TSTP Solution File: COM013+4 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : COM013+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n022.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 02:10:27 EDT 2024
% Result : Theorem 2.91s 1.19s
% Output : CNFRefutation 2.91s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named definition)
% 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(f6,axiom,
! [X0,X1,X2] :
( ( aElement0(X2)
& aRewritingSystem0(X1)
& aElement0(X0) )
=> ( sdtmndtplgtdt0(X0,X1,X2)
<=> ( ? [X3] :
( sdtmndtplgtdt0(X3,X1,X2)
& aReductOfIn0(X3,X0,X1)
& aElement0(X3) )
| aReductOfIn0(X2,X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTCDef) ).
fof(f8,axiom,
! [X0,X1,X2] :
( ( aElement0(X2)
& aRewritingSystem0(X1)
& aElement0(X0) )
=> ( sdtmndtasgtdt0(X0,X1,X2)
<=> ( sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTCRDef) ).
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(f14,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) ) )
& aRewritingSystem0(xR) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__587) ).
fof(f15,conjecture,
! [X0] :
( aElement0(X0)
=> ( ! [X1] :
( aElement0(X1)
=> ( iLess0(X1,X0)
=> ? [X2] :
( aNormalFormOfIn0(X2,X1,xR)
& ~ ? [X3] : aReductOfIn0(X3,X2,xR)
& sdtmndtasgtdt0(X1,xR,X2)
& ( ( sdtmndtplgtdt0(X1,xR,X2)
& ( ? [X3] :
( sdtmndtplgtdt0(X3,xR,X2)
& aReductOfIn0(X3,X1,xR)
& aElement0(X3) )
| aReductOfIn0(X2,X1,xR) ) )
| X1 = X2 )
& aElement0(X2) ) ) )
=> ? [X1] :
( aNormalFormOfIn0(X1,X0,xR)
| ( ~ ? [X2] : aReductOfIn0(X2,X1,xR)
& ( sdtmndtasgtdt0(X0,xR,X1)
| sdtmndtplgtdt0(X0,xR,X1)
| ? [X2] :
( sdtmndtplgtdt0(X2,xR,X1)
& aReductOfIn0(X2,X0,xR)
& aElement0(X2) )
| aReductOfIn0(X1,X0,xR)
| X0 = X1 )
& aElement0(X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f16,negated_conjecture,
~ ! [X0] :
( aElement0(X0)
=> ( ! [X1] :
( aElement0(X1)
=> ( iLess0(X1,X0)
=> ? [X2] :
( aNormalFormOfIn0(X2,X1,xR)
& ~ ? [X3] : aReductOfIn0(X3,X2,xR)
& sdtmndtasgtdt0(X1,xR,X2)
& ( ( sdtmndtplgtdt0(X1,xR,X2)
& ( ? [X3] :
( sdtmndtplgtdt0(X3,xR,X2)
& aReductOfIn0(X3,X1,xR)
& aElement0(X3) )
| aReductOfIn0(X2,X1,xR) ) )
| X1 = X2 )
& aElement0(X2) ) ) )
=> ? [X1] :
( aNormalFormOfIn0(X1,X0,xR)
| ( ~ ? [X2] : aReductOfIn0(X2,X1,xR)
& ( sdtmndtasgtdt0(X0,xR,X1)
| sdtmndtplgtdt0(X0,xR,X1)
| ? [X2] :
( sdtmndtplgtdt0(X2,xR,X1)
& aReductOfIn0(X2,X0,xR)
& aElement0(X2) )
| aReductOfIn0(X1,X0,xR)
| X0 = X1 )
& aElement0(X1) ) ) ) ),
inference(negated_conjecture,[],[f15]) ).
fof(f21,plain,
~ ! [X0] :
( aElement0(X0)
=> ( ! [X1] :
( aElement0(X1)
=> ( iLess0(X1,X0)
=> ? [X2] :
( aNormalFormOfIn0(X2,X1,xR)
& ~ ? [X3] : aReductOfIn0(X3,X2,xR)
& sdtmndtasgtdt0(X1,xR,X2)
& ( ( sdtmndtplgtdt0(X1,xR,X2)
& ( ? [X4] :
( sdtmndtplgtdt0(X4,xR,X2)
& aReductOfIn0(X4,X1,xR)
& aElement0(X4) )
| aReductOfIn0(X2,X1,xR) ) )
| X1 = X2 )
& aElement0(X2) ) ) )
=> ? [X5] :
( aNormalFormOfIn0(X5,X0,xR)
| ( ~ ? [X6] : aReductOfIn0(X6,X5,xR)
& ( sdtmndtasgtdt0(X0,xR,X5)
| sdtmndtplgtdt0(X0,xR,X5)
| ? [X7] :
( sdtmndtplgtdt0(X7,xR,X5)
& aReductOfIn0(X7,X0,xR)
& aElement0(X7) )
| aReductOfIn0(X5,X0,xR)
| X0 = X5 )
& aElement0(X5) ) ) ) ),
inference(rectify,[],[f16]) ).
fof(f22,plain,
! [X0,X1] :
( ! [X2] :
( aElement0(X2)
| ~ aReductOfIn0(X2,X0,X1) )
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f23,plain,
! [X0,X1] :
( ! [X2] :
( aElement0(X2)
| ~ aReductOfIn0(X2,X0,X1) )
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( sdtmndtplgtdt0(X0,X1,X2)
<=> ( ? [X3] :
( sdtmndtplgtdt0(X3,X1,X2)
& aReductOfIn0(X3,X0,X1)
& aElement0(X3) )
| aReductOfIn0(X2,X0,X1) ) )
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( sdtmndtplgtdt0(X0,X1,X2)
<=> ( ? [X3] :
( sdtmndtplgtdt0(X3,X1,X2)
& aReductOfIn0(X3,X0,X1)
& aElement0(X3) )
| aReductOfIn0(X2,X0,X1) ) )
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f24]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ( sdtmndtasgtdt0(X0,X1,X2)
<=> ( sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2 ) )
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ( sdtmndtasgtdt0(X0,X1,X2)
<=> ( sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2 ) )
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f28]) ).
fof(f30,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(f31,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,[],[f30]) ).
fof(f40,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) )
& aRewritingSystem0(xR) ),
inference(ennf_transformation,[],[f14]) ).
fof(f41,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) )
& aRewritingSystem0(xR) ),
inference(flattening,[],[f40]) ).
fof(f42,plain,
? [X0] :
( ! [X5] :
( ~ aNormalFormOfIn0(X5,X0,xR)
& ( ? [X6] : aReductOfIn0(X6,X5,xR)
| ( ~ sdtmndtasgtdt0(X0,xR,X5)
& ~ sdtmndtplgtdt0(X0,xR,X5)
& ! [X7] :
( ~ sdtmndtplgtdt0(X7,xR,X5)
| ~ aReductOfIn0(X7,X0,xR)
| ~ aElement0(X7) )
& ~ aReductOfIn0(X5,X0,xR)
& X0 != X5 )
| ~ aElement0(X5) ) )
& ! [X1] :
( ? [X2] :
( aNormalFormOfIn0(X2,X1,xR)
& ! [X3] : ~ aReductOfIn0(X3,X2,xR)
& sdtmndtasgtdt0(X1,xR,X2)
& ( ( sdtmndtplgtdt0(X1,xR,X2)
& ( ? [X4] :
( sdtmndtplgtdt0(X4,xR,X2)
& aReductOfIn0(X4,X1,xR)
& aElement0(X4) )
| aReductOfIn0(X2,X1,xR) ) )
| X1 = X2 )
& aElement0(X2) )
| ~ iLess0(X1,X0)
| ~ aElement0(X1) )
& aElement0(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f43,plain,
? [X0] :
( ! [X5] :
( ~ aNormalFormOfIn0(X5,X0,xR)
& ( ? [X6] : aReductOfIn0(X6,X5,xR)
| ( ~ sdtmndtasgtdt0(X0,xR,X5)
& ~ sdtmndtplgtdt0(X0,xR,X5)
& ! [X7] :
( ~ sdtmndtplgtdt0(X7,xR,X5)
| ~ aReductOfIn0(X7,X0,xR)
| ~ aElement0(X7) )
& ~ aReductOfIn0(X5,X0,xR)
& X0 != X5 )
| ~ aElement0(X5) ) )
& ! [X1] :
( ? [X2] :
( aNormalFormOfIn0(X2,X1,xR)
& ! [X3] : ~ aReductOfIn0(X3,X2,xR)
& sdtmndtasgtdt0(X1,xR,X2)
& ( ( sdtmndtplgtdt0(X1,xR,X2)
& ( ? [X4] :
( sdtmndtplgtdt0(X4,xR,X2)
& aReductOfIn0(X4,X1,xR)
& aElement0(X4) )
| aReductOfIn0(X2,X1,xR) ) )
| X1 = X2 )
& aElement0(X2) )
| ~ iLess0(X1,X0)
| ~ aElement0(X1) )
& aElement0(X0) ),
inference(flattening,[],[f42]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ( ( sdtmndtplgtdt0(X0,X1,X2)
| ( ! [X3] :
( ~ sdtmndtplgtdt0(X3,X1,X2)
| ~ aReductOfIn0(X3,X0,X1)
| ~ aElement0(X3) )
& ~ aReductOfIn0(X2,X0,X1) ) )
& ( ? [X3] :
( sdtmndtplgtdt0(X3,X1,X2)
& aReductOfIn0(X3,X0,X1)
& aElement0(X3) )
| aReductOfIn0(X2,X0,X1)
| ~ sdtmndtplgtdt0(X0,X1,X2) ) )
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(nnf_transformation,[],[f25]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ( ( sdtmndtplgtdt0(X0,X1,X2)
| ( ! [X3] :
( ~ sdtmndtplgtdt0(X3,X1,X2)
| ~ aReductOfIn0(X3,X0,X1)
| ~ aElement0(X3) )
& ~ aReductOfIn0(X2,X0,X1) ) )
& ( ? [X3] :
( sdtmndtplgtdt0(X3,X1,X2)
& aReductOfIn0(X3,X0,X1)
& aElement0(X3) )
| aReductOfIn0(X2,X0,X1)
| ~ sdtmndtplgtdt0(X0,X1,X2) ) )
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f50]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ( ( sdtmndtplgtdt0(X0,X1,X2)
| ( ! [X3] :
( ~ sdtmndtplgtdt0(X3,X1,X2)
| ~ aReductOfIn0(X3,X0,X1)
| ~ aElement0(X3) )
& ~ aReductOfIn0(X2,X0,X1) ) )
& ( ? [X4] :
( sdtmndtplgtdt0(X4,X1,X2)
& aReductOfIn0(X4,X0,X1)
& aElement0(X4) )
| aReductOfIn0(X2,X0,X1)
| ~ sdtmndtplgtdt0(X0,X1,X2) ) )
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(rectify,[],[f51]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ? [X4] :
( sdtmndtplgtdt0(X4,X1,X2)
& aReductOfIn0(X4,X0,X1)
& aElement0(X4) )
=> ( sdtmndtplgtdt0(sK4(X0,X1,X2),X1,X2)
& aReductOfIn0(sK4(X0,X1,X2),X0,X1)
& aElement0(sK4(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ( ( sdtmndtplgtdt0(X0,X1,X2)
| ( ! [X3] :
( ~ sdtmndtplgtdt0(X3,X1,X2)
| ~ aReductOfIn0(X3,X0,X1)
| ~ aElement0(X3) )
& ~ aReductOfIn0(X2,X0,X1) ) )
& ( ( sdtmndtplgtdt0(sK4(X0,X1,X2),X1,X2)
& aReductOfIn0(sK4(X0,X1,X2),X0,X1)
& aElement0(sK4(X0,X1,X2)) )
| aReductOfIn0(X2,X0,X1)
| ~ sdtmndtplgtdt0(X0,X1,X2) ) )
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f52,f53]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ( ( sdtmndtasgtdt0(X0,X1,X2)
| ( ~ sdtmndtplgtdt0(X0,X1,X2)
& X0 != X2 ) )
& ( sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2
| ~ sdtmndtasgtdt0(X0,X1,X2) ) )
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(nnf_transformation,[],[f29]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ( ( sdtmndtasgtdt0(X0,X1,X2)
| ( ~ sdtmndtplgtdt0(X0,X1,X2)
& X0 != X2 ) )
& ( sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2
| ~ sdtmndtasgtdt0(X0,X1,X2) ) )
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f55]) ).
fof(f78,plain,
? [X0] :
( ! [X1] :
( ~ aNormalFormOfIn0(X1,X0,xR)
& ( ? [X2] : aReductOfIn0(X2,X1,xR)
| ( ~ 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(X1) ) )
& ! [X4] :
( ? [X5] :
( aNormalFormOfIn0(X5,X4,xR)
& ! [X6] : ~ aReductOfIn0(X6,X5,xR)
& sdtmndtasgtdt0(X4,xR,X5)
& ( ( sdtmndtplgtdt0(X4,xR,X5)
& ( ? [X7] :
( sdtmndtplgtdt0(X7,xR,X5)
& aReductOfIn0(X7,X4,xR)
& aElement0(X7) )
| aReductOfIn0(X5,X4,xR) ) )
| X4 = X5 )
& aElement0(X5) )
| ~ iLess0(X4,X0)
| ~ aElement0(X4) )
& aElement0(X0) ),
inference(rectify,[],[f43]) ).
fof(f79,plain,
( ? [X0] :
( ! [X1] :
( ~ aNormalFormOfIn0(X1,X0,xR)
& ( ? [X2] : aReductOfIn0(X2,X1,xR)
| ( ~ 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(X1) ) )
& ! [X4] :
( ? [X5] :
( aNormalFormOfIn0(X5,X4,xR)
& ! [X6] : ~ aReductOfIn0(X6,X5,xR)
& sdtmndtasgtdt0(X4,xR,X5)
& ( ( sdtmndtplgtdt0(X4,xR,X5)
& ( ? [X7] :
( sdtmndtplgtdt0(X7,xR,X5)
& aReductOfIn0(X7,X4,xR)
& aElement0(X7) )
| aReductOfIn0(X5,X4,xR) ) )
| X4 = X5 )
& aElement0(X5) )
| ~ iLess0(X4,X0)
| ~ aElement0(X4) )
& aElement0(X0) )
=> ( ! [X1] :
( ~ aNormalFormOfIn0(X1,sK16,xR)
& ( ? [X2] : aReductOfIn0(X2,X1,xR)
| ( ~ sdtmndtasgtdt0(sK16,xR,X1)
& ~ sdtmndtplgtdt0(sK16,xR,X1)
& ! [X3] :
( ~ sdtmndtplgtdt0(X3,xR,X1)
| ~ aReductOfIn0(X3,sK16,xR)
| ~ aElement0(X3) )
& ~ aReductOfIn0(X1,sK16,xR)
& sK16 != X1 )
| ~ aElement0(X1) ) )
& ! [X4] :
( ? [X5] :
( aNormalFormOfIn0(X5,X4,xR)
& ! [X6] : ~ aReductOfIn0(X6,X5,xR)
& sdtmndtasgtdt0(X4,xR,X5)
& ( ( sdtmndtplgtdt0(X4,xR,X5)
& ( ? [X7] :
( sdtmndtplgtdt0(X7,xR,X5)
& aReductOfIn0(X7,X4,xR)
& aElement0(X7) )
| aReductOfIn0(X5,X4,xR) ) )
| X4 = X5 )
& aElement0(X5) )
| ~ iLess0(X4,sK16)
| ~ aElement0(X4) )
& aElement0(sK16) ) ),
introduced(choice_axiom,[]) ).
fof(f80,plain,
! [X1] :
( ? [X2] : aReductOfIn0(X2,X1,xR)
=> aReductOfIn0(sK17(X1),X1,xR) ),
introduced(choice_axiom,[]) ).
fof(f81,plain,
! [X4] :
( ? [X5] :
( aNormalFormOfIn0(X5,X4,xR)
& ! [X6] : ~ aReductOfIn0(X6,X5,xR)
& sdtmndtasgtdt0(X4,xR,X5)
& ( ( sdtmndtplgtdt0(X4,xR,X5)
& ( ? [X7] :
( sdtmndtplgtdt0(X7,xR,X5)
& aReductOfIn0(X7,X4,xR)
& aElement0(X7) )
| aReductOfIn0(X5,X4,xR) ) )
| X4 = X5 )
& aElement0(X5) )
=> ( aNormalFormOfIn0(sK18(X4),X4,xR)
& ! [X6] : ~ aReductOfIn0(X6,sK18(X4),xR)
& sdtmndtasgtdt0(X4,xR,sK18(X4))
& ( ( sdtmndtplgtdt0(X4,xR,sK18(X4))
& ( ? [X7] :
( sdtmndtplgtdt0(X7,xR,sK18(X4))
& aReductOfIn0(X7,X4,xR)
& aElement0(X7) )
| aReductOfIn0(sK18(X4),X4,xR) ) )
| sK18(X4) = X4 )
& aElement0(sK18(X4)) ) ),
introduced(choice_axiom,[]) ).
fof(f82,plain,
! [X4] :
( ? [X7] :
( sdtmndtplgtdt0(X7,xR,sK18(X4))
& aReductOfIn0(X7,X4,xR)
& aElement0(X7) )
=> ( sdtmndtplgtdt0(sK19(X4),xR,sK18(X4))
& aReductOfIn0(sK19(X4),X4,xR)
& aElement0(sK19(X4)) ) ),
introduced(choice_axiom,[]) ).
fof(f83,plain,
( ! [X1] :
( ~ aNormalFormOfIn0(X1,sK16,xR)
& ( aReductOfIn0(sK17(X1),X1,xR)
| ( ~ sdtmndtasgtdt0(sK16,xR,X1)
& ~ sdtmndtplgtdt0(sK16,xR,X1)
& ! [X3] :
( ~ sdtmndtplgtdt0(X3,xR,X1)
| ~ aReductOfIn0(X3,sK16,xR)
| ~ aElement0(X3) )
& ~ aReductOfIn0(X1,sK16,xR)
& sK16 != X1 )
| ~ aElement0(X1) ) )
& ! [X4] :
( ( aNormalFormOfIn0(sK18(X4),X4,xR)
& ! [X6] : ~ aReductOfIn0(X6,sK18(X4),xR)
& sdtmndtasgtdt0(X4,xR,sK18(X4))
& ( ( sdtmndtplgtdt0(X4,xR,sK18(X4))
& ( ( sdtmndtplgtdt0(sK19(X4),xR,sK18(X4))
& aReductOfIn0(sK19(X4),X4,xR)
& aElement0(sK19(X4)) )
| aReductOfIn0(sK18(X4),X4,xR) ) )
| sK18(X4) = X4 )
& aElement0(sK18(X4)) )
| ~ iLess0(X4,sK16)
| ~ aElement0(X4) )
& aElement0(sK16) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17,sK18,sK19])],[f78,f82,f81,f80,f79]) ).
fof(f84,plain,
! [X2,X0,X1] :
( aElement0(X2)
| ~ aReductOfIn0(X2,X0,X1)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f88,plain,
! [X2,X0,X1] :
( sdtmndtplgtdt0(X0,X1,X2)
| ~ aReductOfIn0(X2,X0,X1)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f93,plain,
! [X2,X0,X1] :
( sdtmndtasgtdt0(X0,X1,X2)
| ~ sdtmndtplgtdt0(X0,X1,X2)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f94,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,[],[f31]) ).
fof(f128,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[],[f41]) ).
fof(f129,plain,
! [X0,X1] :
( iLess0(X1,X0)
| ~ aReductOfIn0(X1,X0,xR)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f133,plain,
aElement0(sK16),
inference(cnf_transformation,[],[f83]) ).
fof(f134,plain,
! [X4] :
( aElement0(sK18(X4))
| ~ iLess0(X4,sK16)
| ~ aElement0(X4) ),
inference(cnf_transformation,[],[f83]) ).
fof(f139,plain,
! [X4] :
( sdtmndtasgtdt0(X4,xR,sK18(X4))
| ~ iLess0(X4,sK16)
| ~ aElement0(X4) ),
inference(cnf_transformation,[],[f83]) ).
fof(f140,plain,
! [X6,X4] :
( ~ aReductOfIn0(X6,sK18(X4),xR)
| ~ iLess0(X4,sK16)
| ~ aElement0(X4) ),
inference(cnf_transformation,[],[f83]) ).
fof(f142,plain,
! [X1] :
( aReductOfIn0(sK17(X1),X1,xR)
| sK16 != X1
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f83]) ).
fof(f146,plain,
! [X1] :
( aReductOfIn0(sK17(X1),X1,xR)
| ~ sdtmndtasgtdt0(sK16,xR,X1)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f83]) ).
fof(f149,plain,
( aReductOfIn0(sK17(sK16),sK16,xR)
| ~ aElement0(sK16) ),
inference(equality_resolution,[],[f142]) ).
cnf(c_49,plain,
( ~ aReductOfIn0(X0,X1,X2)
| ~ aElement0(X1)
| ~ aRewritingSystem0(X2)
| aElement0(X0) ),
inference(cnf_transformation,[],[f84]) ).
cnf(c_51,plain,
( ~ aReductOfIn0(X0,X1,X2)
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aRewritingSystem0(X2)
| sdtmndtplgtdt0(X1,X2,X0) ),
inference(cnf_transformation,[],[f88]) ).
cnf(c_56,plain,
( ~ sdtmndtplgtdt0(X0,X1,X2)
| ~ aElement0(X0)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| sdtmndtasgtdt0(X0,X1,X2) ),
inference(cnf_transformation,[],[f93]) ).
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,[],[f94]) ).
cnf(c_96,plain,
( ~ aReductOfIn0(X0,X1,xR)
| ~ aElement0(X0)
| ~ aElement0(X1)
| iLess0(X0,X1) ),
inference(cnf_transformation,[],[f129]) ).
cnf(c_97,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[],[f128]) ).
cnf(c_99,negated_conjecture,
( ~ sdtmndtasgtdt0(sK16,xR,X0)
| ~ aElement0(X0)
| aReductOfIn0(sK17(X0),X0,xR) ),
inference(cnf_transformation,[],[f146]) ).
cnf(c_103,negated_conjecture,
( ~ aElement0(sK16)
| aReductOfIn0(sK17(sK16),sK16,xR) ),
inference(cnf_transformation,[],[f149]) ).
cnf(c_105,negated_conjecture,
( ~ aReductOfIn0(X0,sK18(X1),xR)
| ~ iLess0(X1,sK16)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f140]) ).
cnf(c_106,negated_conjecture,
( ~ iLess0(X0,sK16)
| ~ aElement0(X0)
| sdtmndtasgtdt0(X0,xR,sK18(X0)) ),
inference(cnf_transformation,[],[f139]) ).
cnf(c_111,negated_conjecture,
( ~ iLess0(X0,sK16)
| ~ aElement0(X0)
| aElement0(sK18(X0)) ),
inference(cnf_transformation,[],[f134]) ).
cnf(c_112,negated_conjecture,
aElement0(sK16),
inference(cnf_transformation,[],[f133]) ).
cnf(c_157,negated_conjecture,
aReductOfIn0(sK17(sK16),sK16,xR),
inference(global_subsumption_just,[status(thm)],[c_103,c_112,c_103]) ).
cnf(c_159,plain,
( ~ aReductOfIn0(X0,X1,X2)
| ~ aElement0(X1)
| ~ aRewritingSystem0(X2)
| sdtmndtplgtdt0(X1,X2,X0) ),
inference(global_subsumption_just,[status(thm)],[c_51,c_49,c_51]) ).
cnf(c_1363,plain,
( X0 != xR
| ~ aReductOfIn0(X1,X2,X0)
| ~ aElement0(X2)
| sdtmndtplgtdt0(X2,X0,X1) ),
inference(resolution_lifted,[status(thm)],[c_159,c_97]) ).
cnf(c_1364,plain,
( ~ aReductOfIn0(X0,X1,xR)
| ~ aElement0(X1)
| sdtmndtplgtdt0(X1,xR,X0) ),
inference(unflattening,[status(thm)],[c_1363]) ).
cnf(c_1375,plain,
( X0 != xR
| ~ aReductOfIn0(X1,X2,X0)
| ~ aElement0(X2)
| aElement0(X1) ),
inference(resolution_lifted,[status(thm)],[c_49,c_97]) ).
cnf(c_1376,plain,
( ~ aReductOfIn0(X0,X1,xR)
| ~ aElement0(X1)
| aElement0(X0) ),
inference(unflattening,[status(thm)],[c_1375]) ).
cnf(c_1390,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_97]) ).
cnf(c_1391,plain,
( ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ sdtmndtasgtdt0(X2,xR,X0)
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2)
| sdtmndtasgtdt0(X2,xR,X1) ),
inference(unflattening,[status(thm)],[c_1390]) ).
cnf(c_1437,plain,
( X0 != xR
| ~ sdtmndtplgtdt0(X1,X0,X2)
| ~ aElement0(X1)
| ~ aElement0(X2)
| sdtmndtasgtdt0(X1,X0,X2) ),
inference(resolution_lifted,[status(thm)],[c_56,c_97]) ).
cnf(c_1438,plain,
( ~ sdtmndtplgtdt0(X0,xR,X1)
| ~ aElement0(X0)
| ~ aElement0(X1)
| sdtmndtasgtdt0(X0,xR,X1) ),
inference(unflattening,[status(thm)],[c_1437]) ).
cnf(c_1550,plain,
( ~ aReductOfIn0(X0,X1,xR)
| ~ aElement0(X1)
| iLess0(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_96,c_1376]) ).
cnf(c_5604,plain,
sK17(sK16) = sP0_iProver_def,
definition ).
cnf(c_5605,negated_conjecture,
aReductOfIn0(sP0_iProver_def,sK16,xR),
inference(demodulation,[status(thm)],[c_157,c_5604]) ).
cnf(c_5606,negated_conjecture,
aElement0(sK16),
inference(demodulation,[status(thm)],[c_112]) ).
cnf(c_5607,negated_conjecture,
( ~ iLess0(X0,sK16)
| ~ aElement0(X0)
| aElement0(sK18(X0)) ),
inference(demodulation,[status(thm)],[c_111]) ).
cnf(c_5612,negated_conjecture,
( ~ iLess0(X0,sK16)
| ~ aElement0(X0)
| sdtmndtasgtdt0(X0,xR,sK18(X0)) ),
inference(demodulation,[status(thm)],[c_106]) ).
cnf(c_5613,negated_conjecture,
( ~ aReductOfIn0(X0,sK18(X1),xR)
| ~ iLess0(X1,sK16)
| ~ aElement0(X1) ),
inference(demodulation,[status(thm)],[c_105]) ).
cnf(c_5617,negated_conjecture,
( ~ sdtmndtasgtdt0(sK16,xR,X0)
| ~ aElement0(X0)
| aReductOfIn0(sK17(X0),X0,xR) ),
inference(demodulation,[status(thm)],[c_99]) ).
cnf(c_6549,plain,
( ~ sdtmndtasgtdt0(sK16,xR,sK18(X0))
| ~ aElement0(sK18(X0))
| ~ iLess0(X0,sK16)
| ~ aElement0(X0) ),
inference(superposition,[status(thm)],[c_5617,c_5613]) ).
cnf(c_6789,plain,
( ~ aElement0(sK16)
| aElement0(sP0_iProver_def) ),
inference(superposition,[status(thm)],[c_5605,c_1376]) ).
cnf(c_6790,plain,
aElement0(sP0_iProver_def),
inference(forward_subsumption_resolution,[status(thm)],[c_6789,c_5606]) ).
cnf(c_6877,plain,
( ~ sdtmndtasgtdt0(sK16,xR,sK18(X0))
| ~ iLess0(X0,sK16)
| ~ aElement0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_6549,c_111,c_6549]) ).
cnf(c_7021,plain,
( ~ aElement0(sK16)
| iLess0(sP0_iProver_def,sK16) ),
inference(superposition,[status(thm)],[c_5605,c_1550]) ).
cnf(c_7023,plain,
iLess0(sP0_iProver_def,sK16),
inference(forward_subsumption_resolution,[status(thm)],[c_7021,c_5606]) ).
cnf(c_7175,plain,
( ~ aElement0(sK16)
| sdtmndtplgtdt0(sK16,xR,sP0_iProver_def) ),
inference(superposition,[status(thm)],[c_5605,c_1364]) ).
cnf(c_7177,plain,
sdtmndtplgtdt0(sK16,xR,sP0_iProver_def),
inference(forward_subsumption_resolution,[status(thm)],[c_7175,c_5606]) ).
cnf(c_7696,plain,
( ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ aElement0(sK18(X1))
| ~ iLess0(X1,sK16)
| ~ aElement0(X0)
| ~ aElement0(X1)
| sdtmndtasgtdt0(X0,xR,sK18(X1)) ),
inference(superposition,[status(thm)],[c_5612,c_1391]) ).
cnf(c_8416,plain,
( ~ aElement0(sK16)
| ~ aElement0(sP0_iProver_def)
| sdtmndtasgtdt0(sK16,xR,sP0_iProver_def) ),
inference(superposition,[status(thm)],[c_7177,c_1438]) ).
cnf(c_8418,plain,
sdtmndtasgtdt0(sK16,xR,sP0_iProver_def),
inference(forward_subsumption_resolution,[status(thm)],[c_8416,c_6790,c_5606]) ).
cnf(c_10349,plain,
( ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ iLess0(X1,sK16)
| ~ aElement0(X0)
| ~ aElement0(X1)
| sdtmndtasgtdt0(X0,xR,sK18(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7696,c_5607]) ).
cnf(c_10365,plain,
( ~ sdtmndtasgtdt0(sK16,xR,X0)
| ~ iLess0(X0,sK16)
| ~ aElement0(X0)
| ~ aElement0(sK16) ),
inference(superposition,[status(thm)],[c_10349,c_6877]) ).
cnf(c_10368,plain,
( ~ sdtmndtasgtdt0(sK16,xR,X0)
| ~ iLess0(X0,sK16)
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10365,c_5606]) ).
cnf(c_10677,plain,
( ~ iLess0(sP0_iProver_def,sK16)
| ~ aElement0(sP0_iProver_def) ),
inference(superposition,[status(thm)],[c_8418,c_10368]) ).
cnf(c_10682,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_10677,c_6790,c_7023]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : COM013+4 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n022.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 00:35:57 EDT 2024
% 0.14/0.35 % 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
% 2.91/1.19 % SZS status Started for theBenchmark.p
% 2.91/1.19 % SZS status Theorem for theBenchmark.p
% 2.91/1.19
% 2.91/1.19 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 2.91/1.19
% 2.91/1.19 ------ iProver source info
% 2.91/1.19
% 2.91/1.19 git: date: 2024-05-02 19:28:25 +0000
% 2.91/1.19 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 2.91/1.19 git: non_committed_changes: false
% 2.91/1.19
% 2.91/1.19 ------ Parsing...
% 2.91/1.19 ------ Clausification by vclausify_rel & Parsing by iProver...
% 2.91/1.19
% 2.91/1.19 ------ 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: 4 0s sf_e pe_s pe_e
% 2.91/1.19
% 2.91/1.19 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.91/1.19
% 2.91/1.19 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.91/1.19 ------ Proving...
% 2.91/1.19 ------ Problem Properties
% 2.91/1.19
% 2.91/1.19
% 2.91/1.19 clauses 49
% 2.91/1.19 conjectures 13
% 2.91/1.19 EPR 14
% 2.91/1.19 Horn 31
% 2.91/1.19 unary 4
% 2.91/1.19 binary 11
% 2.91/1.19 lits 185
% 2.91/1.19 lits eq 6
% 2.91/1.19 fd_pure 0
% 2.91/1.19 fd_pseudo 0
% 2.91/1.19 fd_cond 0
% 2.91/1.19 fd_pseudo_cond 1
% 2.91/1.19 AC symbols 0
% 2.91/1.19
% 2.91/1.19 ------ Schedule dynamic 5 is on
% 2.91/1.19
% 2.91/1.19 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.91/1.19
% 2.91/1.19
% 2.91/1.19 ------
% 2.91/1.19 Current options:
% 2.91/1.19 ------
% 2.91/1.19
% 2.91/1.19
% 2.91/1.19
% 2.91/1.19
% 2.91/1.19 ------ Proving...
% 2.91/1.19
% 2.91/1.19
% 2.91/1.19 % SZS status Theorem for theBenchmark.p
% 2.91/1.19
% 2.91/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.91/1.19
% 2.91/1.19
%------------------------------------------------------------------------------