%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COM019+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 : n003.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 09:39:24 AM UTC 2026
% Result : Theorem 6.84s 1.85s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 16
% Syntax : Number of formulae : 113 ( 22 unt; 5 def)
% Number of atoms : 857 ( 71 equ)
% Maximal formula atoms : 33 ( 7 avg)
% Number of connectives : 1067 ( 323 ~; 381 |; 342 &)
% ( 7 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 2 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 12 con; 0-3 aty)
% Number of variables : 240 ( 0 sgn 180 !; 60 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1,X2] :
( ( aElement0(X0)
& aRewritingSystem0(X1)
& aElement0(X2) )
=> ( sdtmndtplgtdt0(X0,X1,X2)
<=> ( aReductOfIn0(X2,X0,X1)
| ? [X3] :
( aElement0(X3)
& aReductOfIn0(X3,X0,X1)
& sdtmndtplgtdt0(X3,X1,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTCDef) ).
fof(f8,axiom,
! [X0,X1,X2] :
( ( aElement0(X0)
& aRewritingSystem0(X1)
& aElement0(X2) )
=> ( sdtmndtasgtdt0(X0,X1,X2)
<=> ( X0 = X2
| sdtmndtplgtdt0(X0,X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTCRDef) ).
fof(f9,axiom,
! [X0,X1,X2,X3] :
( ( aElement0(X0)
& aRewritingSystem0(X1)
& aElement0(X2)
& aElement0(X3) )
=> ( ( sdtmndtasgtdt0(X0,X1,X2)
& sdtmndtasgtdt0(X2,X1,X3) )
=> sdtmndtasgtdt0(X0,X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTCRTrans) ).
fof(f15,axiom,
aRewritingSystem0(xR),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656) ).
fof(f16,axiom,
( ! [X0,X1,X2] :
( ( aElement0(X0)
& aElement0(X1)
& aElement0(X2)
& aReductOfIn0(X1,X0,xR)
& aReductOfIn0(X2,X0,xR) )
=> ? [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) ) )
& isLocallyConfluent0(xR)
& ! [X0,X1] :
( ( aElement0(X0)
& aElement0(X1) )
=> ( ( aReductOfIn0(X1,X0,xR)
| ? [X2] :
( aElement0(X2)
& aReductOfIn0(X2,X0,xR)
& sdtmndtplgtdt0(X2,xR,X1) )
| sdtmndtplgtdt0(X0,xR,X1) )
=> iLess0(X1,X0) ) )
& isTerminating0(xR) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656_01) ).
fof(f17,axiom,
( aElement0(xa)
& aElement0(xb)
& aElement0(xc) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__731) ).
fof(f18,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) ) )
=> ( iLess0(X0,xa)
=> ? [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(f20,axiom,
( aElement0(xu)
& aReductOfIn0(xu,xa,xR)
& ( xu = xb
| ( ( aReductOfIn0(xb,xu,xR)
| ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xu,xR)
& sdtmndtplgtdt0(X0,xR,xb) ) )
& sdtmndtplgtdt0(xu,xR,xb) ) )
& sdtmndtasgtdt0(xu,xR,xb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__755) ).
fof(f22,axiom,
( aElement0(xw)
& ( xu = xw
| ( ( aReductOfIn0(xw,xu,xR)
| ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xu,xR)
& sdtmndtplgtdt0(X0,xR,xw) ) )
& sdtmndtplgtdt0(xu,xR,xw) ) )
& sdtmndtasgtdt0(xu,xR,xw)
& ( xv = xw
| ( ( aReductOfIn0(xw,xv,xR)
| ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xv,xR)
& sdtmndtplgtdt0(X0,xR,xw) ) )
& sdtmndtplgtdt0(xv,xR,xw) ) )
& sdtmndtasgtdt0(xv,xR,xw) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__799) ).
fof(f23,axiom,
( aElement0(xd)
& ( xw = xd
| ( ( aReductOfIn0(xd,xw,xR)
| ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xw,xR)
& sdtmndtplgtdt0(X0,xR,xd) ) )
& sdtmndtplgtdt0(xw,xR,xd) ) )
& sdtmndtasgtdt0(xw,xR,xd)
& ~ ? [X0] : aReductOfIn0(X0,xd,xR)
& aNormalFormOfIn0(xd,xw,xR) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__818) ).
fof(f24,conjecture,
( xb = xd
| aReductOfIn0(xd,xb,xR)
| ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xb,xR)
& sdtmndtplgtdt0(X0,xR,xd) )
| sdtmndtplgtdt0(xb,xR,xd)
| sdtmndtasgtdt0(xb,xR,xd) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f25,negated_conjecture,
~ ( xb = xd
| aReductOfIn0(xd,xb,xR)
| ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xb,xR)
& sdtmndtplgtdt0(X0,xR,xd) )
| sdtmndtplgtdt0(xb,xR,xd)
| sdtmndtasgtdt0(xb,xR,xd) ),
inference(negated_conjecture,[status(cth)],[f24]) ).
fof(f30,plain,
( ! [X0,X1,X2] :
( ( aElement0(X0)
& aElement0(X1)
& aElement0(X2)
& aReductOfIn0(X1,X0,xR)
& aReductOfIn0(X2,X0,xR) )
=> ? [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)
| ? [X5] :
( aElement0(X5)
& aReductOfIn0(X5,X2,xR)
& sdtmndtplgtdt0(X5,xR,X3) ) )
& sdtmndtplgtdt0(X2,xR,X3) ) )
& sdtmndtasgtdt0(X2,xR,X3) ) )
& isLocallyConfluent0(xR)
& ! [X6,X7] :
( ( aElement0(X6)
& aElement0(X7) )
=> ( ( aReductOfIn0(X7,X6,xR)
| ? [X8] :
( aElement0(X8)
& aReductOfIn0(X8,X6,xR)
& sdtmndtplgtdt0(X8,xR,X7) )
| sdtmndtplgtdt0(X6,xR,X7) )
=> iLess0(X7,X6) ) )
& isTerminating0(xR) ),
inference(rectify,[],[f16]) ).
fof(f31,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) ) )
=> ( iLess0(X0,xa)
=> ? [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,[],[f18]) ).
fof(f33,plain,
( aElement0(xw)
& ( xu = xw
| ( ( aReductOfIn0(xw,xu,xR)
| ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xu,xR)
& sdtmndtplgtdt0(X0,xR,xw) ) )
& sdtmndtplgtdt0(xu,xR,xw) ) )
& sdtmndtasgtdt0(xu,xR,xw)
& ( xv = xw
| ( ( aReductOfIn0(xw,xv,xR)
| ? [X1] :
( aElement0(X1)
& aReductOfIn0(X1,xv,xR)
& sdtmndtplgtdt0(X1,xR,xw) ) )
& sdtmndtplgtdt0(xv,xR,xw) ) )
& sdtmndtasgtdt0(xv,xR,xw) ),
inference(rectify,[],[f22]) ).
fof(f34,plain,
( aElement0(xd)
& ( xw = xd
| ( ( aReductOfIn0(xd,xw,xR)
| ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xw,xR)
& sdtmndtplgtdt0(X0,xR,xd) ) )
& sdtmndtplgtdt0(xw,xR,xd) ) )
& sdtmndtasgtdt0(xw,xR,xd)
& ~ ? [X1] : aReductOfIn0(X1,xd,xR)
& aNormalFormOfIn0(xd,xw,xR) ),
inference(rectify,[],[f23]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ( sdtmndtplgtdt0(X0,X1,X2)
<=> ( aReductOfIn0(X2,X0,X1)
| ? [X3] :
( aElement0(X3)
& aReductOfIn0(X3,X0,X1)
& sdtmndtplgtdt0(X3,X1,X2) ) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(ennf_transformation,[],[f6]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ( sdtmndtplgtdt0(X0,X1,X2)
<=> ( aReductOfIn0(X2,X0,X1)
| ? [X3] :
( aElement0(X3)
& aReductOfIn0(X3,X0,X1)
& sdtmndtplgtdt0(X3,X1,X2) ) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(flattening,[],[f37]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ( sdtmndtasgtdt0(X0,X1,X2)
<=> ( X0 = X2
| sdtmndtplgtdt0(X0,X1,X2) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(ennf_transformation,[],[f8]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ( sdtmndtasgtdt0(X0,X1,X2)
<=> ( X0 = X2
| sdtmndtplgtdt0(X0,X1,X2) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(flattening,[],[f41]) ).
fof(f43,plain,
! [X0,X1,X2,X3] :
( sdtmndtasgtdt0(X0,X1,X3)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| ~ sdtmndtasgtdt0(X2,X1,X3)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(ennf_transformation,[],[f9]) ).
fof(f44,plain,
! [X0,X1,X2,X3] :
( sdtmndtasgtdt0(X0,X1,X3)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| ~ sdtmndtasgtdt0(X2,X1,X3)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(flattening,[],[f43]) ).
fof(f55,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)
& ( X2 = X3
| ( ( aReductOfIn0(X3,X2,xR)
| ? [X5] :
( aElement0(X5)
& aReductOfIn0(X5,X2,xR)
& sdtmndtplgtdt0(X5,xR,X3) ) )
& sdtmndtplgtdt0(X2,xR,X3) ) )
& sdtmndtasgtdt0(X2,xR,X3) )
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aReductOfIn0(X1,X0,xR)
| ~ aReductOfIn0(X2,X0,xR) )
& isLocallyConfluent0(xR)
& ! [X6,X7] :
( iLess0(X7,X6)
| ( ~ aReductOfIn0(X7,X6,xR)
& ! [X8] :
( ~ aElement0(X8)
| ~ aReductOfIn0(X8,X6,xR)
| ~ sdtmndtplgtdt0(X8,xR,X7) )
& ~ sdtmndtplgtdt0(X6,xR,X7) )
| ~ aElement0(X6)
| ~ aElement0(X7) )
& isTerminating0(xR) ),
inference(ennf_transformation,[],[f30]) ).
fof(f56,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)
& ( X2 = X3
| ( ( aReductOfIn0(X3,X2,xR)
| ? [X5] :
( aElement0(X5)
& aReductOfIn0(X5,X2,xR)
& sdtmndtplgtdt0(X5,xR,X3) ) )
& sdtmndtplgtdt0(X2,xR,X3) ) )
& sdtmndtasgtdt0(X2,xR,X3) )
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aReductOfIn0(X1,X0,xR)
| ~ aReductOfIn0(X2,X0,xR) )
& isLocallyConfluent0(xR)
& ! [X6,X7] :
( iLess0(X7,X6)
| ( ~ aReductOfIn0(X7,X6,xR)
& ! [X8] :
( ~ aElement0(X8)
| ~ aReductOfIn0(X8,X6,xR)
| ~ sdtmndtplgtdt0(X8,xR,X7) )
& ~ sdtmndtplgtdt0(X6,xR,X7) )
| ~ aElement0(X6)
| ~ aElement0(X7) )
& isTerminating0(xR) ),
inference(flattening,[],[f55]) ).
fof(f57,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) )
| ~ iLess0(X0,xa)
| ~ 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,[],[f31]) ).
fof(f58,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) )
| ~ iLess0(X0,xa)
| ~ 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,[],[f57]) ).
fof(f59,plain,
( aElement0(xd)
& ( xw = xd
| ( ( aReductOfIn0(xd,xw,xR)
| ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xw,xR)
& sdtmndtplgtdt0(X0,xR,xd) ) )
& sdtmndtplgtdt0(xw,xR,xd) ) )
& sdtmndtasgtdt0(xw,xR,xd)
& ! [X1] : ~ aReductOfIn0(X1,xd,xR)
& aNormalFormOfIn0(xd,xw,xR) ),
inference(ennf_transformation,[],[f34]) ).
fof(f60,plain,
( xb != xd
& ~ aReductOfIn0(xd,xb,xR)
& ! [X0] :
( ~ aElement0(X0)
| ~ aReductOfIn0(X0,xb,xR)
| ~ sdtmndtplgtdt0(X0,xR,xd) )
& ~ sdtmndtplgtdt0(xb,xR,xd)
& ~ sdtmndtasgtdt0(xb,xR,xd) ),
inference(ennf_transformation,[],[f25]) ).
fof(f67,definition,
! [X3,X2] :
( X2 = X3
| ( ( aReductOfIn0(X3,X2,xR)
| ? [X5] :
( aElement0(X5)
& aReductOfIn0(X5,X2,xR)
& sdtmndtplgtdt0(X5,xR,X3) ) )
& sdtmndtplgtdt0(X2,xR,X3) )
| ~ sP4(X3,X2) ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
fof(f68,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)
& sdtmndtasgtdt0(X2,xR,X3) )
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aReductOfIn0(X1,X0,xR)
| ~ aReductOfIn0(X2,X0,xR) )
& isLocallyConfluent0(xR)
& ! [X6,X7] :
( iLess0(X7,X6)
| ( ~ aReductOfIn0(X7,X6,xR)
& ! [X8] :
( ~ aElement0(X8)
| ~ aReductOfIn0(X8,X6,xR)
| ~ sdtmndtplgtdt0(X8,xR,X7) )
& ~ sdtmndtplgtdt0(X6,xR,X7) )
| ~ aElement0(X6)
| ~ aElement0(X7) )
& isTerminating0(xR) ),
inference(definition_folding,[],[f56,f67]) ).
fof(f69,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(f70,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(f71,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(f72,plain,
! [X0,X1,X2] :
( sP6(X1,X2)
| ~ iLess0(X0,xa)
| ~ 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,[],[f58,f71,f70,f69]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ( ( sdtmndtplgtdt0(X0,X1,X2)
| ( ~ aReductOfIn0(X2,X0,X1)
& ! [X3] :
( ~ aElement0(X3)
| ~ aReductOfIn0(X3,X0,X1)
| ~ sdtmndtplgtdt0(X3,X1,X2) ) ) )
& ( aReductOfIn0(X2,X0,X1)
| ? [X3] :
( aElement0(X3)
& aReductOfIn0(X3,X0,X1)
& sdtmndtplgtdt0(X3,X1,X2) )
| ~ sdtmndtplgtdt0(X0,X1,X2) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(nnf_transformation,[],[f38]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ( ( sdtmndtplgtdt0(X0,X1,X2)
| ( ~ aReductOfIn0(X2,X0,X1)
& ! [X3] :
( ~ aElement0(X3)
| ~ aReductOfIn0(X3,X0,X1)
| ~ sdtmndtplgtdt0(X3,X1,X2) ) ) )
& ( aReductOfIn0(X2,X0,X1)
| ? [X3] :
( aElement0(X3)
& aReductOfIn0(X3,X0,X1)
& sdtmndtplgtdt0(X3,X1,X2) )
| ~ sdtmndtplgtdt0(X0,X1,X2) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(flattening,[],[f73]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ( ( sdtmndtplgtdt0(X0,X1,X2)
| ( ~ aReductOfIn0(X2,X0,X1)
& ! [X3] :
( ~ aElement0(X3)
| ~ aReductOfIn0(X3,X0,X1)
| ~ sdtmndtplgtdt0(X3,X1,X2) ) ) )
& ( aReductOfIn0(X2,X0,X1)
| ? [X4] :
( aElement0(X4)
& aReductOfIn0(X4,X0,X1)
& sdtmndtplgtdt0(X4,X1,X2) )
| ~ sdtmndtplgtdt0(X0,X1,X2) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(rectify,[],[f74]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ( ( sdtmndtplgtdt0(X0,X1,X2)
| ( ~ aReductOfIn0(X2,X0,X1)
& ! [X3] :
( ~ aElement0(X3)
| ~ aReductOfIn0(X3,X0,X1)
| ~ sdtmndtplgtdt0(X3,X1,X2) ) ) )
& ( aReductOfIn0(X2,X0,X1)
| ( aElement0(sK8(X0,X1,X2))
& aReductOfIn0(sK8(X0,X1,X2),X0,X1)
& sdtmndtplgtdt0(sK8(X0,X1,X2),X1,X2) )
| ~ sdtmndtplgtdt0(X0,X1,X2) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X4,sK8(X0,X1,X2))],[f75]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ( ( sdtmndtasgtdt0(X0,X1,X2)
| ( X0 != X2
& ~ sdtmndtplgtdt0(X0,X1,X2) ) )
& ( X0 = X2
| sdtmndtplgtdt0(X0,X1,X2)
| ~ sdtmndtasgtdt0(X0,X1,X2) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(nnf_transformation,[],[f42]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ( ( sdtmndtasgtdt0(X0,X1,X2)
| ( X0 != X2
& ~ sdtmndtplgtdt0(X0,X1,X2) ) )
& ( X0 = X2
| sdtmndtplgtdt0(X0,X1,X2)
| ~ sdtmndtasgtdt0(X0,X1,X2) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(flattening,[],[f77]) ).
fof(f98,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)
& sdtmndtasgtdt0(X2,xR,X3) )
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aReductOfIn0(X1,X0,xR)
| ~ aReductOfIn0(X2,X0,xR) )
& isLocallyConfluent0(xR)
& ! [X5,X6] :
( iLess0(X6,X5)
| ( ~ aReductOfIn0(X6,X5,xR)
& ! [X7] :
( ~ aElement0(X7)
| ~ aReductOfIn0(X7,X5,xR)
| ~ sdtmndtplgtdt0(X7,xR,X6) )
& ~ sdtmndtplgtdt0(X5,xR,X6) )
| ~ aElement0(X5)
| ~ aElement0(X6) )
& isTerminating0(xR) ),
inference(rectify,[],[f68]) ).
fof(f99,plain,
( ! [X0,X1,X2] :
( ( aElement0(sK22(X1,X2))
& ( sK22(X1,X2) = X1
| ( ( aReductOfIn0(sK22(X1,X2),X1,xR)
| ( aElement0(sK23(X1,X2))
& aReductOfIn0(sK23(X1,X2),X1,xR)
& sdtmndtplgtdt0(sK23(X1,X2),xR,sK22(X1,X2)) ) )
& sdtmndtplgtdt0(X1,xR,sK22(X1,X2)) ) )
& sdtmndtasgtdt0(X1,xR,sK22(X1,X2))
& sP4(sK22(X1,X2),X2)
& sdtmndtasgtdt0(X2,xR,sK22(X1,X2)) )
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aReductOfIn0(X1,X0,xR)
| ~ aReductOfIn0(X2,X0,xR) )
& isLocallyConfluent0(xR)
& ! [X5,X6] :
( iLess0(X6,X5)
| ( ~ aReductOfIn0(X6,X5,xR)
& ! [X7] :
( ~ aElement0(X7)
| ~ aReductOfIn0(X7,X5,xR)
| ~ sdtmndtplgtdt0(X7,xR,X6) )
& ~ sdtmndtplgtdt0(X5,xR,X6) )
| ~ aElement0(X5)
| ~ aElement0(X6) )
& isTerminating0(xR) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22,sK23]),skolemize(X3,sK22(X1,X2)),skolemize(X4,sK23(X1,X2))],[f98]) ).
fof(f100,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,[],[f71]) ).
fof(f101,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,[],[f100]) ).
fof(f102,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,[],[f70]) ).
fof(f103,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,[],[f102]) ).
fof(f104,plain,
! [X0,X1] :
( ( aElement0(sK24(X0,X1))
& ( sK24(X0,X1) = X0
| ( ( aReductOfIn0(sK24(X0,X1),X0,xR)
| ( aElement0(sK25(X0,X1))
& aReductOfIn0(sK25(X0,X1),X0,xR)
& sdtmndtplgtdt0(sK25(X0,X1),xR,sK24(X0,X1)) ) )
& sdtmndtplgtdt0(X0,xR,sK24(X0,X1)) ) )
& sdtmndtasgtdt0(X0,xR,sK24(X0,X1))
& sP5(sK24(X0,X1),X1)
& sdtmndtasgtdt0(X1,xR,sK24(X0,X1)) )
| ~ sP6(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24,sK25]),skolemize(X2,sK24(X0,X1)),skolemize(X3,sK25(X0,X1))],[f103]) ).
fof(f109,plain,
( aElement0(xu)
& aReductOfIn0(xu,xa,xR)
& ( xu = xb
| ( ( aReductOfIn0(xb,xu,xR)
| ( aElement0(sK29)
& aReductOfIn0(sK29,xu,xR)
& sdtmndtplgtdt0(sK29,xR,xb) ) )
& sdtmndtplgtdt0(xu,xR,xb) ) )
& sdtmndtasgtdt0(xu,xR,xb) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(X0,sK29)],[f20]) ).
fof(f111,plain,
( aElement0(xw)
& ( xu = xw
| ( ( aReductOfIn0(xw,xu,xR)
| ( aElement0(sK31)
& aReductOfIn0(sK31,xu,xR)
& sdtmndtplgtdt0(sK31,xR,xw) ) )
& sdtmndtplgtdt0(xu,xR,xw) ) )
& sdtmndtasgtdt0(xu,xR,xw)
& ( xv = xw
| ( ( aReductOfIn0(xw,xv,xR)
| ( aElement0(sK32)
& aReductOfIn0(sK32,xv,xR)
& sdtmndtplgtdt0(sK32,xR,xw) ) )
& sdtmndtplgtdt0(xv,xR,xw) ) )
& sdtmndtasgtdt0(xv,xR,xw) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31,sK32]),skolemize(X0,sK31),skolemize(X1,sK32)],[f33]) ).
fof(f112,plain,
( aElement0(xd)
& ( xw = xd
| ( ( aReductOfIn0(xd,xw,xR)
| ( aElement0(sK33)
& aReductOfIn0(sK33,xw,xR)
& sdtmndtplgtdt0(sK33,xR,xd) ) )
& sdtmndtplgtdt0(xw,xR,xd) ) )
& sdtmndtasgtdt0(xw,xR,xd)
& ! [X1] : ~ aReductOfIn0(X1,xd,xR)
& aNormalFormOfIn0(xd,xw,xR) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(X0,sK33)],[f59]) ).
fof(f115,plain,
! [X2,X0,X1] :
( aReductOfIn0(sK8(X0,X1,X2),X0,X1)
| aReductOfIn0(X2,X0,X1)
| ~ sdtmndtplgtdt0(X0,X1,X2)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(cnf_transformation,[],[f76]) ).
fof(f120,plain,
! [X2,X0,X1] :
( ~ sdtmndtasgtdt0(X0,X1,X2)
| sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(cnf_transformation,[],[f78]) ).
fof(f123,plain,
! [X2,X3,X0,X1] :
( ~ sdtmndtasgtdt0(X2,X1,X3)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| sdtmndtasgtdt0(X0,X1,X3)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(cnf_transformation,[],[f44]) ).
fof(f158,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[],[f15]) ).
fof(f166,plain,
! [X6,X5] :
( ~ aReductOfIn0(X6,X5,xR)
| iLess0(X6,X5)
| ~ aElement0(X5)
| ~ aElement0(X6) ),
inference(cnf_transformation,[],[f99]) ).
fof(f177,plain,
aElement0(xb),
inference(cnf_transformation,[],[f17]) ).
fof(f178,plain,
aElement0(xa),
inference(cnf_transformation,[],[f17]) ).
fof(f179,plain,
! [X0,X1] :
( ~ sdtmndtasgtdt0(X1,xR,X0)
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f101]) ).
fof(f184,plain,
! [X0,X1] :
( sdtmndtasgtdt0(X1,xR,sK24(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f104]) ).
fof(f187,plain,
! [X0,X1] :
( sdtmndtplgtdt0(X0,xR,sK24(X0,X1))
| sK24(X0,X1) = X0
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f104]) ).
fof(f191,plain,
! [X0,X1] :
( aElement0(sK24(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f104]) ).
fof(f196,plain,
! [X2,X0,X1] :
( ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ iLess0(X0,xa)
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2)
| sP6(X1,X2)
| sP7(X2,X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f209,plain,
sdtmndtasgtdt0(xu,xR,xb),
inference(cnf_transformation,[],[f109]) ).
fof(f214,plain,
aReductOfIn0(xu,xa,xR),
inference(cnf_transformation,[],[f109]) ).
fof(f215,plain,
aElement0(xu),
inference(cnf_transformation,[],[f109]) ).
fof(f228,plain,
sdtmndtasgtdt0(xu,xR,xw),
inference(cnf_transformation,[],[f111]) ).
fof(f233,plain,
aElement0(xw),
inference(cnf_transformation,[],[f111]) ).
fof(f235,plain,
! [X1] : ~ aReductOfIn0(X1,xd,xR),
inference(cnf_transformation,[],[f112]) ).
fof(f236,plain,
sdtmndtasgtdt0(xw,xR,xd),
inference(cnf_transformation,[],[f112]) ).
fof(f241,plain,
aElement0(xd),
inference(cnf_transformation,[],[f112]) ).
fof(f243,plain,
~ sdtmndtplgtdt0(xb,xR,xd),
inference(cnf_transformation,[],[f60]) ).
fof(f246,plain,
xb != xd,
inference(cnf_transformation,[],[f60]) ).
fof(f462,plain,
! [X0] :
( ~ sdtmndtasgtdt0(X0,xR,xw)
| sdtmndtasgtdt0(X0,xR,xd)
| ~ aElement0(X0)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xw)
| ~ aElement0(xd) ),
inference(resolution,[],[f123,f236]) ).
fof(f465,plain,
! [X0] :
( ~ sdtmndtasgtdt0(X0,xR,xw)
| sdtmndtasgtdt0(X0,xR,xd)
| ~ aElement0(X0)
| ~ aElement0(xw)
| ~ aElement0(xd) ),
inference(forward_subsumption_resolution,[],[f462,f158]) ).
fof(f467,plain,
! [X0] :
( ~ sdtmndtasgtdt0(X0,xR,xw)
| sdtmndtasgtdt0(X0,xR,xd)
| ~ aElement0(X0)
| ~ aElement0(xd) ),
inference(forward_subsumption_resolution,[],[f465,f233]) ).
fof(f469,plain,
! [X0] :
( ~ sdtmndtasgtdt0(X0,xR,xw)
| sdtmndtasgtdt0(X0,xR,xd)
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[],[f467,f241]) ).
fof(f474,plain,
! [X0,X1] :
( ~ sP6(X0,X1)
| sdtmndtplgtdt0(X1,xR,sK24(X0,X1))
| sK24(X0,X1) = X1
| ~ aElement0(X1)
| ~ aRewritingSystem0(xR)
| ~ aElement0(sK24(X0,X1)) ),
inference(resolution,[],[f184,f120]) ).
fof(f475,plain,
! [X0,X1] :
( ~ sP6(X0,X1)
| sdtmndtplgtdt0(X1,xR,sK24(X0,X1))
| sK24(X0,X1) = X1
| ~ aElement0(X1)
| ~ aElement0(sK24(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f474,f158]) ).
fof(f477,plain,
! [X0,X1] :
( sdtmndtplgtdt0(X1,xR,sK24(X0,X1))
| ~ sP6(X0,X1)
| sK24(X0,X1) = X1
| ~ aElement0(X1) ),
inference(forward_subsumption_resolution,[],[f475,f191]) ).
fof(f502,definition,
( spl34_40
<=> iLess0(xu,xa) ),
introduced(definition,[new_symbols(definition,[spl34_40])],[avatar_definition]) ).
fof(f503,plain,
( iLess0(xu,xa)
| ~ spl34_40 ),
inference(avatar_component_clause,[],[f502]) ).
fof(f504,plain,
( ~ iLess0(xu,xa)
| spl34_40 ),
inference(avatar_component_clause,[],[f502]) ).
fof(f562,plain,
~ sP7(xb,xu),
inference(resolution,[],[f179,f209]) ).
fof(f737,plain,
( iLess0(xu,xa)
| ~ aElement0(xa)
| ~ aElement0(xu) ),
inference(resolution,[],[f214,f166]) ).
fof(f741,plain,
( ~ aElement0(xa)
| ~ aElement0(xu)
| spl34_40 ),
inference(forward_subsumption_resolution,[],[f737,f504]) ).
fof(f745,plain,
( ~ aElement0(xu)
| spl34_40 ),
inference(forward_subsumption_resolution,[],[f741,f178]) ).
fof(f749,plain,
( $false
| spl34_40 ),
inference(forward_subsumption_resolution,[],[f745,f215]) ).
fof(f750,plain,
spl34_40,
inference(avatar_contradiction_clause,[],[f749]) ).
fof(f795,plain,
! [X0] :
( aReductOfIn0(X0,xd,xR)
| ~ sdtmndtplgtdt0(xd,xR,X0)
| ~ aElement0(xd)
| ~ aRewritingSystem0(xR)
| ~ aElement0(X0) ),
inference(resolution,[],[f115,f235]) ).
fof(f817,plain,
! [X0] :
( aReductOfIn0(X0,xd,xR)
| ~ sdtmndtplgtdt0(xd,xR,X0)
| ~ aRewritingSystem0(xR)
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[],[f795,f241]) ).
fof(f823,plain,
! [X0] :
( aReductOfIn0(X0,xd,xR)
| ~ sdtmndtplgtdt0(xd,xR,X0)
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[],[f817,f158]) ).
fof(f827,plain,
! [X0] :
( ~ sdtmndtplgtdt0(xd,xR,X0)
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[],[f823,f235]) ).
fof(f3728,plain,
( sdtmndtasgtdt0(xu,xR,xd)
| ~ aElement0(xu) ),
inference(resolution,[],[f469,f228]) ).
fof(f3737,plain,
sdtmndtasgtdt0(xu,xR,xd),
inference(forward_subsumption_resolution,[],[f3728,f215]) ).
fof(f4016,plain,
! [X0] :
( ~ aElement0(sK24(xd,X0))
| xd = sK24(xd,X0)
| ~ sP6(xd,X0) ),
inference(resolution,[],[f827,f187]) ).
fof(f4025,plain,
! [X0] :
( ~ sP6(xd,X0)
| xd = sK24(xd,X0) ),
inference(forward_subsumption_resolution,[],[f4016,f191]) ).
fof(f5196,plain,
! [X0] :
( ~ iLess0(xu,xa)
| ~ aElement0(xu)
| ~ aElement0(xd)
| ~ aElement0(X0)
| sP6(xd,X0)
| sP7(X0,xu) ),
inference(resolution,[],[f3737,f196]) ).
fof(f5201,plain,
( ! [X0] :
( ~ aElement0(xu)
| ~ aElement0(xd)
| ~ aElement0(X0)
| sP6(xd,X0)
| sP7(X0,xu) )
| ~ spl34_40 ),
inference(forward_subsumption_resolution,[],[f5196,f503]) ).
fof(f5203,plain,
( ! [X0] :
( ~ aElement0(xd)
| ~ aElement0(X0)
| sP6(xd,X0)
| sP7(X0,xu) )
| ~ spl34_40 ),
inference(forward_subsumption_resolution,[],[f5201,f215]) ).
fof(f5205,plain,
( ! [X0] :
( sP7(X0,xu)
| sP6(xd,X0)
| ~ aElement0(X0) )
| ~ spl34_40 ),
inference(forward_subsumption_resolution,[],[f5203,f241]) ).
fof(f5539,plain,
( sP6(xd,xb)
| ~ aElement0(xb)
| ~ spl34_40 ),
inference(resolution,[],[f5205,f562]) ).
fof(f5564,plain,
( sP6(xd,xb)
| ~ spl34_40 ),
inference(forward_subsumption_resolution,[],[f5539,f177]) ).
fof(f5570,plain,
( xd = sK24(xd,xb)
| ~ spl34_40 ),
inference(resolution,[],[f5564,f4025]) ).
fof(f5582,plain,
( sdtmndtplgtdt0(xb,xR,xd)
| ~ sP6(xd,xb)
| xb = xd
| ~ aElement0(xb)
| ~ spl34_40 ),
inference(superposition,[],[f477,f5570]) ).
fof(f5607,plain,
( ~ sP6(xd,xb)
| xb = xd
| ~ aElement0(xb)
| ~ spl34_40 ),
inference(forward_subsumption_resolution,[],[f5582,f243]) ).
fof(f5618,plain,
( xb = xd
| ~ aElement0(xb)
| ~ spl34_40 ),
inference(forward_subsumption_resolution,[],[f5607,f5564]) ).
fof(f5629,plain,
( ~ aElement0(xb)
| ~ spl34_40 ),
inference(forward_subsumption_resolution,[],[f5618,f246]) ).
fof(f5630,plain,
( $false
| ~ spl34_40 ),
inference(forward_subsumption_resolution,[],[f5629,f177]) ).
fof(f5631,plain,
~ spl34_40,
inference(avatar_contradiction_clause,[],[f5630]) ).
cnf(s34,plain,
spl34_40,
inference(sat_conversion,[],[f750]) ).
cnf(s126,plain,
~ spl34_40,
inference(sat_conversion,[],[f5631]) ).
cnf(s142,plain,
$false,
inference(rat,[],[s34,s126]) ).
fof(f5632,plain,
$false,
inference(avatar_sat_refutation,[],[s142]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM019+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n003.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 21:48:13 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running first-order theorem proving
% 0.08/0.22 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
% 6.84/1.85 % (2066249)Detected formulas, will run a generic FOF schedule.
% 6.84/1.85 % (2066258)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=906362635:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.84/1.85 % (2066258)Instruction limit reached!
% 6.84/1.85 % (2066258)------------------------------
% 6.84/1.85 % (2066258)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.84/1.85 % (2066258)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.84/1.85 % (2066258)CaDiCaL version: 2.1.3
% 6.84/1.85 % (2066258)Termination reason: Instruction limit
% 6.84/1.85 % (2066258)Termination phase: Saturation
% 6.84/1.85 % (2066258)Time elapsed: 0.038 s
% 6.84/1.85 % (2066258)Peak memory usage: 88 MB
% 6.84/1.85 % (2066258)Instructions burned: 122 (million)
% 6.84/1.85 % (2066254)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=2312245028:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.84/1.85 % (2066256)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=722404928:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.84/1.85 % (2066257)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1124530906:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.84/1.85 % (2066255)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=1771162532:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.84/1.85 % (2066259)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1264464945:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.84/1.85 % (2066260)dis-21_1_sil=8000:lcm=predicate:random_seed=2226469802: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)
% 6.84/1.85 % (2066257)Instruction limit reached!
% 6.84/1.85 % (2066257)------------------------------
% 6.84/1.85 % (2066257)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.84/1.85 % (2066257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.84/1.85 % (2066257)CaDiCaL version: 2.1.3
% 6.84/1.85 % (2066257)Termination reason: Instruction limit
% 6.84/1.85 % (2066257)Termination phase: Saturation
% 6.84/1.85 % (2066257)Time elapsed: 0.068 s
% 6.84/1.85 % (2066257)Peak memory usage: 89 MB
% 6.84/1.85 % (2066257)Instructions burned: 110 (million)
% 6.84/1.85 % (2066260)Instruction limit reached!
% 6.84/1.85 % (2066260)------------------------------
% 6.84/1.85 % (2066260)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.84/1.85 % (2066260)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.84/1.85 % (2066260)CaDiCaL version: 2.1.3
% 6.84/1.85 % (2066260)Termination reason: Instruction limit
% 6.84/1.85 % (2066260)Termination phase: Saturation
% 6.84/1.85 % (2066260)Time elapsed: 0.074 s
% 6.84/1.85 % (2066260)Peak memory usage: 89 MB
% 6.84/1.85 % (2066260)Instructions burned: 130 (million)
% 6.84/1.85 % (2066259)Instruction limit reached!
% 6.84/1.85 % (2066259)------------------------------
% 6.84/1.85 % (2066259)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.84/1.85 % (2066259)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.84/1.85 % (2066259)CaDiCaL version: 2.1.3
% 6.84/1.85 % (2066259)Termination reason: Instruction limit
% 6.84/1.85 % (2066259)Termination phase: Saturation
% 6.84/1.85 % (2066259)Time elapsed: 0.098 s
% 6.84/1.85 % (2066259)Peak memory usage: 90 MB
% 6.84/1.85 % (2066259)Instructions burned: 139 (million)
% 6.84/1.85 % (2066266)lrs+10_1_sil=8000:sp=occurrence:random_seed=2668746308:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 6.84/1.85 % (2066266)Instruction limit reached!
% 6.84/1.85 % (2066266)------------------------------
% 6.84/1.85 % (2066266)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.84/1.85 % (2066266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.84/1.85 % (2066266)CaDiCaL version: 2.1.3
% 6.84/1.85 % (2066266)Termination reason: Instruction limit
% 6.84/1.85 % (2066266)Termination phase: Saturation
% 6.84/1.85 % (2066266)Time elapsed: 0.093 s
% 6.84/1.85 % (2066266)Peak memory usage: 91 MB
% 6.84/1.85 % (2066266)Instructions burned: 287 (million)
% 6.84/1.85 % (2066269)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3443022579:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.84/1.85 % (2066270)lrs+1011_1_sil=32000:sp=occurrence:random_seed=145115942:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.84/1.85 % (2066272)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=327472285:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 6.84/1.85 % (2066269)Instruction limit reached!
% 6.84/1.85 % (2066269)------------------------------
% 6.84/1.85 % (2066269)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.84/1.85 % (2066269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.84/1.85 % (2066269)CaDiCaL version: 2.1.3
% 6.84/1.85 % (2066269)Termination reason: Instruction limit
% 6.84/1.85 % (2066269)Termination phase: Saturation
% 6.84/1.85 % (2066269)Time elapsed: 0.089 s
% 6.84/1.85 % (2066269)Peak memory usage: 90 MB
% 6.84/1.85 % (2066269)Instructions burned: 158 (million)
% 6.84/1.85 % (2066273)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3291486207:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 6.84/1.85 % (2066272)Instruction limit reached!
% 6.84/1.85 % (2066272)------------------------------
% 6.84/1.85 % (2066272)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.84/1.85 % (2066272)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.84/1.85 % (2066272)CaDiCaL version: 2.1.3
% 6.84/1.85 % (2066272)Termination reason: Instruction limit
% 6.84/1.85 % (2066272)Termination phase: Saturation
% 6.84/1.85 % (2066272)Time elapsed: 0.137 s
% 6.84/1.85 % (2066272)Peak memory usage: 90 MB
% 6.84/1.85 % (2066272)Instructions burned: 249 (million)
% 6.84/1.85 % (2066273)Instruction limit reached!
% 6.84/1.85 % (2066273)------------------------------
% 6.84/1.85 % (2066273)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.84/1.85 % (2066273)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.84/1.85 % (2066273)CaDiCaL version: 2.1.3
% 6.84/1.85 % (2066273)Termination reason: Instruction limit
% 6.84/1.85 % (2066273)Termination phase: Saturation
% 6.84/1.85 % (2066273)Time elapsed: 0.095 s
% 6.84/1.85 % (2066273)Peak memory usage: 90 MB
% 6.84/1.85 % (2066273)Instructions burned: 295 (million)
% 6.84/1.85 % (2066270)Instruction limit reached!
% 6.84/1.85 % (2066270)------------------------------
% 6.84/1.85 % (2066270)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.84/1.85 % (2066270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.84/1.85 % (2066270)CaDiCaL version: 2.1.3
% 6.84/1.85 % (2066270)Termination reason: Instruction limit
% 6.84/1.85 % (2066270)Termination phase: Saturation
% 6.84/1.85 % (2066270)Time elapsed: 0.194 s
% 6.84/1.85 % (2066270)Peak memory usage: 91 MB
% 6.84/1.85 % (2066270)Instructions burned: 325 (million)
% 6.84/1.85 % (2066277)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2369732283:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 6.84/1.85 % (2066279)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=597897133:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 6.84/1.85 % (2066280)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=318726036:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 6.84/1.85 % (2066281)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2181368656:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 6.84/1.85 % (2066279)Instruction limit reached!
% 6.84/1.85 % (2066279)------------------------------
% 6.84/1.85 % (2066279)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.84/1.85 % (2066279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.84/1.85 % (2066279)CaDiCaL version: 2.1.3
% 6.84/1.85 % (2066279)Termination reason: Instruction limit
% 6.84/1.85 % (2066279)Termination phase: Saturation
% 6.84/1.85 % (2066279)Time elapsed: 0.072 s
% 6.84/1.85 % (2066279)Peak memory usage: 90 MB
% 6.84/1.85 % (2066279)Instructions burned: 113 (million)
% 6.84/1.85 % (2066280)Instruction limit reached!
% 6.84/1.85 % (2066280)------------------------------
% 6.84/1.85 % (2066280)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.84/1.85 % (2066280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.84/1.85 % (2066280)CaDiCaL version: 2.1.3
% 6.84/1.85 % (2066280)Termination reason: Instruction limit
% 6.84/1.85 % (2066280)Termination phase: Saturation
% 6.84/1.85 % (2066280)Time elapsed: 0.069 s
% 6.84/1.85 % (2066280)Peak memory usage: 89 MB
% 6.84/1.85 % (2066280)Instructions burned: 128 (million)
% 6.84/1.85 % (2066281)Instruction limit reached!
% 6.84/1.85 % (2066281)------------------------------
% 6.84/1.85 % (2066281)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.84/1.85 % (2066281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.84/1.85 % (2066281)CaDiCaL version: 2.1.3
% 6.84/1.85 % (2066281)Termination reason: Instruction limit
% 6.84/1.85 % (2066281)Termination phase: Saturation
% 6.84/1.85 % (2066281)Time elapsed: 0.070 s
% 6.84/1.85 % (2066281)Peak memory usage: 89 MB
% 6.84/1.85 % (2066281)Instructions burned: 115 (million)
% 6.84/1.85 % (2066286)lrs+10_1_sil=8000:sp=occurrence:random_seed=760826686:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 6.84/1.85 % (2066287)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3569499717:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 6.84/1.85 % (2066288)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1940458598:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 6.84/1.85 % (2066254)First to succeed.
% 6.84/1.85 % (2066254)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2066249"
% 6.84/1.85 % (2066254)Refutation found. Thanks to Tanya!
% 6.84/1.85 % SZS status Theorem for theBenchmark
% 6.84/1.85 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/2.04 % (2066254)------------------------------
% 0.19/2.04 % (2066254)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/2.04 % (2066254)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/2.04 % (2066254)CaDiCaL version: 2.1.3
% 0.19/2.04 % (2066254)Termination reason: Refutation
% 0.19/2.04 % (2066254)Time elapsed: 0.856 s
% 0.19/2.04 % (2066254)Peak memory usage: 135 MB
% 0.19/2.04 % (2066254)Instructions burned: 1715 (million)
% 0.19/2.04 % (2066254)------------------------------
% 0.19/2.04 % (2066254)------------------------------
% 0.19/2.04 % (2066249)Success in time 1.183 s
% 0.19/2.04 % Vampire exiting
%------------------------------------------------------------------------------