%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COM023+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 09:40:10 AM UTC 2026
% Result : Theorem 0.17s 0.29s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 76 ( 14 unt; 7 def)
% Number of atoms : 666 ( 55 equ)
% Maximal formula atoms : 33 ( 8 avg)
% Number of connectives : 826 ( 236 ~; 265 |; 312 &)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 2 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 194 ( 0 sgn 124 !; 70 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0] :
( aRewritingSystem0(X0)
=> ( isConfluent0(X0)
<=> ! [X1,X2,X3] :
( ( aElement0(X1)
& aElement0(X2)
& aElement0(X3)
& sdtmndtasgtdt0(X1,X0,X2)
& sdtmndtasgtdt0(X1,X0,X3) )
=> ? [X4] :
( aElement0(X4)
& sdtmndtasgtdt0(X2,X0,X4)
& sdtmndtasgtdt0(X3,X0,X4) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCRDef) ).
fof(f15,axiom,
aRewritingSystem0(xR),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656) ).
fof(f17,axiom,
! [X0,X1,X2] :
( ( aElement0(X0)
& aElement0(X1)
& aElement0(X2)
& ( X0 = X1
| aReductOfIn0(X1,X0,xR)
| ? [X3] :
( aElement0(X3)
& aReductOfIn0(X3,X0,xR)
& sdtmndtplgtdt0(X3,xR,X1) )
| sdtmndtplgtdt0(X0,xR,X1)
| sdtmndtasgtdt0(X0,xR,X1) )
& ( X0 = X2
| aReductOfIn0(X2,X0,xR)
| ? [X3] :
( aElement0(X3)
& aReductOfIn0(X3,X0,xR)
& sdtmndtplgtdt0(X3,xR,X2) )
| sdtmndtplgtdt0(X0,xR,X2)
| sdtmndtasgtdt0(X0,xR,X2) ) )
=> ? [X3] :
( aElement0(X3)
& ( X1 = X3
| ( ( aReductOfIn0(X3,X1,xR)
| ? [X4] :
( aElement0(X4)
& aReductOfIn0(X4,X1,xR)
& sdtmndtplgtdt0(X4,xR,X3) ) )
& sdtmndtplgtdt0(X1,xR,X3) ) )
& sdtmndtasgtdt0(X1,xR,X3)
& ( X2 = X3
| ( ( aReductOfIn0(X3,X2,xR)
| ? [X4] :
( aElement0(X4)
& aReductOfIn0(X4,X2,xR)
& sdtmndtplgtdt0(X4,xR,X3) ) )
& sdtmndtplgtdt0(X2,xR,X3) ) )
& sdtmndtasgtdt0(X2,xR,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__715) ).
fof(f18,conjecture,
( ! [X0,X1,X2] :
( ( aElement0(X0)
& aElement0(X1)
& aElement0(X2)
& ( X0 = X1
| ( ( aReductOfIn0(X1,X0,xR)
| ? [X3] :
( aElement0(X3)
& aReductOfIn0(X3,X0,xR)
& sdtmndtplgtdt0(X3,xR,X1) ) )
& sdtmndtplgtdt0(X0,xR,X1) ) )
& sdtmndtasgtdt0(X0,xR,X1)
& ( X0 = X2
| ( ( aReductOfIn0(X2,X0,xR)
| ? [X3] :
( aElement0(X3)
& aReductOfIn0(X3,X0,xR)
& sdtmndtplgtdt0(X3,xR,X2) ) )
& sdtmndtplgtdt0(X0,xR,X2) ) )
& sdtmndtasgtdt0(X0,xR,X2) )
=> ? [X3] :
( aElement0(X3)
& ( X1 = X3
| aReductOfIn0(X3,X1,xR)
| ? [X4] :
( aElement0(X4)
& aReductOfIn0(X4,X1,xR)
& sdtmndtplgtdt0(X4,xR,X3) )
| sdtmndtplgtdt0(X1,xR,X3)
| sdtmndtasgtdt0(X1,xR,X3) )
& ( X2 = X3
| aReductOfIn0(X3,X2,xR)
| ? [X4] :
( aElement0(X4)
& aReductOfIn0(X4,X2,xR)
& sdtmndtplgtdt0(X4,xR,X3) )
| sdtmndtplgtdt0(X2,xR,X3)
| sdtmndtasgtdt0(X2,xR,X3) ) ) )
| isConfluent0(xR) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f19,negated_conjecture,
~ ( ! [X0,X1,X2] :
( ( aElement0(X0)
& aElement0(X1)
& aElement0(X2)
& ( X0 = X1
| ( ( aReductOfIn0(X1,X0,xR)
| ? [X3] :
( aElement0(X3)
& aReductOfIn0(X3,X0,xR)
& sdtmndtplgtdt0(X3,xR,X1) ) )
& sdtmndtplgtdt0(X0,xR,X1) ) )
& sdtmndtasgtdt0(X0,xR,X1)
& ( X0 = X2
| ( ( aReductOfIn0(X2,X0,xR)
| ? [X3] :
( aElement0(X3)
& aReductOfIn0(X3,X0,xR)
& sdtmndtplgtdt0(X3,xR,X2) ) )
& sdtmndtplgtdt0(X0,xR,X2) ) )
& sdtmndtasgtdt0(X0,xR,X2) )
=> ? [X3] :
( aElement0(X3)
& ( X1 = X3
| aReductOfIn0(X3,X1,xR)
| ? [X4] :
( aElement0(X4)
& aReductOfIn0(X4,X1,xR)
& sdtmndtplgtdt0(X4,xR,X3) )
| sdtmndtplgtdt0(X1,xR,X3)
| sdtmndtasgtdt0(X1,xR,X3) )
& ( X2 = X3
| aReductOfIn0(X3,X2,xR)
| ? [X4] :
( aElement0(X4)
& aReductOfIn0(X4,X2,xR)
& sdtmndtplgtdt0(X4,xR,X3) )
| sdtmndtplgtdt0(X2,xR,X3)
| sdtmndtasgtdt0(X2,xR,X3) ) ) )
| isConfluent0(xR) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( aElement0(X0)
& aElement0(X1)
& aElement0(X2)
& ( X0 = X1
| aReductOfIn0(X1,X0,xR)
| ? [X3] :
( aElement0(X3)
& aReductOfIn0(X3,X0,xR)
& sdtmndtplgtdt0(X3,xR,X1) )
| sdtmndtplgtdt0(X0,xR,X1)
| sdtmndtasgtdt0(X0,xR,X1) )
& ( X0 = X2
| aReductOfIn0(X2,X0,xR)
| ? [X4] :
( aElement0(X4)
& aReductOfIn0(X4,X0,xR)
& sdtmndtplgtdt0(X4,xR,X2) )
| sdtmndtplgtdt0(X0,xR,X2)
| sdtmndtasgtdt0(X0,xR,X2) ) )
=> ? [X5] :
( aElement0(X5)
& ( X1 = X5
| ( ( aReductOfIn0(X5,X1,xR)
| ? [X6] :
( aElement0(X6)
& aReductOfIn0(X6,X1,xR)
& sdtmndtplgtdt0(X6,xR,X5) ) )
& sdtmndtplgtdt0(X1,xR,X5) ) )
& sdtmndtasgtdt0(X1,xR,X5)
& ( X2 = X5
| ( ( aReductOfIn0(X5,X2,xR)
| ? [X7] :
( aElement0(X7)
& aReductOfIn0(X7,X2,xR)
& sdtmndtplgtdt0(X7,xR,X5) ) )
& sdtmndtplgtdt0(X2,xR,X5) ) )
& sdtmndtasgtdt0(X2,xR,X5) ) ),
inference(rectify,[],[f17]) ).
fof(f26,plain,
~ ( ! [X0,X1,X2] :
( ( aElement0(X0)
& aElement0(X1)
& aElement0(X2)
& ( X0 = X1
| ( ( aReductOfIn0(X1,X0,xR)
| ? [X3] :
( aElement0(X3)
& aReductOfIn0(X3,X0,xR)
& sdtmndtplgtdt0(X3,xR,X1) ) )
& sdtmndtplgtdt0(X0,xR,X1) ) )
& sdtmndtasgtdt0(X0,xR,X1)
& ( X0 = X2
| ( ( aReductOfIn0(X2,X0,xR)
| ? [X4] :
( aElement0(X4)
& aReductOfIn0(X4,X0,xR)
& sdtmndtplgtdt0(X4,xR,X2) ) )
& sdtmndtplgtdt0(X0,xR,X2) ) )
& sdtmndtasgtdt0(X0,xR,X2) )
=> ? [X5] :
( aElement0(X5)
& ( X1 = X5
| aReductOfIn0(X5,X1,xR)
| ? [X6] :
( aElement0(X6)
& aReductOfIn0(X6,X1,xR)
& sdtmndtplgtdt0(X6,xR,X5) )
| sdtmndtplgtdt0(X1,xR,X5)
| sdtmndtasgtdt0(X1,xR,X5) )
& ( X2 = X5
| aReductOfIn0(X5,X2,xR)
| ? [X7] :
( aElement0(X7)
& aReductOfIn0(X7,X2,xR)
& sdtmndtplgtdt0(X7,xR,X5) )
| sdtmndtplgtdt0(X2,xR,X5)
| sdtmndtasgtdt0(X2,xR,X5) ) ) )
| isConfluent0(xR) ),
inference(rectify,[],[f19]) ).
fof(f37,plain,
! [X0] :
( ( isConfluent0(X0)
<=> ! [X1,X2,X3] :
( ? [X4] :
( aElement0(X4)
& sdtmndtasgtdt0(X2,X0,X4)
& sdtmndtasgtdt0(X3,X0,X4) )
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3)
| ~ sdtmndtasgtdt0(X1,X0,X2)
| ~ sdtmndtasgtdt0(X1,X0,X3) ) )
| ~ aRewritingSystem0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f38,plain,
! [X0] :
( ( isConfluent0(X0)
<=> ! [X1,X2,X3] :
( ? [X4] :
( aElement0(X4)
& sdtmndtasgtdt0(X2,X0,X4)
& sdtmndtasgtdt0(X3,X0,X4) )
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3)
| ~ sdtmndtasgtdt0(X1,X0,X2)
| ~ sdtmndtasgtdt0(X1,X0,X3) ) )
| ~ aRewritingSystem0(X0) ),
inference(flattening,[],[f37]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ? [X5] :
( aElement0(X5)
& ( X1 = X5
| ( ( aReductOfIn0(X5,X1,xR)
| ? [X6] :
( aElement0(X6)
& aReductOfIn0(X6,X1,xR)
& sdtmndtplgtdt0(X6,xR,X5) ) )
& sdtmndtplgtdt0(X1,xR,X5) ) )
& sdtmndtasgtdt0(X1,xR,X5)
& ( X2 = X5
| ( ( aReductOfIn0(X5,X2,xR)
| ? [X7] :
( aElement0(X7)
& aReductOfIn0(X7,X2,xR)
& sdtmndtplgtdt0(X7,xR,X5) ) )
& sdtmndtplgtdt0(X2,xR,X5) ) )
& sdtmndtasgtdt0(X2,xR,X5) )
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ( X0 != X1
& ~ aReductOfIn0(X1,X0,xR)
& ! [X3] :
( ~ aElement0(X3)
| ~ aReductOfIn0(X3,X0,xR)
| ~ sdtmndtplgtdt0(X3,xR,X1) )
& ~ sdtmndtplgtdt0(X0,xR,X1)
& ~ sdtmndtasgtdt0(X0,xR,X1) )
| ( X0 != X2
& ~ aReductOfIn0(X2,X0,xR)
& ! [X4] :
( ~ aElement0(X4)
| ~ aReductOfIn0(X4,X0,xR)
| ~ sdtmndtplgtdt0(X4,xR,X2) )
& ~ sdtmndtplgtdt0(X0,xR,X2)
& ~ sdtmndtasgtdt0(X0,xR,X2) ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ? [X5] :
( aElement0(X5)
& ( X1 = X5
| ( ( aReductOfIn0(X5,X1,xR)
| ? [X6] :
( aElement0(X6)
& aReductOfIn0(X6,X1,xR)
& sdtmndtplgtdt0(X6,xR,X5) ) )
& sdtmndtplgtdt0(X1,xR,X5) ) )
& sdtmndtasgtdt0(X1,xR,X5)
& ( X2 = X5
| ( ( aReductOfIn0(X5,X2,xR)
| ? [X7] :
( aElement0(X7)
& aReductOfIn0(X7,X2,xR)
& sdtmndtplgtdt0(X7,xR,X5) ) )
& sdtmndtplgtdt0(X2,xR,X5) ) )
& sdtmndtasgtdt0(X2,xR,X5) )
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ( X0 != X1
& ~ aReductOfIn0(X1,X0,xR)
& ! [X3] :
( ~ aElement0(X3)
| ~ aReductOfIn0(X3,X0,xR)
| ~ sdtmndtplgtdt0(X3,xR,X1) )
& ~ sdtmndtplgtdt0(X0,xR,X1)
& ~ sdtmndtasgtdt0(X0,xR,X1) )
| ( X0 != X2
& ~ aReductOfIn0(X2,X0,xR)
& ! [X4] :
( ~ aElement0(X4)
| ~ aReductOfIn0(X4,X0,xR)
| ~ sdtmndtplgtdt0(X4,xR,X2) )
& ~ sdtmndtplgtdt0(X0,xR,X2)
& ~ sdtmndtasgtdt0(X0,xR,X2) ) ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
( ? [X0,X1,X2] :
( ! [X5] :
( ~ aElement0(X5)
| ( X1 != X5
& ~ aReductOfIn0(X5,X1,xR)
& ! [X6] :
( ~ aElement0(X6)
| ~ aReductOfIn0(X6,X1,xR)
| ~ sdtmndtplgtdt0(X6,xR,X5) )
& ~ sdtmndtplgtdt0(X1,xR,X5)
& ~ sdtmndtasgtdt0(X1,xR,X5) )
| ( X2 != X5
& ~ aReductOfIn0(X5,X2,xR)
& ! [X7] :
( ~ aElement0(X7)
| ~ aReductOfIn0(X7,X2,xR)
| ~ sdtmndtplgtdt0(X7,xR,X5) )
& ~ sdtmndtplgtdt0(X2,xR,X5)
& ~ sdtmndtasgtdt0(X2,xR,X5) ) )
& aElement0(X0)
& aElement0(X1)
& aElement0(X2)
& ( X0 = X1
| ( ( aReductOfIn0(X1,X0,xR)
| ? [X3] :
( aElement0(X3)
& aReductOfIn0(X3,X0,xR)
& sdtmndtplgtdt0(X3,xR,X1) ) )
& sdtmndtplgtdt0(X0,xR,X1) ) )
& sdtmndtasgtdt0(X0,xR,X1)
& ( X0 = X2
| ( ( aReductOfIn0(X2,X0,xR)
| ? [X4] :
( aElement0(X4)
& aReductOfIn0(X4,X0,xR)
& sdtmndtplgtdt0(X4,xR,X2) ) )
& sdtmndtplgtdt0(X0,xR,X2) ) )
& sdtmndtasgtdt0(X0,xR,X2) )
& ~ isConfluent0(xR) ),
inference(ennf_transformation,[],[f26]) ).
fof(f52,plain,
( ? [X0,X1,X2] :
( ! [X5] :
( ~ aElement0(X5)
| ( X1 != X5
& ~ aReductOfIn0(X5,X1,xR)
& ! [X6] :
( ~ aElement0(X6)
| ~ aReductOfIn0(X6,X1,xR)
| ~ sdtmndtplgtdt0(X6,xR,X5) )
& ~ sdtmndtplgtdt0(X1,xR,X5)
& ~ sdtmndtasgtdt0(X1,xR,X5) )
| ( X2 != X5
& ~ aReductOfIn0(X5,X2,xR)
& ! [X7] :
( ~ aElement0(X7)
| ~ aReductOfIn0(X7,X2,xR)
| ~ sdtmndtplgtdt0(X7,xR,X5) )
& ~ sdtmndtplgtdt0(X2,xR,X5)
& ~ sdtmndtasgtdt0(X2,xR,X5) ) )
& aElement0(X0)
& aElement0(X1)
& aElement0(X2)
& ( X0 = X1
| ( ( aReductOfIn0(X1,X0,xR)
| ? [X3] :
( aElement0(X3)
& aReductOfIn0(X3,X0,xR)
& sdtmndtplgtdt0(X3,xR,X1) ) )
& sdtmndtplgtdt0(X0,xR,X1) ) )
& sdtmndtasgtdt0(X0,xR,X1)
& ( X0 = X2
| ( ( aReductOfIn0(X2,X0,xR)
| ? [X4] :
( aElement0(X4)
& aReductOfIn0(X4,X0,xR)
& sdtmndtplgtdt0(X4,xR,X2) ) )
& sdtmndtplgtdt0(X0,xR,X2) ) )
& sdtmndtasgtdt0(X0,xR,X2) )
& ~ isConfluent0(xR) ),
inference(flattening,[],[f51]) ).
fof(f53,definition,
! [X0] :
( sP0(X0)
<=> ! [X1,X2,X3] :
( ? [X4] :
( aElement0(X4)
& sdtmndtasgtdt0(X2,X0,X4)
& sdtmndtasgtdt0(X3,X0,X4) )
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3)
| ~ sdtmndtasgtdt0(X1,X0,X2)
| ~ sdtmndtasgtdt0(X1,X0,X3) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f54,definition,
! [X0] :
( ( isConfluent0(X0)
<=> sP0(X0) )
| ~ sP1(X0) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f55,plain,
! [X0] :
( sP1(X0)
| ~ aRewritingSystem0(X0) ),
inference(definition_folding,[],[f38,f54,f53]) ).
fof(f61,definition,
! [X5,X2] :
( X2 = X5
| ( ( aReductOfIn0(X5,X2,xR)
| ? [X7] :
( aElement0(X7)
& aReductOfIn0(X7,X2,xR)
& sdtmndtplgtdt0(X7,xR,X5) ) )
& sdtmndtplgtdt0(X2,xR,X5) )
| ~ sP5(X5,X2) ),
introduced(definition,[new_symbols(definition,[sP5])],[predicate_definition_introduction]) ).
fof(f62,definition,
! [X1,X2] :
( ? [X5] :
( aElement0(X5)
& ( X1 = X5
| ( ( aReductOfIn0(X5,X1,xR)
| ? [X6] :
( aElement0(X6)
& aReductOfIn0(X6,X1,xR)
& sdtmndtplgtdt0(X6,xR,X5) ) )
& sdtmndtplgtdt0(X1,xR,X5) ) )
& sdtmndtasgtdt0(X1,xR,X5)
& sP5(X5,X2)
& sdtmndtasgtdt0(X2,xR,X5) )
| ~ sP6(X1,X2) ),
introduced(definition,[new_symbols(definition,[sP6])],[predicate_definition_introduction]) ).
fof(f63,definition,
! [X2,X0] :
( ( X0 != X2
& ~ aReductOfIn0(X2,X0,xR)
& ! [X4] :
( ~ aElement0(X4)
| ~ aReductOfIn0(X4,X0,xR)
| ~ sdtmndtplgtdt0(X4,xR,X2) )
& ~ sdtmndtplgtdt0(X0,xR,X2)
& ~ sdtmndtasgtdt0(X0,xR,X2) )
| ~ sP7(X2,X0) ),
introduced(definition,[new_symbols(definition,[sP7])],[predicate_definition_introduction]) ).
fof(f64,plain,
! [X0,X1,X2] :
( sP6(X1,X2)
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ( X0 != X1
& ~ aReductOfIn0(X1,X0,xR)
& ! [X3] :
( ~ aElement0(X3)
| ~ aReductOfIn0(X3,X0,xR)
| ~ sdtmndtplgtdt0(X3,xR,X1) )
& ~ sdtmndtplgtdt0(X0,xR,X1)
& ~ sdtmndtasgtdt0(X0,xR,X1) )
| sP7(X2,X0) ),
inference(definition_folding,[],[f50,f63,f62,f61]) ).
fof(f65,definition,
! [X5,X2] :
( ( X2 != X5
& ~ aReductOfIn0(X5,X2,xR)
& ! [X7] :
( ~ aElement0(X7)
| ~ aReductOfIn0(X7,X2,xR)
| ~ sdtmndtplgtdt0(X7,xR,X5) )
& ~ sdtmndtplgtdt0(X2,xR,X5)
& ~ sdtmndtasgtdt0(X2,xR,X5) )
| ~ sP8(X5,X2) ),
introduced(definition,[new_symbols(definition,[sP8])],[predicate_definition_introduction]) ).
fof(f66,plain,
( ? [X0,X1,X2] :
( ! [X5] :
( ~ aElement0(X5)
| ( X1 != X5
& ~ aReductOfIn0(X5,X1,xR)
& ! [X6] :
( ~ aElement0(X6)
| ~ aReductOfIn0(X6,X1,xR)
| ~ sdtmndtplgtdt0(X6,xR,X5) )
& ~ sdtmndtplgtdt0(X1,xR,X5)
& ~ sdtmndtasgtdt0(X1,xR,X5) )
| sP8(X5,X2) )
& aElement0(X0)
& aElement0(X1)
& aElement0(X2)
& ( X0 = X1
| ( ( aReductOfIn0(X1,X0,xR)
| ? [X3] :
( aElement0(X3)
& aReductOfIn0(X3,X0,xR)
& sdtmndtplgtdt0(X3,xR,X1) ) )
& sdtmndtplgtdt0(X0,xR,X1) ) )
& sdtmndtasgtdt0(X0,xR,X1)
& ( X0 = X2
| ( ( aReductOfIn0(X2,X0,xR)
| ? [X4] :
( aElement0(X4)
& aReductOfIn0(X4,X0,xR)
& sdtmndtplgtdt0(X4,xR,X2) ) )
& sdtmndtplgtdt0(X0,xR,X2) ) )
& sdtmndtasgtdt0(X0,xR,X2) )
& ~ isConfluent0(xR) ),
inference(definition_folding,[],[f52,f65]) ).
fof(f73,plain,
! [X0] :
( ( ( isConfluent0(X0)
| ~ sP0(X0) )
& ( sP0(X0)
| ~ isConfluent0(X0) ) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f54]) ).
fof(f74,plain,
! [X0] :
( ( sP0(X0)
| ? [X1,X2,X3] :
( ! [X4] :
( ~ aElement0(X4)
| ~ sdtmndtasgtdt0(X2,X0,X4)
| ~ sdtmndtasgtdt0(X3,X0,X4) )
& aElement0(X1)
& aElement0(X2)
& aElement0(X3)
& sdtmndtasgtdt0(X1,X0,X2)
& sdtmndtasgtdt0(X1,X0,X3) ) )
& ( ! [X1,X2,X3] :
( ? [X4] :
( aElement0(X4)
& sdtmndtasgtdt0(X2,X0,X4)
& sdtmndtasgtdt0(X3,X0,X4) )
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3)
| ~ sdtmndtasgtdt0(X1,X0,X2)
| ~ sdtmndtasgtdt0(X1,X0,X3) )
| ~ sP0(X0) ) ),
inference(nnf_transformation,[],[f53]) ).
fof(f75,plain,
! [X0] :
( ( sP0(X0)
| ? [X1,X2,X3] :
( ! [X4] :
( ~ aElement0(X4)
| ~ sdtmndtasgtdt0(X2,X0,X4)
| ~ sdtmndtasgtdt0(X3,X0,X4) )
& aElement0(X1)
& aElement0(X2)
& aElement0(X3)
& sdtmndtasgtdt0(X1,X0,X2)
& sdtmndtasgtdt0(X1,X0,X3) ) )
& ( ! [X5,X6,X7] :
( ? [X8] :
( aElement0(X8)
& sdtmndtasgtdt0(X6,X0,X8)
& sdtmndtasgtdt0(X7,X0,X8) )
| ~ aElement0(X5)
| ~ aElement0(X6)
| ~ aElement0(X7)
| ~ sdtmndtasgtdt0(X5,X0,X6)
| ~ sdtmndtasgtdt0(X5,X0,X7) )
| ~ sP0(X0) ) ),
inference(rectify,[],[f74]) ).
fof(f76,plain,
! [X0] :
( ( sP0(X0)
| ( ! [X4] :
( ~ aElement0(X4)
| ~ sdtmndtasgtdt0(sK11(X0),X0,X4)
| ~ sdtmndtasgtdt0(sK12(X0),X0,X4) )
& aElement0(sK10(X0))
& aElement0(sK11(X0))
& aElement0(sK12(X0))
& sdtmndtasgtdt0(sK10(X0),X0,sK11(X0))
& sdtmndtasgtdt0(sK10(X0),X0,sK12(X0)) ) )
& ( ! [X5,X6,X7] :
( ( aElement0(sK13(X0,X6,X7))
& sdtmndtasgtdt0(X6,X0,sK13(X0,X6,X7))
& sdtmndtasgtdt0(X7,X0,sK13(X0,X6,X7)) )
| ~ aElement0(X5)
| ~ aElement0(X6)
| ~ aElement0(X7)
| ~ sdtmndtasgtdt0(X5,X0,X6)
| ~ sdtmndtasgtdt0(X5,X0,X7) )
| ~ sP0(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13]),skolemize(X1,sK10(X0)),skolemize(X2,sK11(X0)),skolemize(X3,sK12(X0)),skolemize(X8,sK13(X0,X6,X7))],[f75]) ).
fof(f94,plain,
! [X2,X0] :
( ( X0 != X2
& ~ aReductOfIn0(X2,X0,xR)
& ! [X4] :
( ~ aElement0(X4)
| ~ aReductOfIn0(X4,X0,xR)
| ~ sdtmndtplgtdt0(X4,xR,X2) )
& ~ sdtmndtplgtdt0(X0,xR,X2)
& ~ sdtmndtasgtdt0(X0,xR,X2) )
| ~ sP7(X2,X0) ),
inference(nnf_transformation,[],[f63]) ).
fof(f95,plain,
! [X0,X1] :
( ( X0 != X1
& ~ aReductOfIn0(X0,X1,xR)
& ! [X2] :
( ~ aElement0(X2)
| ~ aReductOfIn0(X2,X1,xR)
| ~ sdtmndtplgtdt0(X2,xR,X0) )
& ~ sdtmndtplgtdt0(X1,xR,X0)
& ~ sdtmndtasgtdt0(X1,xR,X0) )
| ~ sP7(X0,X1) ),
inference(rectify,[],[f94]) ).
fof(f96,plain,
! [X1,X2] :
( ? [X5] :
( aElement0(X5)
& ( X1 = X5
| ( ( aReductOfIn0(X5,X1,xR)
| ? [X6] :
( aElement0(X6)
& aReductOfIn0(X6,X1,xR)
& sdtmndtplgtdt0(X6,xR,X5) ) )
& sdtmndtplgtdt0(X1,xR,X5) ) )
& sdtmndtasgtdt0(X1,xR,X5)
& sP5(X5,X2)
& sdtmndtasgtdt0(X2,xR,X5) )
| ~ sP6(X1,X2) ),
inference(nnf_transformation,[],[f62]) ).
fof(f97,plain,
! [X0,X1] :
( ? [X2] :
( aElement0(X2)
& ( X0 = X2
| ( ( aReductOfIn0(X2,X0,xR)
| ? [X3] :
( aElement0(X3)
& aReductOfIn0(X3,X0,xR)
& sdtmndtplgtdt0(X3,xR,X2) ) )
& sdtmndtplgtdt0(X0,xR,X2) ) )
& sdtmndtasgtdt0(X0,xR,X2)
& sP5(X2,X1)
& sdtmndtasgtdt0(X1,xR,X2) )
| ~ sP6(X0,X1) ),
inference(rectify,[],[f96]) ).
fof(f98,plain,
! [X0,X1] :
( ( aElement0(sK25(X0,X1))
& ( sK25(X0,X1) = X0
| ( ( aReductOfIn0(sK25(X0,X1),X0,xR)
| ( aElement0(sK26(X0,X1))
& aReductOfIn0(sK26(X0,X1),X0,xR)
& sdtmndtplgtdt0(sK26(X0,X1),xR,sK25(X0,X1)) ) )
& sdtmndtplgtdt0(X0,xR,sK25(X0,X1)) ) )
& sdtmndtasgtdt0(X0,xR,sK25(X0,X1))
& sP5(sK25(X0,X1),X1)
& sdtmndtasgtdt0(X1,xR,sK25(X0,X1)) )
| ~ sP6(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25,sK26]),skolemize(X2,sK25(X0,X1)),skolemize(X3,sK26(X0,X1))],[f97]) ).
fof(f104,plain,
( ? [X0,X1,X2] :
( ! [X3] :
( ~ aElement0(X3)
| ( X1 != X3
& ~ aReductOfIn0(X3,X1,xR)
& ! [X4] :
( ~ aElement0(X4)
| ~ aReductOfIn0(X4,X1,xR)
| ~ sdtmndtplgtdt0(X4,xR,X3) )
& ~ sdtmndtplgtdt0(X1,xR,X3)
& ~ sdtmndtasgtdt0(X1,xR,X3) )
| sP8(X3,X2) )
& aElement0(X0)
& aElement0(X1)
& aElement0(X2)
& ( X0 = X1
| ( ( aReductOfIn0(X1,X0,xR)
| ? [X5] :
( aElement0(X5)
& aReductOfIn0(X5,X0,xR)
& sdtmndtplgtdt0(X5,xR,X1) ) )
& sdtmndtplgtdt0(X0,xR,X1) ) )
& sdtmndtasgtdt0(X0,xR,X1)
& ( X0 = X2
| ( ( aReductOfIn0(X2,X0,xR)
| ? [X6] :
( aElement0(X6)
& aReductOfIn0(X6,X0,xR)
& sdtmndtplgtdt0(X6,xR,X2) ) )
& sdtmndtplgtdt0(X0,xR,X2) ) )
& sdtmndtasgtdt0(X0,xR,X2) )
& ~ isConfluent0(xR) ),
inference(rectify,[],[f66]) ).
fof(f105,plain,
( ! [X3] :
( ~ aElement0(X3)
| ( sK29 != X3
& ~ aReductOfIn0(X3,sK29,xR)
& ! [X4] :
( ~ aElement0(X4)
| ~ aReductOfIn0(X4,sK29,xR)
| ~ sdtmndtplgtdt0(X4,xR,X3) )
& ~ sdtmndtplgtdt0(sK29,xR,X3)
& ~ sdtmndtasgtdt0(sK29,xR,X3) )
| sP8(X3,sK30) )
& aElement0(sK28)
& aElement0(sK29)
& aElement0(sK30)
& ( sK28 = sK29
| ( ( aReductOfIn0(sK29,sK28,xR)
| ( aElement0(sK31)
& aReductOfIn0(sK31,sK28,xR)
& sdtmndtplgtdt0(sK31,xR,sK29) ) )
& sdtmndtplgtdt0(sK28,xR,sK29) ) )
& sdtmndtasgtdt0(sK28,xR,sK29)
& ( sK28 = sK30
| ( ( aReductOfIn0(sK30,sK28,xR)
| ( aElement0(sK32)
& aReductOfIn0(sK32,sK28,xR)
& sdtmndtplgtdt0(sK32,xR,sK30) ) )
& sdtmndtplgtdt0(sK28,xR,sK30) ) )
& sdtmndtasgtdt0(sK28,xR,sK30)
& ~ isConfluent0(xR) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28,sK29,sK30,sK31,sK32]),skolemize(X0,sK28),skolemize(X1,sK29),skolemize(X2,sK30),skolemize(X5,sK31),skolemize(X6,sK32)],[f104]) ).
fof(f118,plain,
! [X0] :
( ~ sP1(X0)
| ~ sP0(X0)
| isConfluent0(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f122,plain,
! [X0] :
( sdtmndtasgtdt0(sK10(X0),X0,sK12(X0))
| sP0(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f123,plain,
! [X0] :
( sdtmndtasgtdt0(sK10(X0),X0,sK11(X0))
| sP0(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f124,plain,
! [X0] :
( aElement0(sK12(X0))
| sP0(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f125,plain,
! [X0] :
( aElement0(sK11(X0))
| sP0(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f126,plain,
! [X0] :
( aElement0(sK10(X0))
| sP0(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f127,plain,
! [X0,X4] :
( ~ sdtmndtasgtdt0(sK12(X0),X0,X4)
| ~ aElement0(X4)
| ~ sdtmndtasgtdt0(sK11(X0),X0,X4)
| sP0(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f128,plain,
! [X0] :
( ~ aRewritingSystem0(X0)
| sP1(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f151,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[],[f15]) ).
fof(f169,plain,
! [X0,X1] :
( ~ sdtmndtasgtdt0(X1,xR,X0)
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f174,plain,
! [X0,X1] :
( sdtmndtasgtdt0(X1,xR,sK25(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f176,plain,
! [X0,X1] :
( sdtmndtasgtdt0(X0,xR,sK25(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f181,plain,
! [X0,X1] :
( aElement0(sK25(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f186,plain,
! [X2,X0,X1] :
( ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2)
| sP6(X1,X2)
| sP7(X2,X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f196,plain,
~ isConfluent0(xR),
inference(cnf_transformation,[],[f105]) ).
fof(f310,plain,
sP1(xR),
inference(resolution,[],[f128,f151]) ).
fof(f313,plain,
( ~ sP0(xR)
| isConfluent0(xR) ),
inference(resolution,[],[f118,f310]) ).
fof(f314,plain,
~ sP0(xR),
inference(forward_subsumption_resolution,[],[f313,f196]) ).
fof(f344,plain,
( sP0(xR)
| ~ sP7(sK11(xR),sK10(xR)) ),
inference(resolution,[],[f123,f169]) ).
fof(f345,plain,
~ sP7(sK11(xR),sK10(xR)),
inference(forward_subsumption_resolution,[],[f344,f314]) ).
fof(f389,definition,
( spl33_19
<=> aElement0(sK11(xR)) ),
introduced(definition,[new_symbols(definition,[spl33_19])],[avatar_definition]) ).
fof(f390,plain,
( aElement0(sK11(xR))
| ~ spl33_19 ),
inference(avatar_component_clause,[],[f389]) ).
fof(f391,plain,
( ~ aElement0(sK11(xR))
| spl33_19 ),
inference(avatar_component_clause,[],[f389]) ).
fof(f412,plain,
( sP0(xR)
| spl33_19 ),
inference(resolution,[],[f391,f125]) ).
fof(f413,plain,
( $false
| spl33_19 ),
inference(forward_subsumption_resolution,[],[f412,f314]) ).
fof(f414,plain,
spl33_19,
inference(avatar_contradiction_clause,[],[f413]) ).
fof(f473,plain,
! [X0] :
( ~ aElement0(sK25(sK12(xR),X0))
| ~ sdtmndtasgtdt0(sK11(xR),xR,sK25(sK12(xR),X0))
| sP0(xR)
| ~ sP6(sK12(xR),X0) ),
inference(resolution,[],[f127,f176]) ).
fof(f475,plain,
! [X0] :
( ~ aElement0(sK25(sK12(xR),X0))
| ~ sdtmndtasgtdt0(sK11(xR),xR,sK25(sK12(xR),X0))
| ~ sP6(sK12(xR),X0) ),
inference(forward_subsumption_resolution,[],[f473,f314]) ).
fof(f478,plain,
! [X0] :
( ~ sdtmndtasgtdt0(sK11(xR),xR,sK25(sK12(xR),X0))
| ~ sP6(sK12(xR),X0) ),
inference(forward_subsumption_resolution,[],[f475,f181]) ).
fof(f554,plain,
( ~ sP6(sK12(xR),sK11(xR))
| ~ sP6(sK12(xR),sK11(xR)) ),
inference(resolution,[],[f478,f174]) ).
fof(f555,plain,
~ sP6(sK12(xR),sK11(xR)),
inference(duplicate_literal_removal,[],[f554]) ).
fof(f558,plain,
! [X0] :
( ~ aElement0(sK10(xR))
| ~ aElement0(sK12(xR))
| ~ aElement0(X0)
| sP6(sK12(xR),X0)
| sP7(X0,sK10(xR))
| sP0(xR) ),
inference(resolution,[],[f186,f122]) ).
fof(f567,plain,
! [X0] :
( ~ aElement0(sK12(xR))
| ~ aElement0(X0)
| sP6(sK12(xR),X0)
| sP7(X0,sK10(xR))
| sP0(xR) ),
inference(forward_subsumption_resolution,[],[f558,f126]) ).
fof(f571,plain,
! [X0] :
( ~ aElement0(X0)
| sP6(sK12(xR),X0)
| sP7(X0,sK10(xR))
| sP0(xR) ),
inference(forward_subsumption_resolution,[],[f567,f124]) ).
fof(f575,plain,
! [X0] :
( sP7(X0,sK10(xR))
| sP6(sK12(xR),X0)
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[],[f571,f314]) ).
fof(f848,plain,
( sP6(sK12(xR),sK11(xR))
| ~ aElement0(sK11(xR)) ),
inference(resolution,[],[f575,f345]) ).
fof(f851,plain,
~ aElement0(sK11(xR)),
inference(forward_subsumption_resolution,[],[f848,f555]) ).
fof(f853,plain,
( $false
| ~ spl33_19 ),
inference(forward_subsumption_resolution,[],[f851,f390]) ).
fof(f854,plain,
~ spl33_19,
inference(avatar_contradiction_clause,[],[f853]) ).
cnf(s17,plain,
spl33_19,
inference(sat_conversion,[],[f414]) ).
cnf(s20,plain,
~ spl33_19,
inference(sat_conversion,[],[f854]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s17,s20]) ).
fof(f855,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM023+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 % Computer : n010.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Mon Sep 28 21:49:33 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.29 % (2390839)Will run a generic schedule for satisfiability detection.
% 0.17/0.29 % (2390845)% WARNING: option uhcvi not known.
% 0.17/0.29 % (2390845)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=950489206:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.29 % (2390846)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=276750327:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.29 % (2390844)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2775033439_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.29 % (2390848)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=184395349:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.29 % (2390847)dis+10_1_sil=32000:sp=arity:random_seed=3137233406:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.29 % (2390850)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=714823586:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.29 % (2390849)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2694763813:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.29 % TRYING [1]
% 0.17/0.29 % TRYING [2]
% 0.17/0.29 % TRYING [3]
% 0.17/0.29 % (2390847) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2390839-2390847"...
% 0.17/0.29 % TRYING [4]
% 0.17/0.29 % (2390847)...printing done.
% 0.17/0.29 % (2390850) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2390839-2390850"...
% 0.17/0.29 % (2390847)Refutation found. Thanks to Tanya!
% 0.17/0.29 % SZS status Theorem for theBenchmark
% 0.17/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.29 % (2390847)------------------------------
% 0.17/0.29 % (2390847)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.29 % (2390847)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.29 % (2390847)CaDiCaL version: 2.1.3
% 0.17/0.29 % (2390847)Termination reason: Refutation
% 0.17/0.29 % (2390847)Time elapsed: 0.018 s
% 0.17/0.29 % (2390847)Peak memory usage: 12 MB
% 0.17/0.29 % (2390847)Instructions burned: 26 (million)
% 0.17/0.29 % (2390839)Success in time 0.056 s
% 0.17/0.29 % Vampire exiting
%------------------------------------------------------------------------------