TSTP Solution File: COM023+4 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : COM023+4 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 04:55:29 EDT 2024
% Result : Theorem 0.47s 1.15s
% Output : CNFRefutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 68 ( 18 unt; 0 def)
% Number of atoms : 651 ( 65 equ)
% Maximal formula atoms : 52 ( 9 avg)
% Number of connectives : 797 ( 214 ~; 230 |; 343 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 183 ( 0 sgn 91 !; 71 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [X0,X1,X2] :
( ( ( sdtmndtasgtdt0(X0,xR,X2)
| sdtmndtplgtdt0(X0,xR,X2)
| ? [X3] :
( sdtmndtplgtdt0(X3,xR,X2)
& aReductOfIn0(X3,X0,xR)
& aElement0(X3) )
| aReductOfIn0(X2,X0,xR)
| X0 = X2 )
& ( sdtmndtasgtdt0(X0,xR,X1)
| sdtmndtplgtdt0(X0,xR,X1)
| ? [X3] :
( sdtmndtplgtdt0(X3,xR,X1)
& aReductOfIn0(X3,X0,xR)
& aElement0(X3) )
| aReductOfIn0(X1,X0,xR)
| X0 = X1 )
& aElement0(X2)
& aElement0(X1)
& aElement0(X0) )
=> ? [X3] :
( sdtmndtasgtdt0(X2,xR,X3)
& ( ( sdtmndtplgtdt0(X2,xR,X3)
& ( ? [X4] :
( sdtmndtplgtdt0(X4,xR,X3)
& aReductOfIn0(X4,X2,xR)
& aElement0(X4) )
| aReductOfIn0(X3,X2,xR) ) )
| X2 = X3 )
& sdtmndtasgtdt0(X1,xR,X3)
& ( ( sdtmndtplgtdt0(X1,xR,X3)
& ( ? [X4] :
( sdtmndtplgtdt0(X4,xR,X3)
& aReductOfIn0(X4,X1,xR)
& aElement0(X4) )
| aReductOfIn0(X3,X1,xR) ) )
| X1 = X3 )
& aElement0(X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__715) ).
fof(f18,conjecture,
( isConfluent0(xR)
| ! [X0,X1,X2] :
( ( sdtmndtasgtdt0(X0,xR,X2)
& ( ( sdtmndtplgtdt0(X0,xR,X2)
& ( ? [X3] :
( sdtmndtplgtdt0(X3,xR,X2)
& aReductOfIn0(X3,X0,xR)
& aElement0(X3) )
| aReductOfIn0(X2,X0,xR) ) )
| X0 = X2 )
& sdtmndtasgtdt0(X0,xR,X1)
& ( ( sdtmndtplgtdt0(X0,xR,X1)
& ( ? [X3] :
( sdtmndtplgtdt0(X3,xR,X1)
& aReductOfIn0(X3,X0,xR)
& aElement0(X3) )
| aReductOfIn0(X1,X0,xR) ) )
| X0 = X1 )
& aElement0(X2)
& aElement0(X1)
& aElement0(X0) )
=> ? [X3] :
( ( sdtmndtasgtdt0(X2,xR,X3)
| sdtmndtplgtdt0(X2,xR,X3)
| ? [X4] :
( sdtmndtplgtdt0(X4,xR,X3)
& aReductOfIn0(X4,X2,xR)
& aElement0(X4) )
| aReductOfIn0(X3,X2,xR)
| X2 = X3 )
& ( sdtmndtasgtdt0(X1,xR,X3)
| sdtmndtplgtdt0(X1,xR,X3)
| ? [X4] :
( sdtmndtplgtdt0(X4,xR,X3)
& aReductOfIn0(X4,X1,xR)
& aElement0(X4) )
| aReductOfIn0(X3,X1,xR)
| X1 = X3 )
& aElement0(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f19,negated_conjecture,
~ ( isConfluent0(xR)
| ! [X0,X1,X2] :
( ( sdtmndtasgtdt0(X0,xR,X2)
& ( ( sdtmndtplgtdt0(X0,xR,X2)
& ( ? [X3] :
( sdtmndtplgtdt0(X3,xR,X2)
& aReductOfIn0(X3,X0,xR)
& aElement0(X3) )
| aReductOfIn0(X2,X0,xR) ) )
| X0 = X2 )
& sdtmndtasgtdt0(X0,xR,X1)
& ( ( sdtmndtplgtdt0(X0,xR,X1)
& ( ? [X3] :
( sdtmndtplgtdt0(X3,xR,X1)
& aReductOfIn0(X3,X0,xR)
& aElement0(X3) )
| aReductOfIn0(X1,X0,xR) ) )
| X0 = X1 )
& aElement0(X2)
& aElement0(X1)
& aElement0(X0) )
=> ? [X3] :
( ( sdtmndtasgtdt0(X2,xR,X3)
| sdtmndtplgtdt0(X2,xR,X3)
| ? [X4] :
( sdtmndtplgtdt0(X4,xR,X3)
& aReductOfIn0(X4,X2,xR)
& aElement0(X4) )
| aReductOfIn0(X3,X2,xR)
| X2 = X3 )
& ( sdtmndtasgtdt0(X1,xR,X3)
| sdtmndtplgtdt0(X1,xR,X3)
| ? [X4] :
( sdtmndtplgtdt0(X4,xR,X3)
& aReductOfIn0(X4,X1,xR)
& aElement0(X4) )
| aReductOfIn0(X3,X1,xR)
| X1 = X3 )
& aElement0(X3) ) ) ),
inference(negated_conjecture,[],[f18]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( ( sdtmndtasgtdt0(X0,xR,X2)
| sdtmndtplgtdt0(X0,xR,X2)
| ? [X3] :
( sdtmndtplgtdt0(X3,xR,X2)
& aReductOfIn0(X3,X0,xR)
& aElement0(X3) )
| aReductOfIn0(X2,X0,xR)
| X0 = X2 )
& ( sdtmndtasgtdt0(X0,xR,X1)
| sdtmndtplgtdt0(X0,xR,X1)
| ? [X4] :
( sdtmndtplgtdt0(X4,xR,X1)
& aReductOfIn0(X4,X0,xR)
& aElement0(X4) )
| aReductOfIn0(X1,X0,xR)
| X0 = X1 )
& aElement0(X2)
& aElement0(X1)
& aElement0(X0) )
=> ? [X5] :
( sdtmndtasgtdt0(X2,xR,X5)
& ( ( sdtmndtplgtdt0(X2,xR,X5)
& ( ? [X6] :
( sdtmndtplgtdt0(X6,xR,X5)
& aReductOfIn0(X6,X2,xR)
& aElement0(X6) )
| aReductOfIn0(X5,X2,xR) ) )
| X2 = X5 )
& sdtmndtasgtdt0(X1,xR,X5)
& ( ( sdtmndtplgtdt0(X1,xR,X5)
& ( ? [X7] :
( sdtmndtplgtdt0(X7,xR,X5)
& aReductOfIn0(X7,X1,xR)
& aElement0(X7) )
| aReductOfIn0(X5,X1,xR) ) )
| X1 = X5 )
& aElement0(X5) ) ),
inference(rectify,[],[f17]) ).
fof(f26,plain,
~ ( isConfluent0(xR)
| ! [X0,X1,X2] :
( ( sdtmndtasgtdt0(X0,xR,X2)
& ( ( sdtmndtplgtdt0(X0,xR,X2)
& ( ? [X3] :
( sdtmndtplgtdt0(X3,xR,X2)
& aReductOfIn0(X3,X0,xR)
& aElement0(X3) )
| aReductOfIn0(X2,X0,xR) ) )
| X0 = X2 )
& sdtmndtasgtdt0(X0,xR,X1)
& ( ( sdtmndtplgtdt0(X0,xR,X1)
& ( ? [X4] :
( sdtmndtplgtdt0(X4,xR,X1)
& aReductOfIn0(X4,X0,xR)
& aElement0(X4) )
| aReductOfIn0(X1,X0,xR) ) )
| X0 = X1 )
& aElement0(X2)
& aElement0(X1)
& aElement0(X0) )
=> ? [X5] :
( ( sdtmndtasgtdt0(X2,xR,X5)
| sdtmndtplgtdt0(X2,xR,X5)
| ? [X6] :
( sdtmndtplgtdt0(X6,xR,X5)
& aReductOfIn0(X6,X2,xR)
& aElement0(X6) )
| aReductOfIn0(X5,X2,xR)
| X2 = X5 )
& ( sdtmndtasgtdt0(X1,xR,X5)
| sdtmndtplgtdt0(X1,xR,X5)
| ? [X7] :
( sdtmndtplgtdt0(X7,xR,X5)
& aReductOfIn0(X7,X1,xR)
& aElement0(X7) )
| aReductOfIn0(X5,X1,xR)
| X1 = X5 )
& aElement0(X5) ) ) ),
inference(rectify,[],[f19]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ? [X5] :
( sdtmndtasgtdt0(X2,xR,X5)
& ( ( sdtmndtplgtdt0(X2,xR,X5)
& ( ? [X6] :
( sdtmndtplgtdt0(X6,xR,X5)
& aReductOfIn0(X6,X2,xR)
& aElement0(X6) )
| aReductOfIn0(X5,X2,xR) ) )
| X2 = X5 )
& sdtmndtasgtdt0(X1,xR,X5)
& ( ( sdtmndtplgtdt0(X1,xR,X5)
& ( ? [X7] :
( sdtmndtplgtdt0(X7,xR,X5)
& aReductOfIn0(X7,X1,xR)
& aElement0(X7) )
| aReductOfIn0(X5,X1,xR) ) )
| X1 = X5 )
& aElement0(X5) )
| ( ~ sdtmndtasgtdt0(X0,xR,X2)
& ~ sdtmndtplgtdt0(X0,xR,X2)
& ! [X3] :
( ~ sdtmndtplgtdt0(X3,xR,X2)
| ~ aReductOfIn0(X3,X0,xR)
| ~ aElement0(X3) )
& ~ aReductOfIn0(X2,X0,xR)
& X0 != X2 )
| ( ~ sdtmndtasgtdt0(X0,xR,X1)
& ~ sdtmndtplgtdt0(X0,xR,X1)
& ! [X4] :
( ~ sdtmndtplgtdt0(X4,xR,X1)
| ~ aReductOfIn0(X4,X0,xR)
| ~ aElement0(X4) )
& ~ aReductOfIn0(X1,X0,xR)
& X0 != X1 )
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ? [X5] :
( sdtmndtasgtdt0(X2,xR,X5)
& ( ( sdtmndtplgtdt0(X2,xR,X5)
& ( ? [X6] :
( sdtmndtplgtdt0(X6,xR,X5)
& aReductOfIn0(X6,X2,xR)
& aElement0(X6) )
| aReductOfIn0(X5,X2,xR) ) )
| X2 = X5 )
& sdtmndtasgtdt0(X1,xR,X5)
& ( ( sdtmndtplgtdt0(X1,xR,X5)
& ( ? [X7] :
( sdtmndtplgtdt0(X7,xR,X5)
& aReductOfIn0(X7,X1,xR)
& aElement0(X7) )
| aReductOfIn0(X5,X1,xR) ) )
| X1 = X5 )
& aElement0(X5) )
| ( ~ sdtmndtasgtdt0(X0,xR,X2)
& ~ sdtmndtplgtdt0(X0,xR,X2)
& ! [X3] :
( ~ sdtmndtplgtdt0(X3,xR,X2)
| ~ aReductOfIn0(X3,X0,xR)
| ~ aElement0(X3) )
& ~ aReductOfIn0(X2,X0,xR)
& X0 != X2 )
| ( ~ sdtmndtasgtdt0(X0,xR,X1)
& ~ sdtmndtplgtdt0(X0,xR,X1)
& ! [X4] :
( ~ sdtmndtplgtdt0(X4,xR,X1)
| ~ aReductOfIn0(X4,X0,xR)
| ~ aElement0(X4) )
& ~ aReductOfIn0(X1,X0,xR)
& X0 != X1 )
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
( ~ isConfluent0(xR)
& ? [X0,X1,X2] :
( ! [X5] :
( ( ~ sdtmndtasgtdt0(X2,xR,X5)
& ~ sdtmndtplgtdt0(X2,xR,X5)
& ! [X6] :
( ~ sdtmndtplgtdt0(X6,xR,X5)
| ~ aReductOfIn0(X6,X2,xR)
| ~ aElement0(X6) )
& ~ aReductOfIn0(X5,X2,xR)
& X2 != X5 )
| ( ~ sdtmndtasgtdt0(X1,xR,X5)
& ~ sdtmndtplgtdt0(X1,xR,X5)
& ! [X7] :
( ~ sdtmndtplgtdt0(X7,xR,X5)
| ~ aReductOfIn0(X7,X1,xR)
| ~ aElement0(X7) )
& ~ aReductOfIn0(X5,X1,xR)
& X1 != X5 )
| ~ aElement0(X5) )
& sdtmndtasgtdt0(X0,xR,X2)
& ( ( sdtmndtplgtdt0(X0,xR,X2)
& ( ? [X3] :
( sdtmndtplgtdt0(X3,xR,X2)
& aReductOfIn0(X3,X0,xR)
& aElement0(X3) )
| aReductOfIn0(X2,X0,xR) ) )
| X0 = X2 )
& sdtmndtasgtdt0(X0,xR,X1)
& ( ( sdtmndtplgtdt0(X0,xR,X1)
& ( ? [X4] :
( sdtmndtplgtdt0(X4,xR,X1)
& aReductOfIn0(X4,X0,xR)
& aElement0(X4) )
| aReductOfIn0(X1,X0,xR) ) )
| X0 = X1 )
& aElement0(X2)
& aElement0(X1)
& aElement0(X0) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f52,plain,
( ~ isConfluent0(xR)
& ? [X0,X1,X2] :
( ! [X5] :
( ( ~ sdtmndtasgtdt0(X2,xR,X5)
& ~ sdtmndtplgtdt0(X2,xR,X5)
& ! [X6] :
( ~ sdtmndtplgtdt0(X6,xR,X5)
| ~ aReductOfIn0(X6,X2,xR)
| ~ aElement0(X6) )
& ~ aReductOfIn0(X5,X2,xR)
& X2 != X5 )
| ( ~ sdtmndtasgtdt0(X1,xR,X5)
& ~ sdtmndtplgtdt0(X1,xR,X5)
& ! [X7] :
( ~ sdtmndtplgtdt0(X7,xR,X5)
| ~ aReductOfIn0(X7,X1,xR)
| ~ aElement0(X7) )
& ~ aReductOfIn0(X5,X1,xR)
& X1 != X5 )
| ~ aElement0(X5) )
& sdtmndtasgtdt0(X0,xR,X2)
& ( ( sdtmndtplgtdt0(X0,xR,X2)
& ( ? [X3] :
( sdtmndtplgtdt0(X3,xR,X2)
& aReductOfIn0(X3,X0,xR)
& aElement0(X3) )
| aReductOfIn0(X2,X0,xR) ) )
| X0 = X2 )
& sdtmndtasgtdt0(X0,xR,X1)
& ( ( sdtmndtplgtdt0(X0,xR,X1)
& ( ? [X4] :
( sdtmndtplgtdt0(X4,xR,X1)
& aReductOfIn0(X4,X0,xR)
& aElement0(X4) )
| aReductOfIn0(X1,X0,xR) ) )
| X0 = X1 )
& aElement0(X2)
& aElement0(X1)
& aElement0(X0) ) ),
inference(flattening,[],[f51]) ).
fof(f61,plain,
! [X5,X1] :
( ( sdtmndtplgtdt0(X1,xR,X5)
& ( ? [X7] :
( sdtmndtplgtdt0(X7,xR,X5)
& aReductOfIn0(X7,X1,xR)
& aElement0(X7) )
| aReductOfIn0(X5,X1,xR) ) )
| X1 = X5
| ~ sP5(X5,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f62,plain,
! [X2,X1] :
( ? [X5] :
( sdtmndtasgtdt0(X2,xR,X5)
& ( ( sdtmndtplgtdt0(X2,xR,X5)
& ( ? [X6] :
( sdtmndtplgtdt0(X6,xR,X5)
& aReductOfIn0(X6,X2,xR)
& aElement0(X6) )
| aReductOfIn0(X5,X2,xR) ) )
| X2 = X5 )
& sdtmndtasgtdt0(X1,xR,X5)
& sP5(X5,X1)
& aElement0(X5) )
| ~ sP6(X2,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f63,plain,
! [X1,X0] :
( ( ~ sdtmndtasgtdt0(X0,xR,X1)
& ~ sdtmndtplgtdt0(X0,xR,X1)
& ! [X4] :
( ~ sdtmndtplgtdt0(X4,xR,X1)
| ~ aReductOfIn0(X4,X0,xR)
| ~ aElement0(X4) )
& ~ aReductOfIn0(X1,X0,xR)
& X0 != X1 )
| ~ sP7(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f64,plain,
! [X0,X1,X2] :
( sP6(X2,X1)
| ( ~ sdtmndtasgtdt0(X0,xR,X2)
& ~ sdtmndtplgtdt0(X0,xR,X2)
& ! [X3] :
( ~ sdtmndtplgtdt0(X3,xR,X2)
| ~ aReductOfIn0(X3,X0,xR)
| ~ aElement0(X3) )
& ~ aReductOfIn0(X2,X0,xR)
& X0 != X2 )
| sP7(X1,X0)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(definition_folding,[],[f50,f63,f62,f61]) ).
fof(f65,plain,
! [X5,X1] :
( ( ~ sdtmndtasgtdt0(X1,xR,X5)
& ~ sdtmndtplgtdt0(X1,xR,X5)
& ! [X7] :
( ~ sdtmndtplgtdt0(X7,xR,X5)
| ~ aReductOfIn0(X7,X1,xR)
| ~ aElement0(X7) )
& ~ aReductOfIn0(X5,X1,xR)
& X1 != X5 )
| ~ sP8(X5,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f66,plain,
( ~ isConfluent0(xR)
& ? [X0,X1,X2] :
( ! [X5] :
( ( ~ sdtmndtasgtdt0(X2,xR,X5)
& ~ sdtmndtplgtdt0(X2,xR,X5)
& ! [X6] :
( ~ sdtmndtplgtdt0(X6,xR,X5)
| ~ aReductOfIn0(X6,X2,xR)
| ~ aElement0(X6) )
& ~ aReductOfIn0(X5,X2,xR)
& X2 != X5 )
| sP8(X5,X1)
| ~ aElement0(X5) )
& sdtmndtasgtdt0(X0,xR,X2)
& ( ( sdtmndtplgtdt0(X0,xR,X2)
& ( ? [X3] :
( sdtmndtplgtdt0(X3,xR,X2)
& aReductOfIn0(X3,X0,xR)
& aElement0(X3) )
| aReductOfIn0(X2,X0,xR) ) )
| X0 = X2 )
& sdtmndtasgtdt0(X0,xR,X1)
& ( ( sdtmndtplgtdt0(X0,xR,X1)
& ( ? [X4] :
( sdtmndtplgtdt0(X4,xR,X1)
& aReductOfIn0(X4,X0,xR)
& aElement0(X4) )
| aReductOfIn0(X1,X0,xR) ) )
| X0 = X1 )
& aElement0(X2)
& aElement0(X1)
& aElement0(X0) ) ),
inference(definition_folding,[],[f52,f65]) ).
fof(f104,plain,
! [X1,X0] :
( ( ~ sdtmndtasgtdt0(X0,xR,X1)
& ~ sdtmndtplgtdt0(X0,xR,X1)
& ! [X4] :
( ~ sdtmndtplgtdt0(X4,xR,X1)
| ~ aReductOfIn0(X4,X0,xR)
| ~ aElement0(X4) )
& ~ aReductOfIn0(X1,X0,xR)
& X0 != X1 )
| ~ sP7(X1,X0) ),
inference(nnf_transformation,[],[f63]) ).
fof(f105,plain,
! [X0,X1] :
( ( ~ sdtmndtasgtdt0(X1,xR,X0)
& ~ sdtmndtplgtdt0(X1,xR,X0)
& ! [X2] :
( ~ sdtmndtplgtdt0(X2,xR,X0)
| ~ aReductOfIn0(X2,X1,xR)
| ~ aElement0(X2) )
& ~ aReductOfIn0(X0,X1,xR)
& X0 != X1 )
| ~ sP7(X0,X1) ),
inference(rectify,[],[f104]) ).
fof(f106,plain,
! [X2,X1] :
( ? [X5] :
( sdtmndtasgtdt0(X2,xR,X5)
& ( ( sdtmndtplgtdt0(X2,xR,X5)
& ( ? [X6] :
( sdtmndtplgtdt0(X6,xR,X5)
& aReductOfIn0(X6,X2,xR)
& aElement0(X6) )
| aReductOfIn0(X5,X2,xR) ) )
| X2 = X5 )
& sdtmndtasgtdt0(X1,xR,X5)
& sP5(X5,X1)
& aElement0(X5) )
| ~ sP6(X2,X1) ),
inference(nnf_transformation,[],[f62]) ).
fof(f107,plain,
! [X0,X1] :
( ? [X2] :
( sdtmndtasgtdt0(X0,xR,X2)
& ( ( sdtmndtplgtdt0(X0,xR,X2)
& ( ? [X3] :
( sdtmndtplgtdt0(X3,xR,X2)
& aReductOfIn0(X3,X0,xR)
& aElement0(X3) )
| aReductOfIn0(X2,X0,xR) ) )
| X0 = X2 )
& sdtmndtasgtdt0(X1,xR,X2)
& sP5(X2,X1)
& aElement0(X2) )
| ~ sP6(X0,X1) ),
inference(rectify,[],[f106]) ).
fof(f108,plain,
! [X0,X1] :
( ? [X2] :
( sdtmndtasgtdt0(X0,xR,X2)
& ( ( sdtmndtplgtdt0(X0,xR,X2)
& ( ? [X3] :
( sdtmndtplgtdt0(X3,xR,X2)
& aReductOfIn0(X3,X0,xR)
& aElement0(X3) )
| aReductOfIn0(X2,X0,xR) ) )
| X0 = X2 )
& sdtmndtasgtdt0(X1,xR,X2)
& sP5(X2,X1)
& aElement0(X2) )
=> ( sdtmndtasgtdt0(X0,xR,sK25(X0,X1))
& ( ( sdtmndtplgtdt0(X0,xR,sK25(X0,X1))
& ( ? [X3] :
( sdtmndtplgtdt0(X3,xR,sK25(X0,X1))
& aReductOfIn0(X3,X0,xR)
& aElement0(X3) )
| aReductOfIn0(sK25(X0,X1),X0,xR) ) )
| sK25(X0,X1) = X0 )
& sdtmndtasgtdt0(X1,xR,sK25(X0,X1))
& sP5(sK25(X0,X1),X1)
& aElement0(sK25(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f109,plain,
! [X0,X1] :
( ? [X3] :
( sdtmndtplgtdt0(X3,xR,sK25(X0,X1))
& aReductOfIn0(X3,X0,xR)
& aElement0(X3) )
=> ( sdtmndtplgtdt0(sK26(X0,X1),xR,sK25(X0,X1))
& aReductOfIn0(sK26(X0,X1),X0,xR)
& aElement0(sK26(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f110,plain,
! [X0,X1] :
( ( sdtmndtasgtdt0(X0,xR,sK25(X0,X1))
& ( ( sdtmndtplgtdt0(X0,xR,sK25(X0,X1))
& ( ( sdtmndtplgtdt0(sK26(X0,X1),xR,sK25(X0,X1))
& aReductOfIn0(sK26(X0,X1),X0,xR)
& aElement0(sK26(X0,X1)) )
| aReductOfIn0(sK25(X0,X1),X0,xR) ) )
| sK25(X0,X1) = X0 )
& sdtmndtasgtdt0(X1,xR,sK25(X0,X1))
& sP5(sK25(X0,X1),X1)
& aElement0(sK25(X0,X1)) )
| ~ sP6(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25,sK26])],[f107,f109,f108]) ).
fof(f115,plain,
! [X5,X1] :
( ( ~ sdtmndtasgtdt0(X1,xR,X5)
& ~ sdtmndtplgtdt0(X1,xR,X5)
& ! [X7] :
( ~ sdtmndtplgtdt0(X7,xR,X5)
| ~ aReductOfIn0(X7,X1,xR)
| ~ aElement0(X7) )
& ~ aReductOfIn0(X5,X1,xR)
& X1 != X5 )
| ~ sP8(X5,X1) ),
inference(nnf_transformation,[],[f65]) ).
fof(f116,plain,
! [X0,X1] :
( ( ~ sdtmndtasgtdt0(X1,xR,X0)
& ~ sdtmndtplgtdt0(X1,xR,X0)
& ! [X2] :
( ~ sdtmndtplgtdt0(X2,xR,X0)
| ~ aReductOfIn0(X2,X1,xR)
| ~ aElement0(X2) )
& ~ aReductOfIn0(X0,X1,xR)
& X0 != X1 )
| ~ sP8(X0,X1) ),
inference(rectify,[],[f115]) ).
fof(f117,plain,
( ~ isConfluent0(xR)
& ? [X0,X1,X2] :
( ! [X3] :
( ( ~ sdtmndtasgtdt0(X2,xR,X3)
& ~ sdtmndtplgtdt0(X2,xR,X3)
& ! [X4] :
( ~ sdtmndtplgtdt0(X4,xR,X3)
| ~ aReductOfIn0(X4,X2,xR)
| ~ aElement0(X4) )
& ~ aReductOfIn0(X3,X2,xR)
& X2 != X3 )
| sP8(X3,X1)
| ~ aElement0(X3) )
& sdtmndtasgtdt0(X0,xR,X2)
& ( ( sdtmndtplgtdt0(X0,xR,X2)
& ( ? [X5] :
( sdtmndtplgtdt0(X5,xR,X2)
& aReductOfIn0(X5,X0,xR)
& aElement0(X5) )
| aReductOfIn0(X2,X0,xR) ) )
| X0 = X2 )
& sdtmndtasgtdt0(X0,xR,X1)
& ( ( sdtmndtplgtdt0(X0,xR,X1)
& ( ? [X6] :
( sdtmndtplgtdt0(X6,xR,X1)
& aReductOfIn0(X6,X0,xR)
& aElement0(X6) )
| aReductOfIn0(X1,X0,xR) ) )
| X0 = X1 )
& aElement0(X2)
& aElement0(X1)
& aElement0(X0) ) ),
inference(rectify,[],[f66]) ).
fof(f118,plain,
( ? [X0,X1,X2] :
( ! [X3] :
( ( ~ sdtmndtasgtdt0(X2,xR,X3)
& ~ sdtmndtplgtdt0(X2,xR,X3)
& ! [X4] :
( ~ sdtmndtplgtdt0(X4,xR,X3)
| ~ aReductOfIn0(X4,X2,xR)
| ~ aElement0(X4) )
& ~ aReductOfIn0(X3,X2,xR)
& X2 != X3 )
| sP8(X3,X1)
| ~ aElement0(X3) )
& sdtmndtasgtdt0(X0,xR,X2)
& ( ( sdtmndtplgtdt0(X0,xR,X2)
& ( ? [X5] :
( sdtmndtplgtdt0(X5,xR,X2)
& aReductOfIn0(X5,X0,xR)
& aElement0(X5) )
| aReductOfIn0(X2,X0,xR) ) )
| X0 = X2 )
& sdtmndtasgtdt0(X0,xR,X1)
& ( ( sdtmndtplgtdt0(X0,xR,X1)
& ( ? [X6] :
( sdtmndtplgtdt0(X6,xR,X1)
& aReductOfIn0(X6,X0,xR)
& aElement0(X6) )
| aReductOfIn0(X1,X0,xR) ) )
| X0 = X1 )
& aElement0(X2)
& aElement0(X1)
& aElement0(X0) )
=> ( ! [X3] :
( ( ~ sdtmndtasgtdt0(sK30,xR,X3)
& ~ sdtmndtplgtdt0(sK30,xR,X3)
& ! [X4] :
( ~ sdtmndtplgtdt0(X4,xR,X3)
| ~ aReductOfIn0(X4,sK30,xR)
| ~ aElement0(X4) )
& ~ aReductOfIn0(X3,sK30,xR)
& sK30 != X3 )
| sP8(X3,sK29)
| ~ aElement0(X3) )
& sdtmndtasgtdt0(sK28,xR,sK30)
& ( ( sdtmndtplgtdt0(sK28,xR,sK30)
& ( ? [X5] :
( sdtmndtplgtdt0(X5,xR,sK30)
& aReductOfIn0(X5,sK28,xR)
& aElement0(X5) )
| aReductOfIn0(sK30,sK28,xR) ) )
| sK28 = sK30 )
& sdtmndtasgtdt0(sK28,xR,sK29)
& ( ( sdtmndtplgtdt0(sK28,xR,sK29)
& ( ? [X6] :
( sdtmndtplgtdt0(X6,xR,sK29)
& aReductOfIn0(X6,sK28,xR)
& aElement0(X6) )
| aReductOfIn0(sK29,sK28,xR) ) )
| sK28 = sK29 )
& aElement0(sK30)
& aElement0(sK29)
& aElement0(sK28) ) ),
introduced(choice_axiom,[]) ).
fof(f119,plain,
( ? [X5] :
( sdtmndtplgtdt0(X5,xR,sK30)
& aReductOfIn0(X5,sK28,xR)
& aElement0(X5) )
=> ( sdtmndtplgtdt0(sK31,xR,sK30)
& aReductOfIn0(sK31,sK28,xR)
& aElement0(sK31) ) ),
introduced(choice_axiom,[]) ).
fof(f120,plain,
( ? [X6] :
( sdtmndtplgtdt0(X6,xR,sK29)
& aReductOfIn0(X6,sK28,xR)
& aElement0(X6) )
=> ( sdtmndtplgtdt0(sK32,xR,sK29)
& aReductOfIn0(sK32,sK28,xR)
& aElement0(sK32) ) ),
introduced(choice_axiom,[]) ).
fof(f121,plain,
( ~ isConfluent0(xR)
& ! [X3] :
( ( ~ sdtmndtasgtdt0(sK30,xR,X3)
& ~ sdtmndtplgtdt0(sK30,xR,X3)
& ! [X4] :
( ~ sdtmndtplgtdt0(X4,xR,X3)
| ~ aReductOfIn0(X4,sK30,xR)
| ~ aElement0(X4) )
& ~ aReductOfIn0(X3,sK30,xR)
& sK30 != X3 )
| sP8(X3,sK29)
| ~ aElement0(X3) )
& sdtmndtasgtdt0(sK28,xR,sK30)
& ( ( sdtmndtplgtdt0(sK28,xR,sK30)
& ( ( sdtmndtplgtdt0(sK31,xR,sK30)
& aReductOfIn0(sK31,sK28,xR)
& aElement0(sK31) )
| aReductOfIn0(sK30,sK28,xR) ) )
| sK28 = sK30 )
& sdtmndtasgtdt0(sK28,xR,sK29)
& ( ( sdtmndtplgtdt0(sK28,xR,sK29)
& ( ( sdtmndtplgtdt0(sK32,xR,sK29)
& aReductOfIn0(sK32,sK28,xR)
& aElement0(sK32) )
| aReductOfIn0(sK29,sK28,xR) ) )
| sK28 = sK29 )
& aElement0(sK30)
& aElement0(sK29)
& aElement0(sK28) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28,sK29,sK30,sK31,sK32])],[f117,f120,f119,f118]) ).
fof(f189,plain,
! [X0,X1] :
( ~ sdtmndtasgtdt0(X1,xR,X0)
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f105]) ).
fof(f190,plain,
! [X0,X1] :
( aElement0(sK25(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f110]) ).
fof(f192,plain,
! [X0,X1] :
( sdtmndtasgtdt0(X1,xR,sK25(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f110]) ).
fof(f197,plain,
! [X0,X1] :
( sdtmndtasgtdt0(X0,xR,sK25(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f110]) ).
fof(f206,plain,
! [X2,X0,X1] :
( sP6(X2,X1)
| ~ sdtmndtasgtdt0(X0,xR,X2)
| sP7(X1,X0)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f211,plain,
! [X0,X1] :
( ~ sdtmndtasgtdt0(X1,xR,X0)
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f116]) ).
fof(f212,plain,
aElement0(sK28),
inference(cnf_transformation,[],[f121]) ).
fof(f213,plain,
aElement0(sK29),
inference(cnf_transformation,[],[f121]) ).
fof(f214,plain,
aElement0(sK30),
inference(cnf_transformation,[],[f121]) ).
fof(f219,plain,
sdtmndtasgtdt0(sK28,xR,sK29),
inference(cnf_transformation,[],[f121]) ).
fof(f224,plain,
sdtmndtasgtdt0(sK28,xR,sK30),
inference(cnf_transformation,[],[f121]) ).
fof(f229,plain,
! [X3] :
( ~ sdtmndtasgtdt0(sK30,xR,X3)
| sP8(X3,sK29)
| ~ aElement0(X3) ),
inference(cnf_transformation,[],[f121]) ).
cnf(c_112,plain,
( ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ sP7(X1,X0) ),
inference(cnf_transformation,[],[f189]) ).
cnf(c_117,plain,
( ~ sP6(X0,X1)
| sdtmndtasgtdt0(X0,xR,sK25(X0,X1)) ),
inference(cnf_transformation,[],[f197]) ).
cnf(c_122,plain,
( ~ sP6(X0,X1)
| sdtmndtasgtdt0(X1,xR,sK25(X0,X1)) ),
inference(cnf_transformation,[],[f192]) ).
cnf(c_124,plain,
( ~ sP6(X0,X1)
| aElement0(sK25(X0,X1)) ),
inference(cnf_transformation,[],[f190]) ).
cnf(c_129,plain,
( ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2)
| sP7(X2,X0)
| sP6(X1,X2) ),
inference(cnf_transformation,[],[f206]) ).
cnf(c_134,plain,
( ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ sP8(X1,X0) ),
inference(cnf_transformation,[],[f211]) ).
cnf(c_140,negated_conjecture,
( ~ sdtmndtasgtdt0(sK30,xR,X0)
| ~ aElement0(X0)
| sP8(X0,sK29) ),
inference(cnf_transformation,[],[f229]) ).
cnf(c_145,negated_conjecture,
sdtmndtasgtdt0(sK28,xR,sK30),
inference(cnf_transformation,[],[f224]) ).
cnf(c_150,negated_conjecture,
sdtmndtasgtdt0(sK28,xR,sK29),
inference(cnf_transformation,[],[f219]) ).
cnf(c_155,negated_conjecture,
aElement0(sK30),
inference(cnf_transformation,[],[f214]) ).
cnf(c_156,negated_conjecture,
aElement0(sK29),
inference(cnf_transformation,[],[f213]) ).
cnf(c_157,negated_conjecture,
aElement0(sK28),
inference(cnf_transformation,[],[f212]) ).
cnf(c_10921,negated_conjecture,
aElement0(sK28),
inference(demodulation,[status(thm)],[c_157]) ).
cnf(c_10922,negated_conjecture,
aElement0(sK29),
inference(demodulation,[status(thm)],[c_156]) ).
cnf(c_10923,negated_conjecture,
aElement0(sK30),
inference(demodulation,[status(thm)],[c_155]) ).
cnf(c_10928,negated_conjecture,
sdtmndtasgtdt0(sK28,xR,sK29),
inference(demodulation,[status(thm)],[c_150]) ).
cnf(c_10933,negated_conjecture,
sdtmndtasgtdt0(sK28,xR,sK30),
inference(demodulation,[status(thm)],[c_145]) ).
cnf(c_10937,negated_conjecture,
( ~ sdtmndtasgtdt0(sK30,xR,X0)
| ~ aElement0(X0)
| sP8(X0,sK29) ),
inference(demodulation,[status(thm)],[c_140]) ).
cnf(c_12883,plain,
~ sP7(sK30,sK28),
inference(superposition,[status(thm)],[c_10933,c_112]) ).
cnf(c_13054,plain,
( ~ sP8(sK25(X0,X1),X0)
| ~ sP6(X0,X1) ),
inference(superposition,[status(thm)],[c_117,c_134]) ).
cnf(c_13073,plain,
( ~ aElement0(sK25(X0,sK30))
| ~ sP6(X0,sK30)
| sP8(sK25(X0,sK30),sK29) ),
inference(superposition,[status(thm)],[c_122,c_10937]) ).
cnf(c_13135,plain,
( ~ sP6(X0,sK30)
| sP8(sK25(X0,sK30),sK29) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13073,c_124]) ).
cnf(c_13142,plain,
~ sP6(sK29,sK30),
inference(superposition,[status(thm)],[c_13135,c_13054]) ).
cnf(c_14841,plain,
( ~ aElement0(X0)
| ~ aElement0(sK29)
| ~ aElement0(sK28)
| sP7(X0,sK28)
| sP6(sK29,X0) ),
inference(superposition,[status(thm)],[c_10928,c_129]) ).
cnf(c_14846,plain,
( ~ aElement0(X0)
| sP7(X0,sK28)
| sP6(sK29,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14841,c_10921,c_10922]) ).
cnf(c_15030,plain,
( ~ aElement0(sK30)
| sP6(sK29,sK30) ),
inference(superposition,[status(thm)],[c_14846,c_12883]) ).
cnf(c_15035,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_15030,c_13142,c_10923]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : COM023+4 : TPTP v8.2.0. Released v4.0.0.
% 0.11/0.12 % Command : run_iprover %s %d THM
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 21 00:05:09 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 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
% 0.47/1.15 % SZS status Started for theBenchmark.p
% 0.47/1.15 % SZS status Theorem for theBenchmark.p
% 0.47/1.15
% 0.47/1.15 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 0.47/1.15
% 0.47/1.15 ------ iProver source info
% 0.47/1.15
% 0.47/1.15 git: date: 2024-06-12 09:56:46 +0000
% 0.47/1.15 git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 0.47/1.15 git: non_committed_changes: false
% 0.47/1.15
% 0.47/1.15 ------ Parsing...
% 0.47/1.15 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.47/1.15
% 0.47/1.15 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 5 0s sf_e pe_s pe_e
% 0.47/1.15
% 0.47/1.15 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.47/1.15
% 0.47/1.15 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.47/1.15 ------ Proving...
% 0.47/1.15 ------ Problem Properties
% 0.47/1.15
% 0.47/1.15
% 0.47/1.15 clauses 101
% 0.47/1.15 conjectures 18
% 0.47/1.15 EPR 47
% 0.47/1.15 Horn 55
% 0.47/1.15 unary 12
% 0.47/1.15 binary 22
% 0.47/1.15 lits 379
% 0.47/1.15 lits eq 25
% 0.47/1.15 fd_pure 0
% 0.47/1.15 fd_pseudo 0
% 0.47/1.15 fd_cond 0
% 0.47/1.15 fd_pseudo_cond 9
% 0.47/1.15 AC symbols 0
% 0.47/1.15
% 0.47/1.15 ------ Schedule dynamic 5 is on
% 0.47/1.15
% 0.47/1.15 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.47/1.15
% 0.47/1.15
% 0.47/1.15 ------
% 0.47/1.15 Current options:
% 0.47/1.15 ------
% 0.47/1.15
% 0.47/1.15
% 0.47/1.15
% 0.47/1.15
% 0.47/1.15 ------ Proving...
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% 0.47/1.15
% 0.47/1.15 % SZS status Theorem for theBenchmark.p
% 0.47/1.15
% 0.47/1.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
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% 0.47/1.15
%------------------------------------------------------------------------------