TSTP Solution File: COM020+4 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : COM020+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 18:42:07 EDT 2023
% Result : Theorem 7.31s 1.65s
% Output : CNFRefutation 7.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 23
% Syntax : Number of formulae : 113 ( 26 unt; 0 def)
% Number of atoms : 854 ( 66 equ)
% Maximal formula atoms : 33 ( 7 avg)
% Number of connectives : 1028 ( 287 ~; 332 |; 387 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 12 con; 0-2 aty)
% Number of variables : 253 ( 0 sgn; 139 !; 71 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] :
( ( aRewritingSystem0(X1)
& aElement0(X0) )
=> ! [X2] :
( aReductOfIn0(X2,X0,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mReduct) ).
fof(f9,axiom,
! [X0,X1,X2,X3] :
( ( aElement0(X3)
& aElement0(X2)
& aRewritingSystem0(X1)
& aElement0(X0) )
=> ( ( sdtmndtasgtdt0(X2,X1,X3)
& sdtmndtasgtdt0(X0,X1,X2) )
=> 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,
( isTerminating0(xR)
& ! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> ( ( sdtmndtplgtdt0(X0,xR,X1)
| ? [X2] :
( sdtmndtplgtdt0(X2,xR,X1)
& aReductOfIn0(X2,X0,xR)
& aElement0(X2) )
| aReductOfIn0(X1,X0,xR) )
=> iLess0(X1,X0) ) )
& isLocallyConfluent0(xR)
& ! [X0,X1,X2] :
( ( aReductOfIn0(X2,X0,xR)
& aReductOfIn0(X1,X0,xR)
& aElement0(X2)
& aElement0(X1)
& aElement0(X0) )
=> ? [X3] :
( sdtmndtasgtdt0(X2,xR,X3)
& ( ( sdtmndtplgtdt0(X2,xR,X3)
& ( ? [X4] :
( sdtmndtplgtdt0(X4,xR,X3)
& aReductOfIn0(X4,X2,xR)
& aElement0(X4) )
| aReductOfIn0(X3,X2,xR) ) )
| X2 = X3 )
& sdtmndtasgtdt0(X1,xR,X3)
& ( ( sdtmndtplgtdt0(X1,xR,X3)
& ( ? [X4] :
( sdtmndtplgtdt0(X4,xR,X3)
& aReductOfIn0(X4,X1,xR)
& aElement0(X4) )
| aReductOfIn0(X3,X1,xR) ) )
| X1 = X3 )
& aElement0(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656_01) ).
fof(f17,axiom,
( aElement0(xc)
& aElement0(xb)
& aElement0(xa) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__731) ).
fof(f18,axiom,
! [X0,X1,X2] :
( ( ( sdtmndtasgtdt0(X0,xR,X2)
| sdtmndtplgtdt0(X0,xR,X2)
| ? [X3] :
( sdtmndtplgtdt0(X3,xR,X2)
& aReductOfIn0(X3,X0,xR)
& aElement0(X3) )
| aReductOfIn0(X2,X0,xR)
| X0 = X2 )
& ( sdtmndtasgtdt0(X0,xR,X1)
| sdtmndtplgtdt0(X0,xR,X1)
| ? [X3] :
( sdtmndtplgtdt0(X3,xR,X1)
& aReductOfIn0(X3,X0,xR)
& aElement0(X3) )
| aReductOfIn0(X1,X0,xR)
| X0 = X1 )
& aElement0(X2)
& aElement0(X1)
& aElement0(X0) )
=> ( iLess0(X0,xa)
=> ? [X3] :
( sdtmndtasgtdt0(X2,xR,X3)
& ( ( sdtmndtplgtdt0(X2,xR,X3)
& ( ? [X4] :
( sdtmndtplgtdt0(X4,xR,X3)
& aReductOfIn0(X4,X2,xR)
& aElement0(X4) )
| aReductOfIn0(X3,X2,xR) ) )
| X2 = X3 )
& sdtmndtasgtdt0(X1,xR,X3)
& ( ( sdtmndtplgtdt0(X1,xR,X3)
& ( ? [X4] :
( sdtmndtplgtdt0(X4,xR,X3)
& aReductOfIn0(X4,X1,xR)
& aElement0(X4) )
| aReductOfIn0(X3,X1,xR) ) )
| X1 = X3 )
& aElement0(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__715) ).
fof(f20,axiom,
( sdtmndtasgtdt0(xu,xR,xb)
& ( ( sdtmndtplgtdt0(xu,xR,xb)
& ( ? [X0] :
( sdtmndtplgtdt0(X0,xR,xb)
& aReductOfIn0(X0,xu,xR)
& aElement0(X0) )
| aReductOfIn0(xb,xu,xR) ) )
| xb = xu )
& aReductOfIn0(xu,xa,xR)
& aElement0(xu) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__755) ).
fof(f22,axiom,
( sdtmndtasgtdt0(xv,xR,xw)
& ( ( sdtmndtplgtdt0(xv,xR,xw)
& ( ? [X0] :
( sdtmndtplgtdt0(X0,xR,xw)
& aReductOfIn0(X0,xv,xR)
& aElement0(X0) )
| aReductOfIn0(xw,xv,xR) ) )
| xv = xw )
& sdtmndtasgtdt0(xu,xR,xw)
& ( ( sdtmndtplgtdt0(xu,xR,xw)
& ( ? [X0] :
( sdtmndtplgtdt0(X0,xR,xw)
& aReductOfIn0(X0,xu,xR)
& aElement0(X0) )
| aReductOfIn0(xw,xu,xR) ) )
| xu = xw )
& aElement0(xw) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__799) ).
fof(f23,axiom,
( aNormalFormOfIn0(xd,xw,xR)
& ~ ? [X0] : aReductOfIn0(X0,xd,xR)
& sdtmndtasgtdt0(xw,xR,xd)
& ( ( sdtmndtplgtdt0(xw,xR,xd)
& ( ? [X0] :
( sdtmndtplgtdt0(X0,xR,xd)
& aReductOfIn0(X0,xw,xR)
& aElement0(X0) )
| aReductOfIn0(xd,xw,xR) ) )
| xw = xd )
& aElement0(xd) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__818) ).
fof(f24,conjecture,
? [X0] :
( ( sdtmndtasgtdt0(xd,xR,X0)
| sdtmndtplgtdt0(xd,xR,X0)
| ? [X1] :
( sdtmndtplgtdt0(X1,xR,X0)
& aReductOfIn0(X1,xd,xR)
& aElement0(X1) )
| aReductOfIn0(X0,xd,xR)
| xd = X0 )
& ( sdtmndtasgtdt0(xb,xR,X0)
| sdtmndtplgtdt0(xb,xR,X0)
| ? [X1] :
( sdtmndtplgtdt0(X1,xR,X0)
& aReductOfIn0(X1,xb,xR)
& aElement0(X1) )
| aReductOfIn0(X0,xb,xR)
| xb = X0 )
& aElement0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f25,negated_conjecture,
~ ? [X0] :
( ( sdtmndtasgtdt0(xd,xR,X0)
| sdtmndtplgtdt0(xd,xR,X0)
| ? [X1] :
( sdtmndtplgtdt0(X1,xR,X0)
& aReductOfIn0(X1,xd,xR)
& aElement0(X1) )
| aReductOfIn0(X0,xd,xR)
| xd = X0 )
& ( sdtmndtasgtdt0(xb,xR,X0)
| sdtmndtplgtdt0(xb,xR,X0)
| ? [X1] :
( sdtmndtplgtdt0(X1,xR,X0)
& aReductOfIn0(X1,xb,xR)
& aElement0(X1) )
| aReductOfIn0(X0,xb,xR)
| xb = X0 )
& aElement0(X0) ),
inference(negated_conjecture,[],[f24]) ).
fof(f30,plain,
( isTerminating0(xR)
& ! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> ( ( sdtmndtplgtdt0(X0,xR,X1)
| ? [X2] :
( sdtmndtplgtdt0(X2,xR,X1)
& aReductOfIn0(X2,X0,xR)
& aElement0(X2) )
| aReductOfIn0(X1,X0,xR) )
=> iLess0(X1,X0) ) )
& isLocallyConfluent0(xR)
& ! [X3,X4,X5] :
( ( aReductOfIn0(X5,X3,xR)
& aReductOfIn0(X4,X3,xR)
& aElement0(X5)
& aElement0(X4)
& aElement0(X3) )
=> ? [X6] :
( sdtmndtasgtdt0(X5,xR,X6)
& ( ( sdtmndtplgtdt0(X5,xR,X6)
& ( ? [X7] :
( sdtmndtplgtdt0(X7,xR,X6)
& aReductOfIn0(X7,X5,xR)
& aElement0(X7) )
| aReductOfIn0(X6,X5,xR) ) )
| X5 = X6 )
& sdtmndtasgtdt0(X4,xR,X6)
& ( ( sdtmndtplgtdt0(X4,xR,X6)
& ( ? [X8] :
( sdtmndtplgtdt0(X8,xR,X6)
& aReductOfIn0(X8,X4,xR)
& aElement0(X8) )
| aReductOfIn0(X6,X4,xR) ) )
| X4 = X6 )
& aElement0(X6) ) ) ),
inference(rectify,[],[f16]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ( ( sdtmndtasgtdt0(X0,xR,X2)
| sdtmndtplgtdt0(X0,xR,X2)
| ? [X3] :
( sdtmndtplgtdt0(X3,xR,X2)
& aReductOfIn0(X3,X0,xR)
& aElement0(X3) )
| aReductOfIn0(X2,X0,xR)
| X0 = X2 )
& ( sdtmndtasgtdt0(X0,xR,X1)
| sdtmndtplgtdt0(X0,xR,X1)
| ? [X4] :
( sdtmndtplgtdt0(X4,xR,X1)
& aReductOfIn0(X4,X0,xR)
& aElement0(X4) )
| aReductOfIn0(X1,X0,xR)
| X0 = X1 )
& aElement0(X2)
& aElement0(X1)
& aElement0(X0) )
=> ( iLess0(X0,xa)
=> ? [X5] :
( sdtmndtasgtdt0(X2,xR,X5)
& ( ( sdtmndtplgtdt0(X2,xR,X5)
& ( ? [X6] :
( sdtmndtplgtdt0(X6,xR,X5)
& aReductOfIn0(X6,X2,xR)
& aElement0(X6) )
| aReductOfIn0(X5,X2,xR) ) )
| X2 = X5 )
& sdtmndtasgtdt0(X1,xR,X5)
& ( ( sdtmndtplgtdt0(X1,xR,X5)
& ( ? [X7] :
( sdtmndtplgtdt0(X7,xR,X5)
& aReductOfIn0(X7,X1,xR)
& aElement0(X7) )
| aReductOfIn0(X5,X1,xR) ) )
| X1 = X5 )
& aElement0(X5) ) ) ),
inference(rectify,[],[f18]) ).
fof(f33,plain,
( sdtmndtasgtdt0(xv,xR,xw)
& ( ( sdtmndtplgtdt0(xv,xR,xw)
& ( ? [X0] :
( sdtmndtplgtdt0(X0,xR,xw)
& aReductOfIn0(X0,xv,xR)
& aElement0(X0) )
| aReductOfIn0(xw,xv,xR) ) )
| xv = xw )
& sdtmndtasgtdt0(xu,xR,xw)
& ( ( sdtmndtplgtdt0(xu,xR,xw)
& ( ? [X1] :
( sdtmndtplgtdt0(X1,xR,xw)
& aReductOfIn0(X1,xu,xR)
& aElement0(X1) )
| aReductOfIn0(xw,xu,xR) ) )
| xu = xw )
& aElement0(xw) ),
inference(rectify,[],[f22]) ).
fof(f34,plain,
( aNormalFormOfIn0(xd,xw,xR)
& ~ ? [X0] : aReductOfIn0(X0,xd,xR)
& sdtmndtasgtdt0(xw,xR,xd)
& ( ( sdtmndtplgtdt0(xw,xR,xd)
& ( ? [X1] :
( sdtmndtplgtdt0(X1,xR,xd)
& aReductOfIn0(X1,xw,xR)
& aElement0(X1) )
| aReductOfIn0(xd,xw,xR) ) )
| xw = xd )
& aElement0(xd) ),
inference(rectify,[],[f23]) ).
fof(f35,plain,
~ ? [X0] :
( ( sdtmndtasgtdt0(xd,xR,X0)
| sdtmndtplgtdt0(xd,xR,X0)
| ? [X1] :
( sdtmndtplgtdt0(X1,xR,X0)
& aReductOfIn0(X1,xd,xR)
& aElement0(X1) )
| aReductOfIn0(X0,xd,xR)
| xd = X0 )
& ( sdtmndtasgtdt0(xb,xR,X0)
| sdtmndtplgtdt0(xb,xR,X0)
| ? [X2] :
( sdtmndtplgtdt0(X2,xR,X0)
& aReductOfIn0(X2,xb,xR)
& aElement0(X2) )
| aReductOfIn0(X0,xb,xR)
| xb = X0 )
& aElement0(X0) ),
inference(rectify,[],[f25]) ).
fof(f36,plain,
! [X0,X1] :
( ! [X2] :
( aElement0(X2)
| ~ aReductOfIn0(X2,X0,X1) )
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f37,plain,
! [X0,X1] :
( ! [X2] :
( aElement0(X2)
| ~ aReductOfIn0(X2,X0,X1) )
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f36]) ).
fof(f44,plain,
! [X0,X1,X2,X3] :
( sdtmndtasgtdt0(X0,X1,X3)
| ~ sdtmndtasgtdt0(X2,X1,X3)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f45,plain,
! [X0,X1,X2,X3] :
( sdtmndtasgtdt0(X0,X1,X3)
| ~ sdtmndtasgtdt0(X2,X1,X3)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f44]) ).
fof(f56,plain,
( isTerminating0(xR)
& ! [X0,X1] :
( iLess0(X1,X0)
| ( ~ sdtmndtplgtdt0(X0,xR,X1)
& ! [X2] :
( ~ sdtmndtplgtdt0(X2,xR,X1)
| ~ aReductOfIn0(X2,X0,xR)
| ~ aElement0(X2) )
& ~ aReductOfIn0(X1,X0,xR) )
| ~ aElement0(X1)
| ~ aElement0(X0) )
& isLocallyConfluent0(xR)
& ! [X3,X4,X5] :
( ? [X6] :
( sdtmndtasgtdt0(X5,xR,X6)
& ( ( sdtmndtplgtdt0(X5,xR,X6)
& ( ? [X7] :
( sdtmndtplgtdt0(X7,xR,X6)
& aReductOfIn0(X7,X5,xR)
& aElement0(X7) )
| aReductOfIn0(X6,X5,xR) ) )
| X5 = X6 )
& sdtmndtasgtdt0(X4,xR,X6)
& ( ( sdtmndtplgtdt0(X4,xR,X6)
& ( ? [X8] :
( sdtmndtplgtdt0(X8,xR,X6)
& aReductOfIn0(X8,X4,xR)
& aElement0(X8) )
| aReductOfIn0(X6,X4,xR) ) )
| X4 = X6 )
& aElement0(X6) )
| ~ aReductOfIn0(X5,X3,xR)
| ~ aReductOfIn0(X4,X3,xR)
| ~ aElement0(X5)
| ~ aElement0(X4)
| ~ aElement0(X3) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f57,plain,
( isTerminating0(xR)
& ! [X0,X1] :
( iLess0(X1,X0)
| ( ~ sdtmndtplgtdt0(X0,xR,X1)
& ! [X2] :
( ~ sdtmndtplgtdt0(X2,xR,X1)
| ~ aReductOfIn0(X2,X0,xR)
| ~ aElement0(X2) )
& ~ aReductOfIn0(X1,X0,xR) )
| ~ aElement0(X1)
| ~ aElement0(X0) )
& isLocallyConfluent0(xR)
& ! [X3,X4,X5] :
( ? [X6] :
( sdtmndtasgtdt0(X5,xR,X6)
& ( ( sdtmndtplgtdt0(X5,xR,X6)
& ( ? [X7] :
( sdtmndtplgtdt0(X7,xR,X6)
& aReductOfIn0(X7,X5,xR)
& aElement0(X7) )
| aReductOfIn0(X6,X5,xR) ) )
| X5 = X6 )
& sdtmndtasgtdt0(X4,xR,X6)
& ( ( sdtmndtplgtdt0(X4,xR,X6)
& ( ? [X8] :
( sdtmndtplgtdt0(X8,xR,X6)
& aReductOfIn0(X8,X4,xR)
& aElement0(X8) )
| aReductOfIn0(X6,X4,xR) ) )
| X4 = X6 )
& aElement0(X6) )
| ~ aReductOfIn0(X5,X3,xR)
| ~ aReductOfIn0(X4,X3,xR)
| ~ aElement0(X5)
| ~ aElement0(X4)
| ~ aElement0(X3) ) ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ? [X5] :
( sdtmndtasgtdt0(X2,xR,X5)
& ( ( sdtmndtplgtdt0(X2,xR,X5)
& ( ? [X6] :
( sdtmndtplgtdt0(X6,xR,X5)
& aReductOfIn0(X6,X2,xR)
& aElement0(X6) )
| aReductOfIn0(X5,X2,xR) ) )
| X2 = X5 )
& sdtmndtasgtdt0(X1,xR,X5)
& ( ( sdtmndtplgtdt0(X1,xR,X5)
& ( ? [X7] :
( sdtmndtplgtdt0(X7,xR,X5)
& aReductOfIn0(X7,X1,xR)
& aElement0(X7) )
| aReductOfIn0(X5,X1,xR) ) )
| X1 = X5 )
& aElement0(X5) )
| ~ iLess0(X0,xa)
| ( ~ sdtmndtasgtdt0(X0,xR,X2)
& ~ sdtmndtplgtdt0(X0,xR,X2)
& ! [X3] :
( ~ sdtmndtplgtdt0(X3,xR,X2)
| ~ aReductOfIn0(X3,X0,xR)
| ~ aElement0(X3) )
& ~ aReductOfIn0(X2,X0,xR)
& X0 != X2 )
| ( ~ sdtmndtasgtdt0(X0,xR,X1)
& ~ sdtmndtplgtdt0(X0,xR,X1)
& ! [X4] :
( ~ sdtmndtplgtdt0(X4,xR,X1)
| ~ aReductOfIn0(X4,X0,xR)
| ~ aElement0(X4) )
& ~ aReductOfIn0(X1,X0,xR)
& X0 != X1 )
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ? [X5] :
( sdtmndtasgtdt0(X2,xR,X5)
& ( ( sdtmndtplgtdt0(X2,xR,X5)
& ( ? [X6] :
( sdtmndtplgtdt0(X6,xR,X5)
& aReductOfIn0(X6,X2,xR)
& aElement0(X6) )
| aReductOfIn0(X5,X2,xR) ) )
| X2 = X5 )
& sdtmndtasgtdt0(X1,xR,X5)
& ( ( sdtmndtplgtdt0(X1,xR,X5)
& ( ? [X7] :
( sdtmndtplgtdt0(X7,xR,X5)
& aReductOfIn0(X7,X1,xR)
& aElement0(X7) )
| aReductOfIn0(X5,X1,xR) ) )
| X1 = X5 )
& aElement0(X5) )
| ~ iLess0(X0,xa)
| ( ~ sdtmndtasgtdt0(X0,xR,X2)
& ~ sdtmndtplgtdt0(X0,xR,X2)
& ! [X3] :
( ~ sdtmndtplgtdt0(X3,xR,X2)
| ~ aReductOfIn0(X3,X0,xR)
| ~ aElement0(X3) )
& ~ aReductOfIn0(X2,X0,xR)
& X0 != X2 )
| ( ~ sdtmndtasgtdt0(X0,xR,X1)
& ~ sdtmndtplgtdt0(X0,xR,X1)
& ! [X4] :
( ~ sdtmndtplgtdt0(X4,xR,X1)
| ~ aReductOfIn0(X4,X0,xR)
| ~ aElement0(X4) )
& ~ aReductOfIn0(X1,X0,xR)
& X0 != X1 )
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f58]) ).
fof(f60,plain,
( aNormalFormOfIn0(xd,xw,xR)
& ! [X0] : ~ aReductOfIn0(X0,xd,xR)
& sdtmndtasgtdt0(xw,xR,xd)
& ( ( sdtmndtplgtdt0(xw,xR,xd)
& ( ? [X1] :
( sdtmndtplgtdt0(X1,xR,xd)
& aReductOfIn0(X1,xw,xR)
& aElement0(X1) )
| aReductOfIn0(xd,xw,xR) ) )
| xw = xd )
& aElement0(xd) ),
inference(ennf_transformation,[],[f34]) ).
fof(f61,plain,
! [X0] :
( ( ~ sdtmndtasgtdt0(xd,xR,X0)
& ~ sdtmndtplgtdt0(xd,xR,X0)
& ! [X1] :
( ~ sdtmndtplgtdt0(X1,xR,X0)
| ~ aReductOfIn0(X1,xd,xR)
| ~ aElement0(X1) )
& ~ aReductOfIn0(X0,xd,xR)
& xd != X0 )
| ( ~ sdtmndtasgtdt0(xb,xR,X0)
& ~ sdtmndtplgtdt0(xb,xR,X0)
& ! [X2] :
( ~ sdtmndtplgtdt0(X2,xR,X0)
| ~ aReductOfIn0(X2,xb,xR)
| ~ aElement0(X2) )
& ~ aReductOfIn0(X0,xb,xR)
& xb != X0 )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f68,plain,
! [X6,X4] :
( ( sdtmndtplgtdt0(X4,xR,X6)
& ( ? [X8] :
( sdtmndtplgtdt0(X8,xR,X6)
& aReductOfIn0(X8,X4,xR)
& aElement0(X8) )
| aReductOfIn0(X6,X4,xR) ) )
| X4 = X6
| ~ sP4(X6,X4) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f69,plain,
( isTerminating0(xR)
& ! [X0,X1] :
( iLess0(X1,X0)
| ( ~ sdtmndtplgtdt0(X0,xR,X1)
& ! [X2] :
( ~ sdtmndtplgtdt0(X2,xR,X1)
| ~ aReductOfIn0(X2,X0,xR)
| ~ aElement0(X2) )
& ~ aReductOfIn0(X1,X0,xR) )
| ~ aElement0(X1)
| ~ aElement0(X0) )
& isLocallyConfluent0(xR)
& ! [X3,X4,X5] :
( ? [X6] :
( sdtmndtasgtdt0(X5,xR,X6)
& ( ( sdtmndtplgtdt0(X5,xR,X6)
& ( ? [X7] :
( sdtmndtplgtdt0(X7,xR,X6)
& aReductOfIn0(X7,X5,xR)
& aElement0(X7) )
| aReductOfIn0(X6,X5,xR) ) )
| X5 = X6 )
& sdtmndtasgtdt0(X4,xR,X6)
& sP4(X6,X4)
& aElement0(X6) )
| ~ aReductOfIn0(X5,X3,xR)
| ~ aReductOfIn0(X4,X3,xR)
| ~ aElement0(X5)
| ~ aElement0(X4)
| ~ aElement0(X3) ) ),
inference(definition_folding,[],[f57,f68]) ).
fof(f70,plain,
! [X5,X1] :
( ( sdtmndtplgtdt0(X1,xR,X5)
& ( ? [X7] :
( sdtmndtplgtdt0(X7,xR,X5)
& aReductOfIn0(X7,X1,xR)
& aElement0(X7) )
| aReductOfIn0(X5,X1,xR) ) )
| X1 = X5
| ~ sP5(X5,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f71,plain,
! [X2,X1] :
( ? [X5] :
( sdtmndtasgtdt0(X2,xR,X5)
& ( ( sdtmndtplgtdt0(X2,xR,X5)
& ( ? [X6] :
( sdtmndtplgtdt0(X6,xR,X5)
& aReductOfIn0(X6,X2,xR)
& aElement0(X6) )
| aReductOfIn0(X5,X2,xR) ) )
| X2 = X5 )
& sdtmndtasgtdt0(X1,xR,X5)
& sP5(X5,X1)
& aElement0(X5) )
| ~ sP6(X2,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f72,plain,
! [X1,X0] :
( ( ~ sdtmndtasgtdt0(X0,xR,X1)
& ~ sdtmndtplgtdt0(X0,xR,X1)
& ! [X4] :
( ~ sdtmndtplgtdt0(X4,xR,X1)
| ~ aReductOfIn0(X4,X0,xR)
| ~ aElement0(X4) )
& ~ aReductOfIn0(X1,X0,xR)
& X0 != X1 )
| ~ sP7(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f73,plain,
! [X0,X1,X2] :
( sP6(X2,X1)
| ~ iLess0(X0,xa)
| ( ~ sdtmndtasgtdt0(X0,xR,X2)
& ~ sdtmndtplgtdt0(X0,xR,X2)
& ! [X3] :
( ~ sdtmndtplgtdt0(X3,xR,X2)
| ~ aReductOfIn0(X3,X0,xR)
| ~ aElement0(X3) )
& ~ aReductOfIn0(X2,X0,xR)
& X0 != X2 )
| sP7(X1,X0)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(definition_folding,[],[f59,f72,f71,f70]) ).
fof(f74,plain,
! [X0] :
( ( ~ sdtmndtasgtdt0(xb,xR,X0)
& ~ sdtmndtplgtdt0(xb,xR,X0)
& ! [X2] :
( ~ sdtmndtplgtdt0(X2,xR,X0)
| ~ aReductOfIn0(X2,xb,xR)
| ~ aElement0(X2) )
& ~ aReductOfIn0(X0,xb,xR)
& xb != X0 )
| ~ sP8(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f75,plain,
! [X0] :
( ( ~ sdtmndtasgtdt0(xd,xR,X0)
& ~ sdtmndtplgtdt0(xd,xR,X0)
& ! [X1] :
( ~ sdtmndtplgtdt0(X1,xR,X0)
| ~ aReductOfIn0(X1,xd,xR)
| ~ aElement0(X1) )
& ~ aReductOfIn0(X0,xd,xR)
& xd != X0 )
| sP8(X0)
| ~ aElement0(X0) ),
inference(definition_folding,[],[f61,f74]) ).
fof(f110,plain,
! [X4,X5] :
( ? [X6] :
( sdtmndtasgtdt0(X5,xR,X6)
& ( ( sdtmndtplgtdt0(X5,xR,X6)
& ( ? [X7] :
( sdtmndtplgtdt0(X7,xR,X6)
& aReductOfIn0(X7,X5,xR)
& aElement0(X7) )
| aReductOfIn0(X6,X5,xR) ) )
| X5 = X6 )
& sdtmndtasgtdt0(X4,xR,X6)
& sP4(X6,X4)
& aElement0(X6) )
=> ( sdtmndtasgtdt0(X5,xR,sK23(X4,X5))
& ( ( sdtmndtplgtdt0(X5,xR,sK23(X4,X5))
& ( ? [X7] :
( sdtmndtplgtdt0(X7,xR,sK23(X4,X5))
& aReductOfIn0(X7,X5,xR)
& aElement0(X7) )
| aReductOfIn0(sK23(X4,X5),X5,xR) ) )
| sK23(X4,X5) = X5 )
& sdtmndtasgtdt0(X4,xR,sK23(X4,X5))
& sP4(sK23(X4,X5),X4)
& aElement0(sK23(X4,X5)) ) ),
introduced(choice_axiom,[]) ).
fof(f111,plain,
! [X4,X5] :
( ? [X7] :
( sdtmndtplgtdt0(X7,xR,sK23(X4,X5))
& aReductOfIn0(X7,X5,xR)
& aElement0(X7) )
=> ( sdtmndtplgtdt0(sK24(X4,X5),xR,sK23(X4,X5))
& aReductOfIn0(sK24(X4,X5),X5,xR)
& aElement0(sK24(X4,X5)) ) ),
introduced(choice_axiom,[]) ).
fof(f112,plain,
( isTerminating0(xR)
& ! [X0,X1] :
( iLess0(X1,X0)
| ( ~ sdtmndtplgtdt0(X0,xR,X1)
& ! [X2] :
( ~ sdtmndtplgtdt0(X2,xR,X1)
| ~ aReductOfIn0(X2,X0,xR)
| ~ aElement0(X2) )
& ~ aReductOfIn0(X1,X0,xR) )
| ~ aElement0(X1)
| ~ aElement0(X0) )
& isLocallyConfluent0(xR)
& ! [X3,X4,X5] :
( ( sdtmndtasgtdt0(X5,xR,sK23(X4,X5))
& ( ( sdtmndtplgtdt0(X5,xR,sK23(X4,X5))
& ( ( sdtmndtplgtdt0(sK24(X4,X5),xR,sK23(X4,X5))
& aReductOfIn0(sK24(X4,X5),X5,xR)
& aElement0(sK24(X4,X5)) )
| aReductOfIn0(sK23(X4,X5),X5,xR) ) )
| sK23(X4,X5) = X5 )
& sdtmndtasgtdt0(X4,xR,sK23(X4,X5))
& sP4(sK23(X4,X5),X4)
& aElement0(sK23(X4,X5)) )
| ~ aReductOfIn0(X5,X3,xR)
| ~ aReductOfIn0(X4,X3,xR)
| ~ aElement0(X5)
| ~ aElement0(X4)
| ~ aElement0(X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23,sK24])],[f69,f111,f110]) ).
fof(f113,plain,
! [X1,X0] :
( ( ~ sdtmndtasgtdt0(X0,xR,X1)
& ~ sdtmndtplgtdt0(X0,xR,X1)
& ! [X4] :
( ~ sdtmndtplgtdt0(X4,xR,X1)
| ~ aReductOfIn0(X4,X0,xR)
| ~ aElement0(X4) )
& ~ aReductOfIn0(X1,X0,xR)
& X0 != X1 )
| ~ sP7(X1,X0) ),
inference(nnf_transformation,[],[f72]) ).
fof(f114,plain,
! [X0,X1] :
( ( ~ sdtmndtasgtdt0(X1,xR,X0)
& ~ sdtmndtplgtdt0(X1,xR,X0)
& ! [X2] :
( ~ sdtmndtplgtdt0(X2,xR,X0)
| ~ aReductOfIn0(X2,X1,xR)
| ~ aElement0(X2) )
& ~ aReductOfIn0(X0,X1,xR)
& X0 != X1 )
| ~ sP7(X0,X1) ),
inference(rectify,[],[f113]) ).
fof(f115,plain,
! [X2,X1] :
( ? [X5] :
( sdtmndtasgtdt0(X2,xR,X5)
& ( ( sdtmndtplgtdt0(X2,xR,X5)
& ( ? [X6] :
( sdtmndtplgtdt0(X6,xR,X5)
& aReductOfIn0(X6,X2,xR)
& aElement0(X6) )
| aReductOfIn0(X5,X2,xR) ) )
| X2 = X5 )
& sdtmndtasgtdt0(X1,xR,X5)
& sP5(X5,X1)
& aElement0(X5) )
| ~ sP6(X2,X1) ),
inference(nnf_transformation,[],[f71]) ).
fof(f116,plain,
! [X0,X1] :
( ? [X2] :
( sdtmndtasgtdt0(X0,xR,X2)
& ( ( sdtmndtplgtdt0(X0,xR,X2)
& ( ? [X3] :
( sdtmndtplgtdt0(X3,xR,X2)
& aReductOfIn0(X3,X0,xR)
& aElement0(X3) )
| aReductOfIn0(X2,X0,xR) ) )
| X0 = X2 )
& sdtmndtasgtdt0(X1,xR,X2)
& sP5(X2,X1)
& aElement0(X2) )
| ~ sP6(X0,X1) ),
inference(rectify,[],[f115]) ).
fof(f117,plain,
! [X0,X1] :
( ? [X2] :
( sdtmndtasgtdt0(X0,xR,X2)
& ( ( sdtmndtplgtdt0(X0,xR,X2)
& ( ? [X3] :
( sdtmndtplgtdt0(X3,xR,X2)
& aReductOfIn0(X3,X0,xR)
& aElement0(X3) )
| aReductOfIn0(X2,X0,xR) ) )
| X0 = X2 )
& sdtmndtasgtdt0(X1,xR,X2)
& sP5(X2,X1)
& aElement0(X2) )
=> ( sdtmndtasgtdt0(X0,xR,sK25(X0,X1))
& ( ( sdtmndtplgtdt0(X0,xR,sK25(X0,X1))
& ( ? [X3] :
( sdtmndtplgtdt0(X3,xR,sK25(X0,X1))
& aReductOfIn0(X3,X0,xR)
& aElement0(X3) )
| aReductOfIn0(sK25(X0,X1),X0,xR) ) )
| sK25(X0,X1) = X0 )
& sdtmndtasgtdt0(X1,xR,sK25(X0,X1))
& sP5(sK25(X0,X1),X1)
& aElement0(sK25(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f118,plain,
! [X0,X1] :
( ? [X3] :
( sdtmndtplgtdt0(X3,xR,sK25(X0,X1))
& aReductOfIn0(X3,X0,xR)
& aElement0(X3) )
=> ( sdtmndtplgtdt0(sK26(X0,X1),xR,sK25(X0,X1))
& aReductOfIn0(sK26(X0,X1),X0,xR)
& aElement0(sK26(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f119,plain,
! [X0,X1] :
( ( sdtmndtasgtdt0(X0,xR,sK25(X0,X1))
& ( ( sdtmndtplgtdt0(X0,xR,sK25(X0,X1))
& ( ( sdtmndtplgtdt0(sK26(X0,X1),xR,sK25(X0,X1))
& aReductOfIn0(sK26(X0,X1),X0,xR)
& aElement0(sK26(X0,X1)) )
| aReductOfIn0(sK25(X0,X1),X0,xR) ) )
| sK25(X0,X1) = X0 )
& sdtmndtasgtdt0(X1,xR,sK25(X0,X1))
& sP5(sK25(X0,X1),X1)
& aElement0(sK25(X0,X1)) )
| ~ sP6(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25,sK26])],[f116,f118,f117]) ).
fof(f127,plain,
( ? [X0] :
( sdtmndtplgtdt0(X0,xR,xb)
& aReductOfIn0(X0,xu,xR)
& aElement0(X0) )
=> ( sdtmndtplgtdt0(sK30,xR,xb)
& aReductOfIn0(sK30,xu,xR)
& aElement0(sK30) ) ),
introduced(choice_axiom,[]) ).
fof(f128,plain,
( sdtmndtasgtdt0(xu,xR,xb)
& ( ( sdtmndtplgtdt0(xu,xR,xb)
& ( ( sdtmndtplgtdt0(sK30,xR,xb)
& aReductOfIn0(sK30,xu,xR)
& aElement0(sK30) )
| aReductOfIn0(xb,xu,xR) ) )
| xb = xu )
& aReductOfIn0(xu,xa,xR)
& aElement0(xu) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK30])],[f20,f127]) ).
fof(f131,plain,
( ? [X0] :
( sdtmndtplgtdt0(X0,xR,xw)
& aReductOfIn0(X0,xv,xR)
& aElement0(X0) )
=> ( sdtmndtplgtdt0(sK32,xR,xw)
& aReductOfIn0(sK32,xv,xR)
& aElement0(sK32) ) ),
introduced(choice_axiom,[]) ).
fof(f132,plain,
( ? [X1] :
( sdtmndtplgtdt0(X1,xR,xw)
& aReductOfIn0(X1,xu,xR)
& aElement0(X1) )
=> ( sdtmndtplgtdt0(sK33,xR,xw)
& aReductOfIn0(sK33,xu,xR)
& aElement0(sK33) ) ),
introduced(choice_axiom,[]) ).
fof(f133,plain,
( sdtmndtasgtdt0(xv,xR,xw)
& ( ( sdtmndtplgtdt0(xv,xR,xw)
& ( ( sdtmndtplgtdt0(sK32,xR,xw)
& aReductOfIn0(sK32,xv,xR)
& aElement0(sK32) )
| aReductOfIn0(xw,xv,xR) ) )
| xv = xw )
& sdtmndtasgtdt0(xu,xR,xw)
& ( ( sdtmndtplgtdt0(xu,xR,xw)
& ( ( sdtmndtplgtdt0(sK33,xR,xw)
& aReductOfIn0(sK33,xu,xR)
& aElement0(sK33) )
| aReductOfIn0(xw,xu,xR) ) )
| xu = xw )
& aElement0(xw) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK32,sK33])],[f33,f132,f131]) ).
fof(f134,plain,
( ? [X1] :
( sdtmndtplgtdt0(X1,xR,xd)
& aReductOfIn0(X1,xw,xR)
& aElement0(X1) )
=> ( sdtmndtplgtdt0(sK34,xR,xd)
& aReductOfIn0(sK34,xw,xR)
& aElement0(sK34) ) ),
introduced(choice_axiom,[]) ).
fof(f135,plain,
( aNormalFormOfIn0(xd,xw,xR)
& ! [X0] : ~ aReductOfIn0(X0,xd,xR)
& sdtmndtasgtdt0(xw,xR,xd)
& ( ( sdtmndtplgtdt0(xw,xR,xd)
& ( ( sdtmndtplgtdt0(sK34,xR,xd)
& aReductOfIn0(sK34,xw,xR)
& aElement0(sK34) )
| aReductOfIn0(xd,xw,xR) ) )
| xw = xd )
& aElement0(xd) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK34])],[f60,f134]) ).
fof(f136,plain,
! [X0] :
( ( ~ sdtmndtasgtdt0(xb,xR,X0)
& ~ sdtmndtplgtdt0(xb,xR,X0)
& ! [X2] :
( ~ sdtmndtplgtdt0(X2,xR,X0)
| ~ aReductOfIn0(X2,xb,xR)
| ~ aElement0(X2) )
& ~ aReductOfIn0(X0,xb,xR)
& xb != X0 )
| ~ sP8(X0) ),
inference(nnf_transformation,[],[f74]) ).
fof(f137,plain,
! [X0] :
( ( ~ sdtmndtasgtdt0(xb,xR,X0)
& ~ sdtmndtplgtdt0(xb,xR,X0)
& ! [X1] :
( ~ sdtmndtplgtdt0(X1,xR,X0)
| ~ aReductOfIn0(X1,xb,xR)
| ~ aElement0(X1) )
& ~ aReductOfIn0(X0,xb,xR)
& xb != X0 )
| ~ sP8(X0) ),
inference(rectify,[],[f136]) ).
fof(f138,plain,
! [X2,X0,X1] :
( aElement0(X2)
| ~ aReductOfIn0(X2,X0,X1)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f148,plain,
! [X2,X3,X0,X1] :
( sdtmndtasgtdt0(X0,X1,X3)
| ~ sdtmndtasgtdt0(X2,X1,X3)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f183,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[],[f15]) ).
fof(f197,plain,
! [X0,X1] :
( iLess0(X1,X0)
| ~ aReductOfIn0(X1,X0,xR)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f201,plain,
aElement0(xa),
inference(cnf_transformation,[],[f17]) ).
fof(f202,plain,
aElement0(xb),
inference(cnf_transformation,[],[f17]) ).
fof(f208,plain,
! [X0,X1] :
( ~ sdtmndtasgtdt0(X1,xR,X0)
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f114]) ).
fof(f209,plain,
! [X0,X1] :
( aElement0(sK25(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f119]) ).
fof(f211,plain,
! [X0,X1] :
( sdtmndtasgtdt0(X1,xR,sK25(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f119]) ).
fof(f216,plain,
! [X0,X1] :
( sdtmndtasgtdt0(X0,xR,sK25(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f119]) ).
fof(f225,plain,
! [X2,X0,X1] :
( sP6(X2,X1)
| ~ iLess0(X0,xa)
| ~ sdtmndtasgtdt0(X0,xR,X2)
| sP7(X1,X0)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f234,plain,
aElement0(xu),
inference(cnf_transformation,[],[f128]) ).
fof(f235,plain,
aReductOfIn0(xu,xa,xR),
inference(cnf_transformation,[],[f128]) ).
fof(f240,plain,
sdtmndtasgtdt0(xu,xR,xb),
inference(cnf_transformation,[],[f128]) ).
fof(f248,plain,
aElement0(xw),
inference(cnf_transformation,[],[f133]) ).
fof(f253,plain,
sdtmndtasgtdt0(xu,xR,xw),
inference(cnf_transformation,[],[f133]) ).
fof(f259,plain,
aElement0(xd),
inference(cnf_transformation,[],[f135]) ).
fof(f264,plain,
sdtmndtasgtdt0(xw,xR,xd),
inference(cnf_transformation,[],[f135]) ).
fof(f271,plain,
! [X0] :
( ~ sdtmndtasgtdt0(xb,xR,X0)
| ~ sP8(X0) ),
inference(cnf_transformation,[],[f137]) ).
fof(f276,plain,
! [X0] :
( ~ sdtmndtasgtdt0(xd,xR,X0)
| sP8(X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f75]) ).
cnf(c_49,plain,
( ~ aReductOfIn0(X0,X1,X2)
| ~ aElement0(X1)
| ~ aRewritingSystem0(X2)
| aElement0(X0) ),
inference(cnf_transformation,[],[f138]) ).
cnf(c_59,plain,
( ~ sdtmndtasgtdt0(X0,X1,X2)
| ~ sdtmndtasgtdt0(X3,X1,X0)
| ~ aElement0(X0)
| ~ aElement0(X2)
| ~ aElement0(X3)
| ~ aRewritingSystem0(X1)
| sdtmndtasgtdt0(X3,X1,X2) ),
inference(cnf_transformation,[],[f148]) ).
cnf(c_94,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[],[f183]) ).
cnf(c_102,plain,
( ~ aReductOfIn0(X0,X1,xR)
| ~ aElement0(X0)
| ~ aElement0(X1)
| iLess0(X0,X1) ),
inference(cnf_transformation,[],[f197]) ).
cnf(c_113,plain,
aElement0(xb),
inference(cnf_transformation,[],[f202]) ).
cnf(c_114,plain,
aElement0(xa),
inference(cnf_transformation,[],[f201]) ).
cnf(c_115,plain,
( ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ sP7(X1,X0) ),
inference(cnf_transformation,[],[f208]) ).
cnf(c_120,plain,
( ~ sP6(X0,X1)
| sdtmndtasgtdt0(X0,xR,sK25(X0,X1)) ),
inference(cnf_transformation,[],[f216]) ).
cnf(c_125,plain,
( ~ sP6(X0,X1)
| sdtmndtasgtdt0(X1,xR,sK25(X0,X1)) ),
inference(cnf_transformation,[],[f211]) ).
cnf(c_127,plain,
( ~ sP6(X0,X1)
| aElement0(sK25(X0,X1)) ),
inference(cnf_transformation,[],[f209]) ).
cnf(c_132,plain,
( ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ iLess0(X0,xa)
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2)
| sP7(X2,X0)
| sP6(X1,X2) ),
inference(cnf_transformation,[],[f225]) ).
cnf(c_145,plain,
sdtmndtasgtdt0(xu,xR,xb),
inference(cnf_transformation,[],[f240]) ).
cnf(c_150,plain,
aReductOfIn0(xu,xa,xR),
inference(cnf_transformation,[],[f235]) ).
cnf(c_151,plain,
aElement0(xu),
inference(cnf_transformation,[],[f234]) ).
cnf(c_164,plain,
sdtmndtasgtdt0(xu,xR,xw),
inference(cnf_transformation,[],[f253]) ).
cnf(c_169,plain,
aElement0(xw),
inference(cnf_transformation,[],[f248]) ).
cnf(c_172,plain,
sdtmndtasgtdt0(xw,xR,xd),
inference(cnf_transformation,[],[f264]) ).
cnf(c_177,plain,
aElement0(xd),
inference(cnf_transformation,[],[f259]) ).
cnf(c_178,plain,
( ~ sdtmndtasgtdt0(xb,xR,X0)
| ~ sP8(X0) ),
inference(cnf_transformation,[],[f271]) ).
cnf(c_183,negated_conjecture,
( ~ sdtmndtasgtdt0(xd,xR,X0)
| ~ aElement0(X0)
| sP8(X0) ),
inference(cnf_transformation,[],[f276]) ).
cnf(c_2619,plain,
( X0 != xR
| ~ aReductOfIn0(X1,X2,X0)
| ~ aElement0(X2)
| aElement0(X1) ),
inference(resolution_lifted,[status(thm)],[c_49,c_94]) ).
cnf(c_2620,plain,
( ~ aReductOfIn0(X0,X1,xR)
| ~ aElement0(X1)
| aElement0(X0) ),
inference(unflattening,[status(thm)],[c_2619]) ).
cnf(c_2670,plain,
( X0 != xR
| ~ sdtmndtasgtdt0(X1,X0,X2)
| ~ sdtmndtasgtdt0(X3,X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3)
| sdtmndtasgtdt0(X3,X0,X2) ),
inference(resolution_lifted,[status(thm)],[c_59,c_94]) ).
cnf(c_2671,plain,
( ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ sdtmndtasgtdt0(X2,xR,X0)
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2)
| sdtmndtasgtdt0(X2,xR,X1) ),
inference(unflattening,[status(thm)],[c_2670]) ).
cnf(c_2840,plain,
( ~ aReductOfIn0(X0,X1,xR)
| ~ aElement0(X1)
| iLess0(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_102,c_2620]) ).
cnf(c_14274,plain,
( ~ sP8(sK25(xb,X0))
| ~ sP6(xb,X0) ),
inference(superposition,[status(thm)],[c_120,c_178]) ).
cnf(c_14323,plain,
( ~ aElement0(sK25(X0,xd))
| ~ sP6(X0,xd)
| sP8(sK25(X0,xd)) ),
inference(superposition,[status(thm)],[c_125,c_183]) ).
cnf(c_14440,plain,
( ~ sP6(X0,xd)
| sP8(sK25(X0,xd)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14323,c_127]) ).
cnf(c_14453,plain,
~ sP6(xb,xd),
inference(superposition,[status(thm)],[c_14440,c_14274]) ).
cnf(c_14479,plain,
( ~ sdtmndtasgtdt0(X0,xR,xw)
| ~ aElement0(X0)
| ~ aElement0(xw)
| ~ aElement0(xd)
| sdtmndtasgtdt0(X0,xR,xd) ),
inference(superposition,[status(thm)],[c_172,c_2671]) ).
cnf(c_14482,plain,
( ~ sdtmndtasgtdt0(X0,xR,xw)
| ~ aElement0(X0)
| sdtmndtasgtdt0(X0,xR,xd) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14479,c_177,c_169]) ).
cnf(c_14659,plain,
( ~ aElement0(xa)
| iLess0(xu,xa) ),
inference(superposition,[status(thm)],[c_150,c_2840]) ).
cnf(c_14666,plain,
iLess0(xu,xa),
inference(forward_subsumption_resolution,[status(thm)],[c_14659,c_114]) ).
cnf(c_18486,plain,
( ~ iLess0(xu,xa)
| ~ aElement0(X0)
| ~ aElement0(xb)
| ~ aElement0(xu)
| sP7(X0,xu)
| sP6(xb,X0) ),
inference(superposition,[status(thm)],[c_145,c_132]) ).
cnf(c_18540,plain,
( ~ aElement0(X0)
| sP7(X0,xu)
| sP6(xb,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18486,c_151,c_113,c_14666]) ).
cnf(c_27166,plain,
( ~ aElement0(xu)
| sdtmndtasgtdt0(xu,xR,xd) ),
inference(superposition,[status(thm)],[c_164,c_14482]) ).
cnf(c_27168,plain,
sdtmndtasgtdt0(xu,xR,xd),
inference(forward_subsumption_resolution,[status(thm)],[c_27166,c_151]) ).
cnf(c_27181,plain,
~ sP7(xd,xu),
inference(superposition,[status(thm)],[c_27168,c_115]) ).
cnf(c_27311,plain,
( ~ aElement0(xd)
| sP6(xb,xd) ),
inference(superposition,[status(thm)],[c_18540,c_27181]) ).
cnf(c_27316,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_27311,c_14453,c_177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : COM020+4 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 13:31:07 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.31/1.65 % SZS status Started for theBenchmark.p
% 7.31/1.65 % SZS status Theorem for theBenchmark.p
% 7.31/1.65
% 7.31/1.65 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 7.31/1.65
% 7.31/1.65 ------ iProver source info
% 7.31/1.65
% 7.31/1.65 git: date: 2023-05-31 18:12:56 +0000
% 7.31/1.65 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 7.31/1.65 git: non_committed_changes: false
% 7.31/1.65 git: last_make_outside_of_git: false
% 7.31/1.65
% 7.31/1.65 ------ Parsing...
% 7.31/1.65 ------ Clausification by vclausify_rel & Parsing by iProver...
% 7.31/1.65
% 7.31/1.65 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 5 0s sf_e pe_s pe_e
% 7.31/1.65
% 7.31/1.65 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 7.31/1.65
% 7.31/1.65 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.31/1.65 ------ Proving...
% 7.31/1.65 ------ Problem Properties
% 7.31/1.65
% 7.31/1.65
% 7.31/1.65 clauses 122
% 7.31/1.65 conjectures 3
% 7.31/1.65 EPR 75
% 7.31/1.65 Horn 61
% 7.31/1.65 unary 21
% 7.31/1.65 binary 35
% 7.31/1.65 lits 381
% 7.31/1.65 lits eq 37
% 7.31/1.65 fd_pure 0
% 7.31/1.65 fd_pseudo 0
% 7.31/1.65 fd_cond 0
% 7.31/1.65 fd_pseudo_cond 9
% 7.31/1.65 AC symbols 0
% 7.31/1.65
% 7.31/1.65 ------ Schedule dynamic 5 is on
% 7.31/1.65
% 7.31/1.65 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.31/1.65
% 7.31/1.65
% 7.31/1.65 ------
% 7.31/1.65 Current options:
% 7.31/1.65 ------
% 7.31/1.65
% 7.31/1.65
% 7.31/1.65
% 7.31/1.65
% 7.31/1.65 ------ Proving...
% 7.31/1.65
% 7.31/1.65
% 7.31/1.65 % SZS status Theorem for theBenchmark.p
% 7.31/1.65
% 7.31/1.65 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.31/1.65
% 7.31/1.65
%------------------------------------------------------------------------------