TSTP Solution File: SET765+4 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET765+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n015.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 : Thu Aug 31 15:09:31 EDT 2023
% Result : Theorem 32.29s 5.25s
% Output : CNFRefutation 32.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 131 ( 10 unt; 0 def)
% Number of atoms : 568 ( 22 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 722 ( 285 ~; 305 |; 104 &)
% ( 9 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 288 ( 0 sgn; 162 !; 33 ?)
% 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(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(f17,conjecture,
! [X3,X6,X2] :
( ( subset(X2,X3)
& equivalence(X6,X3) )
=> equivalence(X6,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIII01) ).
fof(f18,negated_conjecture,
~ ! [X3,X6,X2] :
( ( subset(X2,X3)
& equivalence(X6,X3) )
=> equivalence(X6,X2) ),
inference(negated_conjecture,[],[f17]) ).
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(f32,plain,
~ ! [X0,X1,X2] :
( ( subset(X2,X0)
& equivalence(X1,X0) )
=> equivalence(X1,X2) ),
inference(rectify,[],[f18]) ).
fof(f33,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f35,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,[],[f29]) ).
fof(f36,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,[],[f35]) ).
fof(f37,plain,
? [X0,X1,X2] :
( ~ equivalence(X1,X2)
& subset(X2,X0)
& equivalence(X1,X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f38,plain,
? [X0,X1,X2] :
( ~ equivalence(X1,X2)
& subset(X2,X0)
& equivalence(X1,X0) ),
inference(flattening,[],[f37]) ).
fof(f39,plain,
! [X1,X0] :
( sP0(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) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f40,plain,
! [X0,X1] :
( sP1(X0,X1)
<=> ( 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) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f41,plain,
! [X0,X1] :
( equivalence(X1,X0)
<=> sP1(X0,X1) ),
inference(definition_folding,[],[f36,f40,f39]) ).
fof(f42,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,[],[f33]) ).
fof(f43,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,[],[f42]) ).
fof(f44,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK2(X0,X1),X1)
& member(sK2(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f45,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK2(X0,X1),X1)
& member(sK2(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f43,f44]) ).
fof(f64,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ~ 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) ) )
& ( ( 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) ) )
| ~ sP1(X0,X1) ) ),
inference(nnf_transformation,[],[f40]) ).
fof(f65,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ~ 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) ) )
& ( ( 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) ) )
| ~ sP1(X0,X1) ) ),
inference(flattening,[],[f64]) ).
fof(f66,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ~ 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) ) )
& ( ( 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) ) )
| ~ sP1(X0,X1) ) ),
inference(rectify,[],[f65]) ).
fof(f67,plain,
! [X0,X1] :
( ? [X2,X3] :
( ~ apply(X1,X3,X2)
& apply(X1,X2,X3)
& member(X3,X0)
& member(X2,X0) )
=> ( ~ apply(X1,sK6(X0,X1),sK5(X0,X1))
& apply(X1,sK5(X0,X1),sK6(X0,X1))
& member(sK6(X0,X1),X0)
& member(sK5(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f68,plain,
! [X0,X1] :
( ? [X4] :
( ~ apply(X1,X4,X4)
& member(X4,X0) )
=> ( ~ apply(X1,sK7(X0,X1),sK7(X0,X1))
& member(sK7(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f69,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ~ sP0(X1,X0)
| ( ~ apply(X1,sK6(X0,X1),sK5(X0,X1))
& apply(X1,sK5(X0,X1),sK6(X0,X1))
& member(sK6(X0,X1),X0)
& member(sK5(X0,X1),X0) )
| ( ~ apply(X1,sK7(X0,X1),sK7(X0,X1))
& member(sK7(X0,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) ) )
| ~ sP1(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f66,f68,f67]) ).
fof(f70,plain,
! [X1,X0] :
( ( sP0(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) ) )
& ( ! [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,[],[f39]) ).
fof(f71,plain,
! [X0,X1] :
( ( sP0(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) ) )
& ( ! [X5,X6,X7] :
( apply(X0,X5,X7)
| ~ apply(X0,X6,X7)
| ~ apply(X0,X5,X6)
| ~ member(X7,X1)
| ~ member(X6,X1)
| ~ member(X5,X1) )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f70]) ).
fof(f72,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,sK8(X0,X1),sK10(X0,X1))
& apply(X0,sK9(X0,X1),sK10(X0,X1))
& apply(X0,sK8(X0,X1),sK9(X0,X1))
& member(sK10(X0,X1),X1)
& member(sK9(X0,X1),X1)
& member(sK8(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f73,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ~ apply(X0,sK8(X0,X1),sK10(X0,X1))
& apply(X0,sK9(X0,X1),sK10(X0,X1))
& apply(X0,sK8(X0,X1),sK9(X0,X1))
& member(sK10(X0,X1),X1)
& member(sK9(X0,X1),X1)
& member(sK8(X0,X1),X1) ) )
& ( ! [X5,X6,X7] :
( apply(X0,X5,X7)
| ~ apply(X0,X6,X7)
| ~ apply(X0,X5,X6)
| ~ member(X7,X1)
| ~ member(X6,X1)
| ~ member(X5,X1) )
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f71,f72]) ).
fof(f74,plain,
! [X0,X1] :
( ( equivalence(X1,X0)
| ~ sP1(X0,X1) )
& ( sP1(X0,X1)
| ~ equivalence(X1,X0) ) ),
inference(nnf_transformation,[],[f41]) ).
fof(f77,plain,
( ? [X0,X1,X2] :
( ~ equivalence(X1,X2)
& subset(X2,X0)
& equivalence(X1,X0) )
=> ( ~ equivalence(sK12,sK13)
& subset(sK13,sK11)
& equivalence(sK12,sK11) ) ),
introduced(choice_axiom,[]) ).
fof(f78,plain,
( ~ equivalence(sK12,sK13)
& subset(sK13,sK11)
& equivalence(sK12,sK11) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13])],[f38,f77]) ).
fof(f79,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f105,plain,
! [X0,X1,X7] :
( apply(X1,X7,X7)
| ~ member(X7,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f106,plain,
! [X0,X1,X6,X5] :
( apply(X1,X6,X5)
| ~ apply(X1,X5,X6)
| ~ member(X6,X0)
| ~ member(X5,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f107,plain,
! [X0,X1] :
( sP0(X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f108,plain,
! [X0,X1] :
( sP1(X0,X1)
| ~ sP0(X1,X0)
| member(sK5(X0,X1),X0)
| member(sK7(X0,X1),X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f109,plain,
! [X0,X1] :
( sP1(X0,X1)
| ~ sP0(X1,X0)
| member(sK5(X0,X1),X0)
| ~ apply(X1,sK7(X0,X1),sK7(X0,X1)) ),
inference(cnf_transformation,[],[f69]) ).
fof(f110,plain,
! [X0,X1] :
( sP1(X0,X1)
| ~ sP0(X1,X0)
| member(sK6(X0,X1),X0)
| member(sK7(X0,X1),X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f111,plain,
! [X0,X1] :
( sP1(X0,X1)
| ~ sP0(X1,X0)
| member(sK6(X0,X1),X0)
| ~ apply(X1,sK7(X0,X1),sK7(X0,X1)) ),
inference(cnf_transformation,[],[f69]) ).
fof(f112,plain,
! [X0,X1] :
( sP1(X0,X1)
| ~ sP0(X1,X0)
| apply(X1,sK5(X0,X1),sK6(X0,X1))
| member(sK7(X0,X1),X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f113,plain,
! [X0,X1] :
( sP1(X0,X1)
| ~ sP0(X1,X0)
| apply(X1,sK5(X0,X1),sK6(X0,X1))
| ~ apply(X1,sK7(X0,X1),sK7(X0,X1)) ),
inference(cnf_transformation,[],[f69]) ).
fof(f114,plain,
! [X0,X1] :
( sP1(X0,X1)
| ~ sP0(X1,X0)
| ~ apply(X1,sK6(X0,X1),sK5(X0,X1))
| member(sK7(X0,X1),X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f115,plain,
! [X0,X1] :
( sP1(X0,X1)
| ~ sP0(X1,X0)
| ~ apply(X1,sK6(X0,X1),sK5(X0,X1))
| ~ apply(X1,sK7(X0,X1),sK7(X0,X1)) ),
inference(cnf_transformation,[],[f69]) ).
fof(f116,plain,
! [X0,X1,X6,X7,X5] :
( apply(X0,X5,X7)
| ~ apply(X0,X6,X7)
| ~ apply(X0,X5,X6)
| ~ member(X7,X1)
| ~ member(X6,X1)
| ~ member(X5,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f117,plain,
! [X0,X1] :
( sP0(X0,X1)
| member(sK8(X0,X1),X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f118,plain,
! [X0,X1] :
( sP0(X0,X1)
| member(sK9(X0,X1),X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f119,plain,
! [X0,X1] :
( sP0(X0,X1)
| member(sK10(X0,X1),X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f120,plain,
! [X0,X1] :
( sP0(X0,X1)
| apply(X0,sK8(X0,X1),sK9(X0,X1)) ),
inference(cnf_transformation,[],[f73]) ).
fof(f121,plain,
! [X0,X1] :
( sP0(X0,X1)
| apply(X0,sK9(X0,X1),sK10(X0,X1)) ),
inference(cnf_transformation,[],[f73]) ).
fof(f122,plain,
! [X0,X1] :
( sP0(X0,X1)
| ~ apply(X0,sK8(X0,X1),sK10(X0,X1)) ),
inference(cnf_transformation,[],[f73]) ).
fof(f123,plain,
! [X0,X1] :
( sP1(X0,X1)
| ~ equivalence(X1,X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f124,plain,
! [X0,X1] :
( equivalence(X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f128,plain,
equivalence(sK12,sK11),
inference(cnf_transformation,[],[f78]) ).
fof(f129,plain,
subset(sK13,sK11),
inference(cnf_transformation,[],[f78]) ).
fof(f130,plain,
~ equivalence(sK12,sK13),
inference(cnf_transformation,[],[f78]) ).
cnf(c_51,plain,
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f79]) ).
cnf(c_75,plain,
( ~ apply(X0,sK6(X1,X0),sK5(X1,X0))
| ~ apply(X0,sK7(X1,X0),sK7(X1,X0))
| ~ sP0(X0,X1)
| sP1(X1,X0) ),
inference(cnf_transformation,[],[f115]) ).
cnf(c_76,plain,
( ~ apply(X0,sK6(X1,X0),sK5(X1,X0))
| ~ sP0(X0,X1)
| member(sK7(X1,X0),X1)
| sP1(X1,X0) ),
inference(cnf_transformation,[],[f114]) ).
cnf(c_77,plain,
( ~ apply(X0,sK7(X1,X0),sK7(X1,X0))
| ~ sP0(X0,X1)
| apply(X0,sK5(X1,X0),sK6(X1,X0))
| sP1(X1,X0) ),
inference(cnf_transformation,[],[f113]) ).
cnf(c_78,plain,
( ~ sP0(X0,X1)
| apply(X0,sK5(X1,X0),sK6(X1,X0))
| member(sK7(X1,X0),X1)
| sP1(X1,X0) ),
inference(cnf_transformation,[],[f112]) ).
cnf(c_79,plain,
( ~ apply(X0,sK7(X1,X0),sK7(X1,X0))
| ~ sP0(X0,X1)
| member(sK6(X1,X0),X1)
| sP1(X1,X0) ),
inference(cnf_transformation,[],[f111]) ).
cnf(c_80,plain,
( ~ sP0(X0,X1)
| member(sK6(X1,X0),X1)
| member(sK7(X1,X0),X1)
| sP1(X1,X0) ),
inference(cnf_transformation,[],[f110]) ).
cnf(c_81,plain,
( ~ apply(X0,sK7(X1,X0),sK7(X1,X0))
| ~ sP0(X0,X1)
| member(sK5(X1,X0),X1)
| sP1(X1,X0) ),
inference(cnf_transformation,[],[f109]) ).
cnf(c_82,plain,
( ~ sP0(X0,X1)
| member(sK5(X1,X0),X1)
| member(sK7(X1,X0),X1)
| sP1(X1,X0) ),
inference(cnf_transformation,[],[f108]) ).
cnf(c_83,plain,
( ~ sP1(X0,X1)
| sP0(X1,X0) ),
inference(cnf_transformation,[],[f107]) ).
cnf(c_84,plain,
( ~ apply(X0,X1,X2)
| ~ member(X1,X3)
| ~ member(X2,X3)
| ~ sP1(X3,X0)
| apply(X0,X2,X1) ),
inference(cnf_transformation,[],[f106]) ).
cnf(c_85,plain,
( ~ member(X0,X1)
| ~ sP1(X1,X2)
| apply(X2,X0,X0) ),
inference(cnf_transformation,[],[f105]) ).
cnf(c_86,plain,
( ~ apply(X0,sK8(X0,X1),sK10(X0,X1))
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f122]) ).
cnf(c_87,plain,
( apply(X0,sK9(X0,X1),sK10(X0,X1))
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f121]) ).
cnf(c_88,plain,
( apply(X0,sK8(X0,X1),sK9(X0,X1))
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f120]) ).
cnf(c_89,plain,
( member(sK10(X0,X1),X1)
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f119]) ).
cnf(c_90,plain,
( member(sK9(X0,X1),X1)
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f118]) ).
cnf(c_91,plain,
( member(sK8(X0,X1),X1)
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f117]) ).
cnf(c_92,plain,
( ~ apply(X0,X1,X2)
| ~ apply(X0,X3,X1)
| ~ member(X1,X4)
| ~ member(X2,X4)
| ~ member(X3,X4)
| ~ sP0(X0,X4)
| apply(X0,X3,X2) ),
inference(cnf_transformation,[],[f116]) ).
cnf(c_93,plain,
( ~ sP1(X0,X1)
| equivalence(X1,X0) ),
inference(cnf_transformation,[],[f124]) ).
cnf(c_94,plain,
( ~ equivalence(X0,X1)
| sP1(X1,X0) ),
inference(cnf_transformation,[],[f123]) ).
cnf(c_98,negated_conjecture,
~ equivalence(sK12,sK13),
inference(cnf_transformation,[],[f130]) ).
cnf(c_99,negated_conjecture,
subset(sK13,sK11),
inference(cnf_transformation,[],[f129]) ).
cnf(c_100,negated_conjecture,
equivalence(sK12,sK11),
inference(cnf_transformation,[],[f128]) ).
cnf(c_188,plain,
( ~ sP1(X0,X1)
| sP0(X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_83]) ).
cnf(c_190,plain,
( ~ sP1(X0,X1)
| equivalence(X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_93]) ).
cnf(c_210,plain,
( ~ equivalence(X0,X1)
| sP1(X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_94]) ).
cnf(c_832,plain,
( X0 != sK13
| X1 != sK12
| ~ sP1(X0,X1) ),
inference(resolution_lifted,[status(thm)],[c_190,c_98]) ).
cnf(c_833,plain,
~ sP1(sK13,sK12),
inference(unflattening,[status(thm)],[c_832]) ).
cnf(c_837,plain,
( X0 != sK12
| X1 != sK11
| sP1(X1,X0) ),
inference(resolution_lifted,[status(thm)],[c_210,c_100]) ).
cnf(c_838,plain,
sP1(sK11,sK12),
inference(unflattening,[status(thm)],[c_837]) ).
cnf(c_952,plain,
( X0 != sK11
| X1 != sK12
| sP0(X1,X0) ),
inference(resolution_lifted,[status(thm)],[c_188,c_838]) ).
cnf(c_953,plain,
sP0(sK12,sK11),
inference(unflattening,[status(thm)],[c_952]) ).
cnf(c_1285,plain,
( X0 != sK12
| X1 != sK13
| ~ sP0(X0,X1)
| member(sK5(X1,X0),X1)
| member(sK7(X1,X0),X1) ),
inference(resolution_lifted,[status(thm)],[c_82,c_833]) ).
cnf(c_1286,plain,
( ~ sP0(sK12,sK13)
| member(sK5(sK13,sK12),sK13)
| member(sK7(sK13,sK12),sK13) ),
inference(unflattening,[status(thm)],[c_1285]) ).
cnf(c_1296,plain,
( X0 != sK12
| X1 != sK13
| ~ apply(X0,sK7(X1,X0),sK7(X1,X0))
| ~ sP0(X0,X1)
| member(sK5(X1,X0),X1) ),
inference(resolution_lifted,[status(thm)],[c_81,c_833]) ).
cnf(c_1297,plain,
( ~ apply(sK12,sK7(sK13,sK12),sK7(sK13,sK12))
| ~ sP0(sK12,sK13)
| member(sK5(sK13,sK12),sK13) ),
inference(unflattening,[status(thm)],[c_1296]) ).
cnf(c_1307,plain,
( X0 != sK12
| X1 != sK13
| ~ sP0(X0,X1)
| member(sK6(X1,X0),X1)
| member(sK7(X1,X0),X1) ),
inference(resolution_lifted,[status(thm)],[c_80,c_833]) ).
cnf(c_1308,plain,
( ~ sP0(sK12,sK13)
| member(sK6(sK13,sK12),sK13)
| member(sK7(sK13,sK12),sK13) ),
inference(unflattening,[status(thm)],[c_1307]) ).
cnf(c_1318,plain,
( X0 != sK12
| X1 != sK13
| ~ apply(X0,sK7(X1,X0),sK7(X1,X0))
| ~ sP0(X0,X1)
| member(sK6(X1,X0),X1) ),
inference(resolution_lifted,[status(thm)],[c_79,c_833]) ).
cnf(c_1319,plain,
( ~ apply(sK12,sK7(sK13,sK12),sK7(sK13,sK12))
| ~ sP0(sK12,sK13)
| member(sK6(sK13,sK12),sK13) ),
inference(unflattening,[status(thm)],[c_1318]) ).
cnf(c_1329,plain,
( X0 != sK12
| X1 != sK13
| ~ sP0(X0,X1)
| apply(X0,sK5(X1,X0),sK6(X1,X0))
| member(sK7(X1,X0),X1) ),
inference(resolution_lifted,[status(thm)],[c_78,c_833]) ).
cnf(c_1330,plain,
( ~ sP0(sK12,sK13)
| apply(sK12,sK5(sK13,sK12),sK6(sK13,sK12))
| member(sK7(sK13,sK12),sK13) ),
inference(unflattening,[status(thm)],[c_1329]) ).
cnf(c_1340,plain,
( X0 != sK12
| X1 != sK13
| ~ apply(X0,sK7(X1,X0),sK7(X1,X0))
| ~ sP0(X0,X1)
| apply(X0,sK5(X1,X0),sK6(X1,X0)) ),
inference(resolution_lifted,[status(thm)],[c_77,c_833]) ).
cnf(c_1341,plain,
( ~ apply(sK12,sK7(sK13,sK12),sK7(sK13,sK12))
| ~ sP0(sK12,sK13)
| apply(sK12,sK5(sK13,sK12),sK6(sK13,sK12)) ),
inference(unflattening,[status(thm)],[c_1340]) ).
cnf(c_1351,plain,
( X0 != sK12
| X1 != sK13
| ~ apply(X0,sK6(X1,X0),sK5(X1,X0))
| ~ sP0(X0,X1)
| member(sK7(X1,X0),X1) ),
inference(resolution_lifted,[status(thm)],[c_76,c_833]) ).
cnf(c_1352,plain,
( ~ apply(sK12,sK6(sK13,sK12),sK5(sK13,sK12))
| ~ sP0(sK12,sK13)
| member(sK7(sK13,sK12),sK13) ),
inference(unflattening,[status(thm)],[c_1351]) ).
cnf(c_1362,plain,
( X0 != sK12
| X1 != sK13
| ~ apply(X0,sK6(X1,X0),sK5(X1,X0))
| ~ apply(X0,sK7(X1,X0),sK7(X1,X0))
| ~ sP0(X0,X1) ),
inference(resolution_lifted,[status(thm)],[c_75,c_833]) ).
cnf(c_1363,plain,
( ~ apply(sK12,sK6(sK13,sK12),sK5(sK13,sK12))
| ~ apply(sK12,sK7(sK13,sK12),sK7(sK13,sK12))
| ~ sP0(sK12,sK13) ),
inference(unflattening,[status(thm)],[c_1362]) ).
cnf(c_7194,plain,
( apply(sK12,sK8(sK12,sK13),sK9(sK12,sK13))
| sP0(sK12,sK13) ),
inference(instantiation,[status(thm)],[c_88]) ).
cnf(c_7195,plain,
( apply(sK12,sK9(sK12,sK13),sK10(sK12,sK13))
| sP0(sK12,sK13) ),
inference(instantiation,[status(thm)],[c_87]) ).
cnf(c_7196,plain,
( ~ apply(sK12,sK8(sK12,sK13),sK10(sK12,sK13))
| sP0(sK12,sK13) ),
inference(instantiation,[status(thm)],[c_86]) ).
cnf(c_7197,plain,
( member(sK8(sK12,sK13),sK13)
| sP0(sK12,sK13) ),
inference(instantiation,[status(thm)],[c_91]) ).
cnf(c_7198,plain,
( member(sK9(sK12,sK13),sK13)
| sP0(sK12,sK13) ),
inference(instantiation,[status(thm)],[c_90]) ).
cnf(c_7199,plain,
( member(sK10(sK12,sK13),sK13)
| sP0(sK12,sK13) ),
inference(instantiation,[status(thm)],[c_89]) ).
cnf(c_12197,plain,
( ~ member(sK7(X0,X1),X0)
| ~ subset(X0,X2)
| member(sK7(X0,X1),X2) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_17145,plain,
( ~ member(X0,sK11)
| ~ sP1(sK11,sK12)
| apply(sK12,X0,X0) ),
inference(instantiation,[status(thm)],[c_85]) ).
cnf(c_18877,plain,
( ~ apply(sK12,X0,X1)
| ~ member(X0,sK11)
| ~ member(X1,sK11)
| ~ sP1(sK11,sK12)
| apply(sK12,X1,X0) ),
inference(instantiation,[status(thm)],[c_84]) ).
cnf(c_19154,plain,
( ~ member(sK7(sK13,sK12),sK11)
| ~ sP1(sK11,sK12)
| apply(sK12,sK7(sK13,sK12),sK7(sK13,sK12)) ),
inference(instantiation,[status(thm)],[c_17145]) ).
cnf(c_19170,plain,
( ~ apply(sK12,sK5(sK13,sK12),sK6(sK13,sK12))
| ~ member(sK6(sK13,sK12),sK11)
| ~ member(sK5(sK13,sK12),sK11)
| ~ sP1(sK11,sK12)
| apply(sK12,sK6(sK13,sK12),sK5(sK13,sK12)) ),
inference(instantiation,[status(thm)],[c_18877]) ).
cnf(c_32243,plain,
( ~ member(sK7(sK13,sK12),sK13)
| ~ subset(sK13,X0)
| member(sK7(sK13,sK12),X0) ),
inference(instantiation,[status(thm)],[c_12197]) ).
cnf(c_32244,plain,
( ~ member(sK7(sK13,sK12),sK13)
| ~ subset(sK13,sK11)
| member(sK7(sK13,sK12),sK11) ),
inference(instantiation,[status(thm)],[c_32243]) ).
cnf(c_36696,plain,
( ~ member(sK8(sK12,X0),X1)
| ~ subset(X1,sK11)
| member(sK8(sK12,X0),sK11) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_38221,plain,
( ~ member(sK5(sK13,sK12),sK13)
| ~ subset(sK13,X0)
| member(sK5(sK13,sK12),X0) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_38222,plain,
( ~ member(sK5(sK13,sK12),sK13)
| ~ subset(sK13,sK11)
| member(sK5(sK13,sK12),sK11) ),
inference(instantiation,[status(thm)],[c_38221]) ).
cnf(c_38223,plain,
( ~ member(sK6(sK13,sK12),sK13)
| ~ subset(sK13,X0)
| member(sK6(sK13,sK12),X0) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_38224,plain,
( ~ member(sK6(sK13,sK12),sK13)
| ~ subset(sK13,sK11)
| member(sK6(sK13,sK12),sK11) ),
inference(instantiation,[status(thm)],[c_38223]) ).
cnf(c_41342,plain,
( ~ member(sK9(sK12,sK13),sK13)
| ~ subset(sK13,X0)
| member(sK9(sK12,sK13),X0) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_41343,plain,
( ~ member(sK9(sK12,sK13),sK13)
| ~ subset(sK13,sK11)
| member(sK9(sK12,sK13),sK11) ),
inference(instantiation,[status(thm)],[c_41342]) ).
cnf(c_41441,plain,
( ~ member(sK10(sK12,sK13),sK13)
| ~ subset(sK13,X0)
| member(sK10(sK12,sK13),X0) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_41442,plain,
( ~ member(sK10(sK12,sK13),sK13)
| ~ subset(sK13,sK11)
| member(sK10(sK12,sK13),sK11) ),
inference(instantiation,[status(thm)],[c_41441]) ).
cnf(c_69740,plain,
( ~ member(sK8(sK12,sK13),sK13)
| ~ subset(sK13,sK11)
| member(sK8(sK12,sK13),sK11) ),
inference(instantiation,[status(thm)],[c_36696]) ).
cnf(c_187066,plain,
( ~ apply(sK12,sK8(sK12,sK13),X0)
| ~ apply(sK12,X0,sK10(sK12,sK13))
| ~ member(sK8(sK12,sK13),X1)
| ~ member(sK10(sK12,sK13),X1)
| ~ member(X0,X1)
| ~ sP0(sK12,X1)
| apply(sK12,sK8(sK12,sK13),sK10(sK12,sK13)) ),
inference(instantiation,[status(thm)],[c_92]) ).
cnf(c_190578,plain,
( ~ apply(sK12,sK8(sK12,sK13),sK9(sK12,sK13))
| ~ apply(sK12,sK9(sK12,sK13),sK10(sK12,sK13))
| ~ member(sK8(sK12,sK13),X0)
| ~ member(sK10(sK12,sK13),X0)
| ~ member(sK9(sK12,sK13),X0)
| ~ sP0(sK12,X0)
| apply(sK12,sK8(sK12,sK13),sK10(sK12,sK13)) ),
inference(instantiation,[status(thm)],[c_187066]) ).
cnf(c_190579,plain,
( ~ apply(sK12,sK8(sK12,sK13),sK9(sK12,sK13))
| ~ apply(sK12,sK9(sK12,sK13),sK10(sK12,sK13))
| ~ member(sK8(sK12,sK13),sK11)
| ~ member(sK10(sK12,sK13),sK11)
| ~ member(sK9(sK12,sK13),sK11)
| ~ sP0(sK12,sK11)
| apply(sK12,sK8(sK12,sK13),sK10(sK12,sK13)) ),
inference(instantiation,[status(thm)],[c_190578]) ).
cnf(c_190580,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_190579,c_69740,c_41442,c_41343,c_38224,c_38222,c_32244,c_19170,c_19154,c_7194,c_7195,c_7196,c_7197,c_7198,c_7199,c_1363,c_1352,c_1341,c_1330,c_1319,c_1308,c_1297,c_1286,c_953,c_838,c_99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET765+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 14:58:38 EDT 2023
% 0.13/0.35 % 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 --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 32.29/5.25 % SZS status Started for theBenchmark.p
% 32.29/5.25 % SZS status Theorem for theBenchmark.p
% 32.29/5.25
% 32.29/5.25 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 32.29/5.25
% 32.29/5.25 ------ iProver source info
% 32.29/5.25
% 32.29/5.25 git: date: 2023-05-31 18:12:56 +0000
% 32.29/5.25 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 32.29/5.25 git: non_committed_changes: false
% 32.29/5.25 git: last_make_outside_of_git: false
% 32.29/5.25
% 32.29/5.25 ------ Parsing...
% 32.29/5.25 ------ Clausification by vclausify_rel & Parsing by iProver...
% 32.29/5.25
% 32.29/5.25 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e
% 32.29/5.25
% 32.29/5.25 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 32.29/5.25
% 32.29/5.25 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 32.29/5.25 ------ Proving...
% 32.29/5.25 ------ Problem Properties
% 32.29/5.25
% 32.29/5.25
% 32.29/5.25 clauses 51
% 32.29/5.25 conjectures 1
% 32.29/5.25 EPR 10
% 32.29/5.25 Horn 34
% 32.29/5.25 unary 8
% 32.29/5.25 binary 24
% 32.29/5.25 lits 127
% 32.29/5.25 lits eq 4
% 32.29/5.25 fd_pure 0
% 32.29/5.25 fd_pseudo 0
% 32.29/5.25 fd_cond 0
% 32.29/5.25 fd_pseudo_cond 2
% 32.29/5.25 AC symbols 0
% 32.29/5.25
% 32.29/5.25 ------ Schedule dynamic 5 is on
% 32.29/5.25
% 32.29/5.25 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 32.29/5.25
% 32.29/5.25
% 32.29/5.25 ------
% 32.29/5.25 Current options:
% 32.29/5.25 ------
% 32.29/5.25
% 32.29/5.25
% 32.29/5.25
% 32.29/5.25
% 32.29/5.25 ------ Proving...
% 32.29/5.25
% 32.29/5.25
% 32.29/5.25 % SZS status Theorem for theBenchmark.p
% 32.29/5.25
% 32.29/5.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 32.29/5.25
% 32.29/5.25
%------------------------------------------------------------------------------