%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n013.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 09:39:26 AM UTC 2026
% Result : Theorem 0.67s 0.97s
% Output : Refutation 2.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 66 ( 9 unt; 6 def)
% Number of atoms : 651 ( 55 equ)
% Maximal formula atoms : 33 ( 9 avg)
% Number of connectives : 819 ( 234 ~; 261 |; 312 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 9 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 194 ( 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(f21,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(f22,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(f29,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,[],[f21]) ).
fof(f30,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,[],[f29]) ).
fof(f31,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,[],[f22]) ).
fof(f32,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,[],[f31]) ).
fof(f47,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(f48,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,[],[f47]) ).
fof(f51,definition,
! [X5,X2] :
( X2 = X5
| ( ( aReductOfIn0(X5,X2,xR)
| ? [X7] :
( aElement0(X7)
& aReductOfIn0(X7,X2,xR)
& sdtmndtplgtdt0(X7,xR,X5) ) )
& sdtmndtplgtdt0(X2,xR,X5) )
| ~ sP1(X5,X2) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f52,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)
& sP1(X5,X2)
& sdtmndtasgtdt0(X2,xR,X5) )
| ~ sP2(X1,X2) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f53,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) )
| ~ sP3(X2,X0) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f54,plain,
! [X0,X1,X2] :
( sP2(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) )
| sP3(X2,X0) ),
inference(definition_folding,[],[f30,f53,f52,f51]) ).
fof(f55,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) )
| ~ sP4(X5,X2) ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
fof(f56,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) )
| sP4(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,[],[f32,f55]) ).
fof(f60,definition,
! [X0] :
( sP7(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,[sP7])],[predicate_definition_introduction]) ).
fof(f61,definition,
! [X0] :
( ( isConfluent0(X0)
<=> sP7(X0) )
| ~ sP8(X0) ),
introduced(definition,[new_symbols(definition,[sP8])],[predicate_definition_introduction]) ).
fof(f62,plain,
! [X0] :
( sP8(X0)
| ~ aRewritingSystem0(X0) ),
inference(definition_folding,[],[f48,f61,f60]) ).
fof(f68,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) )
| ~ sP3(X2,X0) ),
inference(nnf_transformation,[],[f53]) ).
fof(f69,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) )
| ~ sP3(X0,X1) ),
inference(rectify,[],[f68]) ).
fof(f70,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)
& sP1(X5,X2)
& sdtmndtasgtdt0(X2,xR,X5) )
| ~ sP2(X1,X2) ),
inference(nnf_transformation,[],[f52]) ).
fof(f71,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)
& sP1(X2,X1)
& sdtmndtasgtdt0(X1,xR,X2) )
| ~ sP2(X0,X1) ),
inference(rectify,[],[f70]) ).
fof(f72,plain,
! [X0,X1] :
( ( aElement0(sK12(X0,X1))
& ( sK12(X0,X1) = X0
| ( ( aReductOfIn0(sK12(X0,X1),X0,xR)
| ( aElement0(sK13(X0,X1))
& aReductOfIn0(sK13(X0,X1),X0,xR)
& sdtmndtplgtdt0(sK13(X0,X1),xR,sK12(X0,X1)) ) )
& sdtmndtplgtdt0(X0,xR,sK12(X0,X1)) ) )
& sdtmndtasgtdt0(X0,xR,sK12(X0,X1))
& sP1(sK12(X0,X1),X1)
& sdtmndtasgtdt0(X1,xR,sK12(X0,X1)) )
| ~ sP2(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X2,sK12(X0,X1)),skolemize(X3,sK13(X0,X1))],[f71]) ).
fof(f78,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) )
| sP4(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,[],[f56]) ).
fof(f79,plain,
( ! [X3] :
( ~ aElement0(X3)
| ( sK16 != X3
& ~ aReductOfIn0(X3,sK16,xR)
& ! [X4] :
( ~ aElement0(X4)
| ~ aReductOfIn0(X4,sK16,xR)
| ~ sdtmndtplgtdt0(X4,xR,X3) )
& ~ sdtmndtplgtdt0(sK16,xR,X3)
& ~ sdtmndtasgtdt0(sK16,xR,X3) )
| sP4(X3,sK17) )
& aElement0(sK15)
& aElement0(sK16)
& aElement0(sK17)
& ( sK15 = sK16
| ( ( aReductOfIn0(sK16,sK15,xR)
| ( aElement0(sK18)
& aReductOfIn0(sK18,sK15,xR)
& sdtmndtplgtdt0(sK18,xR,sK16) ) )
& sdtmndtplgtdt0(sK15,xR,sK16) ) )
& sdtmndtasgtdt0(sK15,xR,sK16)
& ( sK15 = sK17
| ( ( aReductOfIn0(sK17,sK15,xR)
| ( aElement0(sK19)
& aReductOfIn0(sK19,sK15,xR)
& sdtmndtplgtdt0(sK19,xR,sK17) ) )
& sdtmndtplgtdt0(sK15,xR,sK17) ) )
& sdtmndtasgtdt0(sK15,xR,sK17)
& ~ isConfluent0(xR) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16,sK17,sK18,sK19]),skolemize(X0,sK15),skolemize(X1,sK16),skolemize(X2,sK17),skolemize(X5,sK18),skolemize(X6,sK19)],[f78]) ).
fof(f93,plain,
! [X0] :
( ( ( isConfluent0(X0)
| ~ sP7(X0) )
& ( sP7(X0)
| ~ isConfluent0(X0) ) )
| ~ sP8(X0) ),
inference(nnf_transformation,[],[f61]) ).
fof(f94,plain,
! [X0] :
( ( sP7(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) )
| ~ sP7(X0) ) ),
inference(nnf_transformation,[],[f60]) ).
fof(f95,plain,
! [X0] :
( ( sP7(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) )
| ~ sP7(X0) ) ),
inference(rectify,[],[f94]) ).
fof(f96,plain,
! [X0] :
( ( sP7(X0)
| ( ! [X4] :
( ~ aElement0(X4)
| ~ sdtmndtasgtdt0(sK28(X0),X0,X4)
| ~ sdtmndtasgtdt0(sK29(X0),X0,X4) )
& aElement0(sK27(X0))
& aElement0(sK28(X0))
& aElement0(sK29(X0))
& sdtmndtasgtdt0(sK27(X0),X0,sK28(X0))
& sdtmndtasgtdt0(sK27(X0),X0,sK29(X0)) ) )
& ( ! [X5,X6,X7] :
( ( aElement0(sK30(X0,X6,X7))
& sdtmndtasgtdt0(X6,X0,sK30(X0,X6,X7))
& sdtmndtasgtdt0(X7,X0,sK30(X0,X6,X7)) )
| ~ aElement0(X5)
| ~ aElement0(X6)
| ~ aElement0(X7)
| ~ sdtmndtasgtdt0(X5,X0,X6)
| ~ sdtmndtasgtdt0(X5,X0,X7) )
| ~ sP7(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27,sK28,sK29,sK30]),skolemize(X1,sK27(X0)),skolemize(X2,sK28(X0)),skolemize(X3,sK29(X0)),skolemize(X8,sK30(X0,X6,X7))],[f95]) ).
fof(f97,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[],[f15]) ).
fof(f115,plain,
! [X0,X1] :
( ~ sdtmndtasgtdt0(X1,xR,X0)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f120,plain,
! [X0,X1] :
( sdtmndtasgtdt0(X1,xR,sK12(X0,X1))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f122,plain,
! [X0,X1] :
( sdtmndtasgtdt0(X0,xR,sK12(X0,X1))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f127,plain,
! [X0,X1] :
( aElement0(sK12(X0,X1))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f132,plain,
! [X2,X0,X1] :
( ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2)
| sP2(X1,X2)
| sP3(X2,X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f142,plain,
~ isConfluent0(xR),
inference(cnf_transformation,[],[f79]) ).
fof(f190,plain,
! [X0] :
( isConfluent0(X0)
| ~ sP7(X0)
| ~ sP8(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f194,plain,
! [X0] :
( sdtmndtasgtdt0(sK27(X0),X0,sK29(X0))
| sP7(X0) ),
inference(cnf_transformation,[],[f96]) ).
fof(f195,plain,
! [X0] :
( sdtmndtasgtdt0(sK27(X0),X0,sK28(X0))
| sP7(X0) ),
inference(cnf_transformation,[],[f96]) ).
fof(f196,plain,
! [X0] :
( aElement0(sK29(X0))
| sP7(X0) ),
inference(cnf_transformation,[],[f96]) ).
fof(f197,plain,
! [X0] :
( aElement0(sK28(X0))
| sP7(X0) ),
inference(cnf_transformation,[],[f96]) ).
fof(f198,plain,
! [X0] :
( aElement0(sK27(X0))
| sP7(X0) ),
inference(cnf_transformation,[],[f96]) ).
fof(f199,plain,
! [X0,X4] :
( ~ sdtmndtasgtdt0(sK29(X0),X0,X4)
| ~ aElement0(X4)
| ~ sdtmndtasgtdt0(sK28(X0),X0,X4)
| sP7(X0) ),
inference(cnf_transformation,[],[f96]) ).
fof(f200,plain,
! [X0] :
( sP8(X0)
| ~ aRewritingSystem0(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f217,plain,
( ~ sP8(xR)
| ~ sP7(xR) ),
inference(resolution,[],[f190,f142]) ).
fof(f218,plain,
( ~ sP7(xR)
| ~ aRewritingSystem0(xR) ),
inference(resolution,[],[f217,f200]) ).
fof(f219,plain,
~ sP7(xR),
inference(forward_subsumption_resolution,[],[f218,f97]) ).
fof(f268,plain,
( sP7(xR)
| ~ sP3(sK28(xR),sK27(xR)) ),
inference(resolution,[],[f195,f115]) ).
fof(f269,plain,
~ sP3(sK28(xR),sK27(xR)),
inference(forward_subsumption_resolution,[],[f268,f219]) ).
fof(f491,plain,
! [X0] :
( ~ aElement0(sK12(sK29(xR),X0))
| ~ sdtmndtasgtdt0(sK28(xR),xR,sK12(sK29(xR),X0))
| sP7(xR)
| ~ sP2(sK29(xR),X0) ),
inference(resolution,[],[f199,f122]) ).
fof(f494,plain,
! [X0] :
( ~ aElement0(sK12(sK29(xR),X0))
| ~ sdtmndtasgtdt0(sK28(xR),xR,sK12(sK29(xR),X0))
| ~ sP2(sK29(xR),X0) ),
inference(forward_subsumption_resolution,[],[f491,f219]) ).
fof(f498,plain,
! [X0] :
( ~ sdtmndtasgtdt0(sK28(xR),xR,sK12(sK29(xR),X0))
| ~ sP2(sK29(xR),X0) ),
inference(forward_subsumption_resolution,[],[f494,f127]) ).
fof(f500,plain,
( ~ sP2(sK29(xR),sK28(xR))
| ~ sP2(sK29(xR),sK28(xR)) ),
inference(resolution,[],[f498,f120]) ).
fof(f502,plain,
~ sP2(sK29(xR),sK28(xR)),
inference(duplicate_literal_removal,[],[f500]) ).
fof(f526,plain,
! [X0] :
( ~ aElement0(sK27(xR))
| ~ aElement0(sK29(xR))
| ~ aElement0(X0)
| sP2(sK29(xR),X0)
| sP3(X0,sK27(xR))
| sP7(xR) ),
inference(resolution,[],[f132,f194]) ).
fof(f538,plain,
! [X0] :
( ~ aElement0(sK29(xR))
| ~ aElement0(X0)
| sP2(sK29(xR),X0)
| sP3(X0,sK27(xR))
| sP7(xR) ),
inference(forward_subsumption_resolution,[],[f526,f198]) ).
fof(f542,plain,
! [X0] :
( ~ aElement0(X0)
| sP2(sK29(xR),X0)
| sP3(X0,sK27(xR))
| sP7(xR) ),
inference(forward_subsumption_resolution,[],[f538,f196]) ).
fof(f546,plain,
! [X0] :
( sP3(X0,sK27(xR))
| sP2(sK29(xR),X0)
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[],[f542,f219]) ).
fof(f730,plain,
( sP2(sK29(xR),sK28(xR))
| ~ aElement0(sK28(xR)) ),
inference(resolution,[],[f546,f269]) ).
fof(f732,plain,
~ aElement0(sK28(xR)),
inference(forward_subsumption_resolution,[],[f730,f502]) ).
fof(f733,plain,
sP7(xR),
inference(resolution,[],[f732,f197]) ).
fof(f734,plain,
$false,
inference(forward_subsumption_resolution,[],[f733,f219]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM023+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n013.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Mon Sep 28 21:48:21 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running first-order theorem proving
% 0.10/0.23 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.67/0.97 % (1615412)Detected formulas, will run a generic FOF schedule.
% 0.67/0.97 % (1615421)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1195579716:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.67/0.97 % (1615421)First to succeed.
% 0.67/0.97 % (1615421)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1615412"
% 0.67/0.97 % (1615420)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2626013883:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.67/0.97 % (1615417)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1427951465:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.67/0.97 % (1615419)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3116389172:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.67/0.97 % (1615418)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3896581254:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.67/0.97 % (1615423)dis-21_1_sil=8000:lcm=predicate:random_seed=2986757967:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 0.67/0.97 % (1615422)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=145562090:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.67/0.97 % (1615420)Instruction limit reached!
% 0.67/0.97 % (1615420)------------------------------
% 0.67/0.97 % (1615420)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.67/0.97 % (1615420)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.97 % (1615420)CaDiCaL version: 2.1.3
% 0.67/0.97 % (1615420)Termination reason: Instruction limit
% 0.67/0.97 % (1615420)Termination phase: Saturation
% 0.67/0.97 % (1615420)Time elapsed: 0.066 s
% 0.67/0.97 % (1615420)Peak memory usage: 89 MB
% 0.67/0.97 % (1615420)Instructions burned: 110 (million)
% 0.67/0.97 % (1615423)Instruction limit reached!
% 0.67/0.97 % (1615423)------------------------------
% 0.67/0.97 % (1615423)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.67/0.97 % (1615423)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.97 % (1615423)CaDiCaL version: 2.1.3
% 0.67/0.97 % (1615423)Termination reason: Instruction limit
% 0.67/0.97 % (1615423)Termination phase: Saturation
% 0.67/0.97 % (1615423)Time elapsed: 0.079 s
% 0.67/0.97 % (1615423)Peak memory usage: 91 MB
% 0.67/0.97 % (1615423)Instructions burned: 129 (million)
% 0.67/0.97 % (1615422)Instruction limit reached!
% 0.67/0.97 % (1615422)------------------------------
% 0.67/0.97 % (1615422)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.67/0.97 % (1615422)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.97 % (1615422)CaDiCaL version: 2.1.3
% 0.67/0.97 % (1615422)Termination reason: Instruction limit
% 0.67/0.97 % (1615422)Termination phase: Saturation
% 0.67/0.97 % (1615422)Time elapsed: 0.098 s
% 0.67/0.97 % (1615422)Peak memory usage: 90 MB
% 0.67/0.97 % (1615422)Instructions burned: 139 (million)
% 0.67/0.97 % (1615421)Refutation found. Thanks to Tanya!
% 0.67/0.97 % SZS status Theorem for theBenchmark
% 0.67/0.97 % SZS output start Proof for theBenchmark
% See solution above
% 2.80/1.16 % (1615421)------------------------------
% 2.80/1.16 % (1615421)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.16 % (1615421)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.16 % (1615421)CaDiCaL version: 2.1.3
% 2.80/1.16 % (1615421)Termination reason: Refutation
% 2.80/1.16 % (1615421)Time elapsed: 0.008 s
% 2.80/1.16 % (1615421)Peak memory usage: 88 MB
% 2.80/1.16 % (1615421)Instructions burned: 23 (million)
% 2.80/1.16 % (1615421)------------------------------
% 2.80/1.16 % (1615421)------------------------------
% 2.80/1.16 % (1615412)Success in time 0.299 s
% 2.80/1.16 % Vampire exiting
%------------------------------------------------------------------------------