TSTP Solution File: COM019+4 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : COM019+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n026.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 : Fri May 3 02:10:29 EDT 2024
% Result : Theorem 8.16s 1.66s
% Output : CNFRefutation 8.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 23
% Syntax : Number of formulae : 115 ( 32 unt; 0 def)
% Number of atoms : 811 ( 66 equ)
% Maximal formula atoms : 33 ( 7 avg)
% Number of connectives : 940 ( 244 ~; 307 |; 366 &)
% ( 0 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 12 con; 0-2 aty)
% Number of variables : 245 ( 1 sgn 136 !; 67 ?)
% 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,
( sdtmndtasgtdt0(xb,xR,xd)
| sdtmndtplgtdt0(xb,xR,xd)
| ? [X0] :
( sdtmndtplgtdt0(X0,xR,xd)
& aReductOfIn0(X0,xb,xR)
& aElement0(X0) )
| aReductOfIn0(xd,xb,xR)
| xb = xd ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f25,negated_conjecture,
~ ( sdtmndtasgtdt0(xb,xR,xd)
| sdtmndtplgtdt0(xb,xR,xd)
| ? [X0] :
( sdtmndtplgtdt0(X0,xR,xd)
& aReductOfIn0(X0,xb,xR)
& aElement0(X0) )
| aReductOfIn0(xd,xb,xR)
| xb = xd ),
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,X1] :
( ! [X2] :
( aElement0(X2)
| ~ aReductOfIn0(X2,X0,X1) )
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f36,plain,
! [X0,X1] :
( ! [X2] :
( aElement0(X2)
| ~ aReductOfIn0(X2,X0,X1) )
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f35]) ).
fof(f43,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(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(flattening,[],[f43]) ).
fof(f55,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(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(flattening,[],[f55]) ).
fof(f57,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(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(flattening,[],[f57]) ).
fof(f59,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(f60,plain,
( ~ sdtmndtasgtdt0(xb,xR,xd)
& ~ sdtmndtplgtdt0(xb,xR,xd)
& ! [X0] :
( ~ sdtmndtplgtdt0(X0,xR,xd)
| ~ aReductOfIn0(X0,xb,xR)
| ~ aElement0(X0) )
& ~ aReductOfIn0(xd,xb,xR)
& xb != xd ),
inference(ennf_transformation,[],[f25]) ).
fof(f67,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(f68,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,[],[f56,f67]) ).
fof(f69,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(f70,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(f71,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(f72,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,[],[f58,f71,f70,f69]) ).
fof(f107,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,sK22(X4,X5))
& ( ( sdtmndtplgtdt0(X5,xR,sK22(X4,X5))
& ( ? [X7] :
( sdtmndtplgtdt0(X7,xR,sK22(X4,X5))
& aReductOfIn0(X7,X5,xR)
& aElement0(X7) )
| aReductOfIn0(sK22(X4,X5),X5,xR) ) )
| sK22(X4,X5) = X5 )
& sdtmndtasgtdt0(X4,xR,sK22(X4,X5))
& sP4(sK22(X4,X5),X4)
& aElement0(sK22(X4,X5)) ) ),
introduced(choice_axiom,[]) ).
fof(f108,plain,
! [X4,X5] :
( ? [X7] :
( sdtmndtplgtdt0(X7,xR,sK22(X4,X5))
& aReductOfIn0(X7,X5,xR)
& aElement0(X7) )
=> ( sdtmndtplgtdt0(sK23(X4,X5),xR,sK22(X4,X5))
& aReductOfIn0(sK23(X4,X5),X5,xR)
& aElement0(sK23(X4,X5)) ) ),
introduced(choice_axiom,[]) ).
fof(f109,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,sK22(X4,X5))
& ( ( sdtmndtplgtdt0(X5,xR,sK22(X4,X5))
& ( ( sdtmndtplgtdt0(sK23(X4,X5),xR,sK22(X4,X5))
& aReductOfIn0(sK23(X4,X5),X5,xR)
& aElement0(sK23(X4,X5)) )
| aReductOfIn0(sK22(X4,X5),X5,xR) ) )
| sK22(X4,X5) = X5 )
& sdtmndtasgtdt0(X4,xR,sK22(X4,X5))
& sP4(sK22(X4,X5),X4)
& aElement0(sK22(X4,X5)) )
| ~ aReductOfIn0(X5,X3,xR)
| ~ aReductOfIn0(X4,X3,xR)
| ~ aElement0(X5)
| ~ aElement0(X4)
| ~ aElement0(X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22,sK23])],[f68,f108,f107]) ).
fof(f110,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,[],[f71]) ).
fof(f111,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,[],[f110]) ).
fof(f112,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,[],[f70]) ).
fof(f113,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,[],[f112]) ).
fof(f114,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,sK24(X0,X1))
& ( ( sdtmndtplgtdt0(X0,xR,sK24(X0,X1))
& ( ? [X3] :
( sdtmndtplgtdt0(X3,xR,sK24(X0,X1))
& aReductOfIn0(X3,X0,xR)
& aElement0(X3) )
| aReductOfIn0(sK24(X0,X1),X0,xR) ) )
| sK24(X0,X1) = X0 )
& sdtmndtasgtdt0(X1,xR,sK24(X0,X1))
& sP5(sK24(X0,X1),X1)
& aElement0(sK24(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f115,plain,
! [X0,X1] :
( ? [X3] :
( sdtmndtplgtdt0(X3,xR,sK24(X0,X1))
& aReductOfIn0(X3,X0,xR)
& aElement0(X3) )
=> ( sdtmndtplgtdt0(sK25(X0,X1),xR,sK24(X0,X1))
& aReductOfIn0(sK25(X0,X1),X0,xR)
& aElement0(sK25(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f116,plain,
! [X0,X1] :
( ( sdtmndtasgtdt0(X0,xR,sK24(X0,X1))
& ( ( sdtmndtplgtdt0(X0,xR,sK24(X0,X1))
& ( ( sdtmndtplgtdt0(sK25(X0,X1),xR,sK24(X0,X1))
& aReductOfIn0(sK25(X0,X1),X0,xR)
& aElement0(sK25(X0,X1)) )
| aReductOfIn0(sK24(X0,X1),X0,xR) ) )
| sK24(X0,X1) = X0 )
& sdtmndtasgtdt0(X1,xR,sK24(X0,X1))
& sP5(sK24(X0,X1),X1)
& aElement0(sK24(X0,X1)) )
| ~ sP6(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24,sK25])],[f113,f115,f114]) ).
fof(f117,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) ),
inference(nnf_transformation,[],[f69]) ).
fof(f118,plain,
! [X0,X1] :
( ( sdtmndtplgtdt0(X1,xR,X0)
& ( ? [X2] :
( sdtmndtplgtdt0(X2,xR,X0)
& aReductOfIn0(X2,X1,xR)
& aElement0(X2) )
| aReductOfIn0(X0,X1,xR) ) )
| X0 = X1
| ~ sP5(X0,X1) ),
inference(rectify,[],[f117]) ).
fof(f119,plain,
! [X0,X1] :
( ? [X2] :
( sdtmndtplgtdt0(X2,xR,X0)
& aReductOfIn0(X2,X1,xR)
& aElement0(X2) )
=> ( sdtmndtplgtdt0(sK26(X0,X1),xR,X0)
& aReductOfIn0(sK26(X0,X1),X1,xR)
& aElement0(sK26(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f120,plain,
! [X0,X1] :
( ( sdtmndtplgtdt0(X1,xR,X0)
& ( ( sdtmndtplgtdt0(sK26(X0,X1),xR,X0)
& aReductOfIn0(sK26(X0,X1),X1,xR)
& aElement0(sK26(X0,X1)) )
| aReductOfIn0(X0,X1,xR) ) )
| X0 = X1
| ~ sP5(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f118,f119]) ).
fof(f124,plain,
( ? [X0] :
( sdtmndtplgtdt0(X0,xR,xb)
& aReductOfIn0(X0,xu,xR)
& aElement0(X0) )
=> ( sdtmndtplgtdt0(sK29,xR,xb)
& aReductOfIn0(sK29,xu,xR)
& aElement0(sK29) ) ),
introduced(choice_axiom,[]) ).
fof(f125,plain,
( sdtmndtasgtdt0(xu,xR,xb)
& ( ( sdtmndtplgtdt0(xu,xR,xb)
& ( ( sdtmndtplgtdt0(sK29,xR,xb)
& aReductOfIn0(sK29,xu,xR)
& aElement0(sK29) )
| aReductOfIn0(xb,xu,xR) ) )
| xb = xu )
& aReductOfIn0(xu,xa,xR)
& aElement0(xu) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29])],[f20,f124]) ).
fof(f128,plain,
( ? [X0] :
( sdtmndtplgtdt0(X0,xR,xw)
& aReductOfIn0(X0,xv,xR)
& aElement0(X0) )
=> ( sdtmndtplgtdt0(sK31,xR,xw)
& aReductOfIn0(sK31,xv,xR)
& aElement0(sK31) ) ),
introduced(choice_axiom,[]) ).
fof(f129,plain,
( ? [X1] :
( sdtmndtplgtdt0(X1,xR,xw)
& aReductOfIn0(X1,xu,xR)
& aElement0(X1) )
=> ( sdtmndtplgtdt0(sK32,xR,xw)
& aReductOfIn0(sK32,xu,xR)
& aElement0(sK32) ) ),
introduced(choice_axiom,[]) ).
fof(f130,plain,
( sdtmndtasgtdt0(xv,xR,xw)
& ( ( sdtmndtplgtdt0(xv,xR,xw)
& ( ( sdtmndtplgtdt0(sK31,xR,xw)
& aReductOfIn0(sK31,xv,xR)
& aElement0(sK31) )
| aReductOfIn0(xw,xv,xR) ) )
| xv = xw )
& sdtmndtasgtdt0(xu,xR,xw)
& ( ( sdtmndtplgtdt0(xu,xR,xw)
& ( ( sdtmndtplgtdt0(sK32,xR,xw)
& aReductOfIn0(sK32,xu,xR)
& aElement0(sK32) )
| aReductOfIn0(xw,xu,xR) ) )
| xu = xw )
& aElement0(xw) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK31,sK32])],[f33,f129,f128]) ).
fof(f131,plain,
( ? [X1] :
( sdtmndtplgtdt0(X1,xR,xd)
& aReductOfIn0(X1,xw,xR)
& aElement0(X1) )
=> ( sdtmndtplgtdt0(sK33,xR,xd)
& aReductOfIn0(sK33,xw,xR)
& aElement0(sK33) ) ),
introduced(choice_axiom,[]) ).
fof(f132,plain,
( aNormalFormOfIn0(xd,xw,xR)
& ! [X0] : ~ aReductOfIn0(X0,xd,xR)
& sdtmndtasgtdt0(xw,xR,xd)
& ( ( sdtmndtplgtdt0(xw,xR,xd)
& ( ( sdtmndtplgtdt0(sK33,xR,xd)
& aReductOfIn0(sK33,xw,xR)
& aElement0(sK33) )
| aReductOfIn0(xd,xw,xR) ) )
| xw = xd )
& aElement0(xd) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK33])],[f59,f131]) ).
fof(f133,plain,
! [X2,X0,X1] :
( aElement0(X2)
| ~ aReductOfIn0(X2,X0,X1)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f36]) ).
fof(f143,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,[],[f44]) ).
fof(f178,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[],[f15]) ).
fof(f192,plain,
! [X0,X1] :
( iLess0(X1,X0)
| ~ aReductOfIn0(X1,X0,xR)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f196,plain,
aElement0(xa),
inference(cnf_transformation,[],[f17]) ).
fof(f197,plain,
aElement0(xb),
inference(cnf_transformation,[],[f17]) ).
fof(f203,plain,
! [X0,X1] :
( ~ sdtmndtasgtdt0(X1,xR,X0)
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f111]) ).
fof(f205,plain,
! [X0,X1] :
( sP5(sK24(X0,X1),X1)
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f116]) ).
fof(f211,plain,
! [X0,X1] :
( sdtmndtasgtdt0(X0,xR,sK24(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f116]) ).
fof(f213,plain,
! [X0,X1] :
( aReductOfIn0(sK26(X0,X1),X1,xR)
| aReductOfIn0(X0,X1,xR)
| X0 = X1
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f120]) ).
fof(f220,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,[],[f72]) ).
fof(f229,plain,
aElement0(xu),
inference(cnf_transformation,[],[f125]) ).
fof(f230,plain,
aReductOfIn0(xu,xa,xR),
inference(cnf_transformation,[],[f125]) ).
fof(f235,plain,
sdtmndtasgtdt0(xu,xR,xb),
inference(cnf_transformation,[],[f125]) ).
fof(f243,plain,
aElement0(xw),
inference(cnf_transformation,[],[f130]) ).
fof(f248,plain,
sdtmndtasgtdt0(xu,xR,xw),
inference(cnf_transformation,[],[f130]) ).
fof(f254,plain,
aElement0(xd),
inference(cnf_transformation,[],[f132]) ).
fof(f259,plain,
sdtmndtasgtdt0(xw,xR,xd),
inference(cnf_transformation,[],[f132]) ).
fof(f260,plain,
! [X0] : ~ aReductOfIn0(X0,xd,xR),
inference(cnf_transformation,[],[f132]) ).
fof(f266,plain,
~ sdtmndtasgtdt0(xb,xR,xd),
inference(cnf_transformation,[],[f60]) ).
cnf(c_49,plain,
( ~ aReductOfIn0(X0,X1,X2)
| ~ aElement0(X1)
| ~ aRewritingSystem0(X2)
| aElement0(X0) ),
inference(cnf_transformation,[],[f133]) ).
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,[],[f143]) ).
cnf(c_94,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[],[f178]) ).
cnf(c_102,plain,
( ~ aReductOfIn0(X0,X1,xR)
| ~ aElement0(X0)
| ~ aElement0(X1)
| iLess0(X0,X1) ),
inference(cnf_transformation,[],[f192]) ).
cnf(c_113,plain,
aElement0(xb),
inference(cnf_transformation,[],[f197]) ).
cnf(c_114,plain,
aElement0(xa),
inference(cnf_transformation,[],[f196]) ).
cnf(c_115,plain,
( ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ sP7(X1,X0) ),
inference(cnf_transformation,[],[f203]) ).
cnf(c_120,plain,
( ~ sP6(X0,X1)
| sdtmndtasgtdt0(X0,xR,sK24(X0,X1)) ),
inference(cnf_transformation,[],[f211]) ).
cnf(c_126,plain,
( ~ sP6(X0,X1)
| sP5(sK24(X0,X1),X1) ),
inference(cnf_transformation,[],[f205]) ).
cnf(c_130,plain,
( ~ sP5(X0,X1)
| X0 = X1
| aReductOfIn0(sK26(X0,X1),X1,xR)
| aReductOfIn0(X0,X1,xR) ),
inference(cnf_transformation,[],[f213]) ).
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,[],[f220]) ).
cnf(c_145,plain,
sdtmndtasgtdt0(xu,xR,xb),
inference(cnf_transformation,[],[f235]) ).
cnf(c_150,plain,
aReductOfIn0(xu,xa,xR),
inference(cnf_transformation,[],[f230]) ).
cnf(c_151,plain,
aElement0(xu),
inference(cnf_transformation,[],[f229]) ).
cnf(c_164,plain,
sdtmndtasgtdt0(xu,xR,xw),
inference(cnf_transformation,[],[f248]) ).
cnf(c_169,plain,
aElement0(xw),
inference(cnf_transformation,[],[f243]) ).
cnf(c_171,plain,
~ aReductOfIn0(X0,xd,xR),
inference(cnf_transformation,[],[f260]) ).
cnf(c_172,plain,
sdtmndtasgtdt0(xw,xR,xd),
inference(cnf_transformation,[],[f259]) ).
cnf(c_177,plain,
aElement0(xd),
inference(cnf_transformation,[],[f254]) ).
cnf(c_178,negated_conjecture,
~ sdtmndtasgtdt0(xb,xR,xd),
inference(cnf_transformation,[],[f266]) ).
cnf(c_2365,plain,
( X0 != xR
| ~ aReductOfIn0(X1,X2,X0)
| ~ aElement0(X2)
| aElement0(X1) ),
inference(resolution_lifted,[status(thm)],[c_49,c_94]) ).
cnf(c_2366,plain,
( ~ aReductOfIn0(X0,X1,xR)
| ~ aElement0(X1)
| aElement0(X0) ),
inference(unflattening,[status(thm)],[c_2365]) ).
cnf(c_2416,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_2417,plain,
( ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ sdtmndtasgtdt0(X2,xR,X0)
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2)
| sdtmndtasgtdt0(X2,xR,X1) ),
inference(unflattening,[status(thm)],[c_2416]) ).
cnf(c_2586,plain,
( ~ aReductOfIn0(X0,X1,xR)
| ~ aElement0(X1)
| iLess0(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_102,c_2366]) ).
cnf(c_11726,negated_conjecture,
~ sdtmndtasgtdt0(xb,xR,xd),
inference(demodulation,[status(thm)],[c_178]) ).
cnf(c_13914,plain,
( ~ aElement0(xa)
| iLess0(xu,xa) ),
inference(superposition,[status(thm)],[c_150,c_2586]) ).
cnf(c_13921,plain,
iLess0(xu,xa),
inference(forward_subsumption_resolution,[status(thm)],[c_13914,c_114]) ).
cnf(c_14007,plain,
( ~ sdtmndtasgtdt0(X0,xR,xw)
| ~ aElement0(X0)
| ~ aElement0(xw)
| ~ aElement0(xd)
| sdtmndtasgtdt0(X0,xR,xd) ),
inference(superposition,[status(thm)],[c_172,c_2417]) ).
cnf(c_14010,plain,
( ~ sdtmndtasgtdt0(X0,xR,xw)
| ~ aElement0(X0)
| sdtmndtasgtdt0(X0,xR,xd) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14007,c_177,c_169]) ).
cnf(c_16213,plain,
( ~ sP5(X0,xd)
| X0 = xd
| aReductOfIn0(X0,xd,xR) ),
inference(superposition,[status(thm)],[c_130,c_171]) ).
cnf(c_16216,plain,
( ~ sP5(X0,xd)
| X0 = xd ),
inference(forward_subsumption_resolution,[status(thm)],[c_16213,c_171]) ).
cnf(c_16432,plain,
( ~ sP6(X0,xd)
| sK24(X0,xd) = xd ),
inference(superposition,[status(thm)],[c_126,c_16216]) ).
cnf(c_16793,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_16841,plain,
( ~ aElement0(X0)
| sP7(X0,xu)
| sP6(xb,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16793,c_151,c_113,c_13921]) ).
cnf(c_32968,plain,
( ~ aElement0(xu)
| sdtmndtasgtdt0(xu,xR,xd) ),
inference(superposition,[status(thm)],[c_164,c_14010]) ).
cnf(c_32970,plain,
sdtmndtasgtdt0(xu,xR,xd),
inference(forward_subsumption_resolution,[status(thm)],[c_32968,c_151]) ).
cnf(c_32978,plain,
~ sP7(xd,xu),
inference(superposition,[status(thm)],[c_32970,c_115]) ).
cnf(c_33118,plain,
( ~ aElement0(xd)
| sP6(xb,xd) ),
inference(superposition,[status(thm)],[c_16841,c_32978]) ).
cnf(c_33123,plain,
sP6(xb,xd),
inference(forward_subsumption_resolution,[status(thm)],[c_33118,c_177]) ).
cnf(c_33784,plain,
sK24(xb,xd) = xd,
inference(superposition,[status(thm)],[c_33123,c_16432]) ).
cnf(c_36329,plain,
( ~ sP6(xb,xd)
| sdtmndtasgtdt0(xb,xR,xd) ),
inference(superposition,[status(thm)],[c_33784,c_120]) ).
cnf(c_36346,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_36329,c_11726,c_33123]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : COM019+4 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri May 3 01:00:36 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 8.16/1.66 % SZS status Started for theBenchmark.p
% 8.16/1.66 % SZS status Theorem for theBenchmark.p
% 8.16/1.66
% 8.16/1.66 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 8.16/1.66
% 8.16/1.66 ------ iProver source info
% 8.16/1.66
% 8.16/1.66 git: date: 2024-05-02 19:28:25 +0000
% 8.16/1.66 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 8.16/1.66 git: non_committed_changes: false
% 8.16/1.66
% 8.16/1.66 ------ Parsing...
% 8.16/1.66 ------ Clausification by vclausify_rel & Parsing by iProver...
% 8.16/1.66
% 8.16/1.66 ------ 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
% 8.16/1.66
% 8.16/1.66 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 8.16/1.66
% 8.16/1.66 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 8.16/1.66 ------ Proving...
% 8.16/1.66 ------ Problem Properties
% 8.16/1.66
% 8.16/1.66
% 8.16/1.66 clauses 119
% 8.16/1.66 conjectures 5
% 8.16/1.66 EPR 72
% 8.16/1.66 Horn 58
% 8.16/1.66 unary 23
% 8.16/1.66 binary 32
% 8.16/1.66 lits 370
% 8.16/1.66 lits eq 38
% 8.16/1.66 fd_pure 0
% 8.16/1.66 fd_pseudo 0
% 8.16/1.66 fd_cond 0
% 8.16/1.66 fd_pseudo_cond 9
% 8.16/1.66 AC symbols 0
% 8.16/1.66
% 8.16/1.66 ------ Schedule dynamic 5 is on
% 8.16/1.66
% 8.16/1.66 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 8.16/1.66
% 8.16/1.66
% 8.16/1.66 ------
% 8.16/1.66 Current options:
% 8.16/1.66 ------
% 8.16/1.66
% 8.16/1.66
% 8.16/1.66
% 8.16/1.66
% 8.16/1.66 ------ Proving...
% 8.16/1.66
% 8.16/1.66
% 8.16/1.66 % SZS status Theorem for theBenchmark.p
% 8.16/1.66
% 8.16/1.66 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.16/1.66
% 8.16/1.66
%------------------------------------------------------------------------------