16) ),
inference(unflattening,[status(thm)],[c_1097]) ).
cnf(c_1106,plain,
( X0 != sK15
| X1 != sK16
| X2 != sK17
| ~ member(X3,X2)
| apply(X0,sK10(X0,X1,X3),X3) ),
inference(resolution_lifted,[status(thm)],[c_92,c_1091]) ).
cnf(c_1107,plain,
( ~ member(X0,sK17)
| apply(sK15,sK10(sK15,sK16,X0),X0) ),
inference(unflattening,[status(thm)],[c_1106]) ).
cnf(c_1119,plain,
( X0 != sK15
| X1 != sK16
| X2 != sK17
| ~ apply(X0,X3,X4)
| ~ apply(X0,X5,X4)
| ~ member(X3,X1)
| ~ member(X4,X2)
| ~ member(X5,X1)
| X3 = X5 ),
inference(resolution_lifted,[status(thm)],[c_91,c_1086]) ).
cnf(c_1120,plain,
( ~ apply(sK15,X0,X1)
| ~ apply(sK15,X2,X1)
| ~ member(X0,sK16)
| ~ member(X1,sK17)
| ~ member(X2,sK16)
| X0 = X2 ),
inference(unflattening,[status(thm)],[c_1119]) ).
cnf(c_1317,plain,
( inverse_function(sK15,sK16,sK17) != X0
| X1 != sK16
| X2 != sK17
| ~ sP0(X0,X1,X2)
| member(sK7(X0,X2,X1),X2) ),
inference(resolution_lifted,[status(thm)],[c_83,c_112]) ).
cnf(c_1318,plain,
( ~ sP0(inverse_function(sK15,sK16,sK17),sK16,sK17)
| member(sK7(inverse_function(sK15,sK16,sK17),sK17,sK16),sK17) ),
inference(unflattening,[status(thm)],[c_1317]) ).
cnf(c_1911,plain,
( ~ member(X0,sK17)
| member(sK10(sK15,sK16,X0),sK16) ),
inference(prop_impl_just,[status(thm)],[c_1098]) ).
cnf(c_1913,plain,
( ~ member(X0,sK17)
| apply(sK15,sK10(sK15,sK16,X0),X0) ),
inference(prop_impl_just,[status(thm)],[c_1107]) ).
cnf(c_4849,plain,
( apply(inverse_function(sK15,sK16,sK17),sK4(inverse_function(sK15,sK16,sK17),sK16,sK17),sK5(inverse_function(sK15,sK16,sK17),sK16,sK17))
| sP0(inverse_function(sK15,sK16,sK17),sK16,sK17) ),
inference(instantiation,[status(thm)],[c_77]) ).
cnf(c_4850,plain,
( apply(inverse_function(sK15,sK16,sK17),sK4(inverse_function(sK15,sK16,sK17),sK16,sK17),sK6(inverse_function(sK15,sK16,sK17),sK16,sK17))
| sP0(inverse_function(sK15,sK16,sK17),sK16,sK17) ),
inference(instantiation,[status(thm)],[c_76]) ).
cnf(c_4851,plain,
( sK5(inverse_function(sK15,sK16,sK17),sK16,sK17) != sK6(inverse_function(sK15,sK16,sK17),sK16,sK17)
| sP0(inverse_function(sK15,sK16,sK17),sK16,sK17) ),
inference(instantiation,[status(thm)],[c_75]) ).
cnf(c_4852,plain,
( member(sK4(inverse_function(sK15,sK16,sK17),sK16,sK17),sK17)
| sP0(inverse_function(sK15,sK16,sK17),sK16,sK17) ),
inference(instantiation,[status(thm)],[c_80]) ).
cnf(c_4853,plain,
( member(sK5(inverse_function(sK15,sK16,sK17),sK16,sK17),sK16)
| sP0(inverse_function(sK15,sK16,sK17),sK16,sK17) ),
inference(instantiation,[status(thm)],[c_79]) ).
cnf(c_4854,plain,
( member(sK6(inverse_function(sK15,sK16,sK17),sK16,sK17),sK16)
| sP0(inverse_function(sK15,sK16,sK17),sK16,sK17) ),
inference(instantiation,[status(thm)],[c_78]) ).
cnf(c_7075,plain,
( ~ apply(inverse_function(X0,X1,X2),sK4(inverse_function(X0,X1,X2),X3,X4),sK6(inverse_function(X0,X1,X2),X3,X4))
| ~ member(sK6(inverse_function(X0,X1,X2),X3,X4),X1)
| ~ member(sK4(inverse_function(X0,X1,X2),X3,X4),X2)
| apply(X0,sK6(inverse_function(X0,X1,X2),X3,X4),sK4(inverse_function(X0,X1,X2),X3,X4)) ),
inference(instantiation,[status(thm)],[c_96]) ).
cnf(c_7190,plain,
( ~ apply(inverse_function(X0,X1,X2),sK4(inverse_function(X0,X1,X2),X3,X4),sK5(inverse_function(X0,X1,X2),X3,X4))
| ~ member(sK5(inverse_function(X0,X1,X2),X3,X4),X1)
| ~ member(sK4(inverse_function(X0,X1,X2),X3,X4),X2)
| apply(X0,sK5(inverse_function(X0,X1,X2),X3,X4),sK4(inverse_function(X0,X1,X2),X3,X4)) ),
inference(instantiation,[status(thm)],[c_96]) ).
cnf(c_8104,plain,
( ~ apply(sK15,sK5(X0,X1,X2),X3)
| ~ apply(sK15,sK6(X0,X1,X2),X3)
| ~ member(sK5(X0,X1,X2),sK16)
| ~ member(sK6(X0,X1,X2),sK16)
| ~ member(X3,sK17)
| sK5(X0,X1,X2) = sK6(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_1120]) ).
cnf(c_8149,plain,
( ~ member(sK7(inverse_function(sK15,sK16,sK17),sK17,sK16),sK17)
| apply(sK15,sK10(sK15,sK16,sK7(inverse_function(sK15,sK16,sK17),sK17,sK16)),sK7(inverse_function(sK15,sK16,sK17),sK17,sK16)) ),
inference(instantiation,[status(thm)],[c_1913]) ).
cnf(c_8150,plain,
( ~ member(sK7(inverse_function(sK15,sK16,sK17),sK17,sK16),sK17)
| member(sK10(sK15,sK16,sK7(inverse_function(sK15,sK16,sK17),sK17,sK16)),sK16) ),
inference(instantiation,[status(thm)],[c_1911]) ).
cnf(c_10169,plain,
( ~ apply(sK15,sK10(sK15,sK16,sK7(inverse_function(sK15,sK16,sK17),sK17,sK16)),sK7(inverse_function(sK15,sK16,sK17),sK17,sK16))
| ~ member(sK10(sK15,sK16,sK7(inverse_function(sK15,sK16,sK17),sK17,sK16)),X0)
| ~ member(sK7(inverse_function(sK15,sK16,sK17),sK17,sK16),X1)
| apply(inverse_function(sK15,X0,X1),sK7(inverse_function(sK15,sK16,sK17),sK17,sK16),sK10(sK15,sK16,sK7(inverse_function(sK15,sK16,sK17),sK17,sK16))) ),
inference(instantiation,[status(thm)],[c_97]) ).
cnf(c_12911,plain,
( ~ apply(sK15,sK5(inverse_function(sK15,sK16,sK17),sK16,sK17),X0)
| ~ apply(sK15,sK6(inverse_function(sK15,sK16,sK17),sK16,sK17),X0)
| ~ member(sK5(inverse_function(sK15,sK16,sK17),sK16,sK17),sK16)
| ~ member(sK6(inverse_function(sK15,sK16,sK17),sK16,sK17),sK16)
| ~ member(X0,sK17)
| sK5(inverse_function(sK15,sK16,sK17),sK16,sK17) = sK6(inverse_function(sK15,sK16,sK17),sK16,sK17) ),
inference(instantiation,[status(thm)],[c_8104]) ).
cnf(c_13849,plain,
( ~ apply(inverse_function(sK15,sK16,sK17),sK4(inverse_function(sK15,sK16,sK17),sK16,sK17),sK6(inverse_function(sK15,sK16,sK17),sK16,sK17))
| ~ member(sK6(inverse_function(sK15,sK16,sK17),sK16,sK17),sK16)
| ~ member(sK4(inverse_function(sK15,sK16,sK17),sK16,sK17),sK17)
| apply(sK15,sK6(inverse_function(sK15,sK16,sK17),sK16,sK17),sK4(inverse_function(sK15,sK16,sK17),sK16,sK17)) ),
inference(instantiation,[status(thm)],[c_7075]) ).
cnf(c_13851,plain,
( ~ apply(inverse_function(sK15,sK16,sK17),sK4(inverse_function(sK15,sK16,sK17),sK16,sK17),sK5(inverse_function(sK15,sK16,sK17),sK16,sK17))
| ~ member(sK5(inverse_function(sK15,sK16,sK17),sK16,sK17),sK16)
| ~ member(sK4(inverse_function(sK15,sK16,sK17),sK16,sK17),sK17)
| apply(sK15,sK5(inverse_function(sK15,sK16,sK17),sK16,sK17),sK4(inverse_function(sK15,sK16,sK17),sK16,sK17)) ),
inference(instantiation,[status(thm)],[c_7190]) ).
cnf(c_21499,plain,
( ~ apply(sK15,sK10(sK15,sK16,sK7(inverse_function(sK15,sK16,sK17),sK17,sK16)),sK7(inverse_function(sK15,sK16,sK17),sK17,sK16))
| ~ member(sK10(sK15,sK16,sK7(inverse_function(sK15,sK16,sK17),sK17,sK16)),X0)
| ~ member(sK7(inverse_function(sK15,sK16,sK17),sK17,sK16),sK17)
| apply(inverse_function(sK15,X0,sK17),sK7(inverse_function(sK15,sK16,sK17),sK17,sK16),sK10(sK15,sK16,sK7(inverse_function(sK15,sK16,sK17),sK17,sK16))) ),
inference(instantiation,[status(thm)],[c_10169]) ).
cnf(c_21500,plain,
( ~ apply(sK15,sK10(sK15,sK16,sK7(inverse_function(sK15,sK16,sK17),sK17,sK16)),sK7(inverse_function(sK15,sK16,sK17),sK17,sK16))
| ~ member(sK10(sK15,sK16,sK7(inverse_function(sK15,sK16,sK17),sK17,sK16)),sK16)
| ~ member(sK7(inverse_function(sK15,sK16,sK17),sK17,sK16),sK17)
| apply(inverse_function(sK15,sK16,sK17),sK7(inverse_function(sK15,sK16,sK17),sK17,sK16),sK10(sK15,sK16,sK7(inverse_function(sK15,sK16,sK17),sK17,sK16))) ),
inference(instantiation,[status(thm)],[c_21499]) ).
cnf(c_22311,plain,
( ~ apply(sK15,sK5(inverse_function(sK15,sK16,sK17),sK16,sK17),sK4(inverse_function(sK15,sK16,sK17),sK16,sK17))
| ~ apply(sK15,sK6(inverse_function(sK15,sK16,sK17),sK16,sK17),sK4(inverse_function(sK15,sK16,sK17),sK16,sK17))
| ~ member(sK5(inverse_function(sK15,sK16,sK17),sK16,sK17),sK16)
| ~ member(sK6(inverse_function(sK15,sK16,sK17),sK16,sK17),sK16)
| ~ member(sK4(inverse_function(sK15,sK16,sK17),sK16,sK17),sK17)
| sK5(inverse_function(sK15,sK16,sK17),sK16,sK17) = sK6(inverse_function(sK15,sK16,sK17),sK16,sK17) ),
inference(instantiation,[status(thm)],[c_12911]) ).
cnf(c_24649,plain,
( ~ apply(inverse_function(sK15,sK16,sK17),sK7(inverse_function(sK15,sK16,sK17),sK17,sK16),sK10(sK15,sK16,sK7(inverse_function(sK15,sK16,sK17),sK17,sK16)))
| ~ member(sK10(sK15,sK16,sK7(inverse_function(sK15,sK16,sK17),sK17,sK16)),sK16)
| ~ sP0(inverse_function(sK15,sK16,sK17),sK16,sK17)
| maps(inverse_function(sK15,sK16,sK17),sK17,sK16) ),
inference(instantiation,[status(thm)],[c_82]) ).
cnf(c_24650,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_24649,c_22311,c_21500,c_13851,c_13849,c_8149,c_8150,c_4849,c_4850,c_4851,c_4852,c_4853,c_4854,c_1318,c_112]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET712+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.10/0.11 % Command : run_iprover %s %d THM
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu May 2 20:23:17 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.16/0.43 Running first-order theorem proving
% 0.16/0.43 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
% 42.78/6.68 % SZS status Started for theBenchmark.p
% 42.78/6.68 % SZS status Theorem for theBenchmark.p
% 42.78/6.68
% 42.78/6.68 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 42.78/6.68
% 42.78/6.68 ------ iProver source info
% 42.78/6.68
% 42.78/6.68 git: date: 2024-05-02 19:28:25 +0000
% 42.78/6.68 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 42.78/6.68 git: non_committed_changes: false
% 42.78/6.68
% 42.78/6.68 ------ Parsing...
% 42.78/6.68 ------ Clausification by vclausify_rel & Parsing by iProver...
% 42.78/6.68
% 42.78/6.68 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e
% 42.78/6.68
% 42.78/6.68 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 42.78/6.68
% 42.78/6.68 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 42.78/6.68 ------ Proving...
% 42.78/6.68 ------ Problem Properties
% 42.78/6.68
% 42.78/6.68
% 42.78/6.68 clauses 63
% 42.78/6.68 conjectures 2
% 42.78/6.68 EPR 6
% 42.78/6.68 Horn 52
% 42.78/6.68 unary 6
% 42.78/6.68 binary 34
% 42.78/6.68 lits 161
% 42.78/6.68 lits eq 6
% 42.78/6.68 fd_pure 0
% 42.78/6.68 fd_pseudo 0
% 42.78/6.68 fd_cond 0
% 42.78/6.68 fd_pseudo_cond 4
% 42.78/6.68 AC symbols 0
% 42.78/6.68
% 42.78/6.68 ------ Input Options Time Limit: Unbounded
% 42.78/6.68
% 42.78/6.68
% 42.78/6.68 ------
% 42.78/6.68 Current options:
% 42.78/6.68 ------
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% 42.78/6.68
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% 42.78/6.68
% 42.78/6.68 ------ Proving...
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% 42.78/6.68 % SZS status Theorem for theBenchmark.p
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% 42.78/6.68 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
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% 42.78/6.68
%------------------------------------------------------------------------------