%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COM013+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 09:39:23 AM UTC 2026
% Result : Theorem 2.15s 0.72s
% Output : Refutation 2.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 30
% Syntax : Number of formulae : 207 ( 30 unt; 22 def)
% Number of atoms : 916 ( 8 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 1307 ( 598 ~; 577 |; 76 &)
% ( 34 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 32 ( 30 usr; 23 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 273 ( 0 sgn 247 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] :
( ( aElement0(X0)
& aRewritingSystem0(X1) )
=> ! [X2] :
( aReductOfIn0(X2,X0,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mReduct) ).
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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mTCRTrans) ).
fof(f12,axiom,
! [X0] :
( aRewritingSystem0(X0)
=> ( isTerminating0(X0)
<=> ! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> ( sdtmndtplgtdt0(X1,X0,X2)
=> iLess0(X2,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTermin) ).
fof(f13,axiom,
! [X0,X1] :
( ( aElement0(X0)
& aRewritingSystem0(X1) )
=> ! [X2] :
( aNormalFormOfIn0(X2,X0,X1)
<=> ( aElement0(X2)
& sdtmndtasgtdt0(X0,X1,X2)
& ~ ? [X3] : aReductOfIn0(X3,X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNFRDef) ).
fof(f14,axiom,
( aRewritingSystem0(xR)
& isTerminating0(xR) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__587) ).
fof(f15,conjecture,
! [X0] :
( aElement0(X0)
=> ( ! [X1] :
( aElement0(X1)
=> ( iLess0(X1,X0)
=> ? [X2] : aNormalFormOfIn0(X2,X1,xR) ) )
=> ? [X1] : aNormalFormOfIn0(X1,X0,xR) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f16,negated_conjecture,
~ ! [X0] :
( aElement0(X0)
=> ( ! [X1] :
( aElement0(X1)
=> ( iLess0(X1,X0)
=> ? [X2] : aNormalFormOfIn0(X2,X1,xR) ) )
=> ? [X1] : aNormalFormOfIn0(X1,X0,xR) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f21,plain,
~ ! [X0] :
( aElement0(X0)
=> ( ! [X1] :
( aElement0(X1)
=> ( iLess0(X1,X0)
=> ? [X2] : aNormalFormOfIn0(X2,X1,xR) ) )
=> ? [X3] : aNormalFormOfIn0(X3,X0,xR) ) ),
inference(rectify,[],[f16]) ).
fof(f22,plain,
! [X0,X1] :
( ! [X2] :
( aElement0(X2)
| ~ aReductOfIn0(X2,X0,X1) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(ennf_transformation,[],[f3]) ).
fof(f23,plain,
! [X0,X1] :
( ! [X2] :
( aElement0(X2)
| ~ aReductOfIn0(X2,X0,X1) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(flattening,[],[f22]) ).
fof(f24,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(f25,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,[],[f24]) ).
fof(f28,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(f29,plain,
! [X0,X1,X2] :
( ( sdtmndtasgtdt0(X0,X1,X2)
<=> ( X0 = X2
| sdtmndtplgtdt0(X0,X1,X2) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(flattening,[],[f28]) ).
fof(f30,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(f31,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,[],[f30]) ).
fof(f36,plain,
! [X0] :
( ( isTerminating0(X0)
<=> ! [X1,X2] :
( iLess0(X2,X1)
| ~ sdtmndtplgtdt0(X1,X0,X2)
| ~ aElement0(X1)
| ~ aElement0(X2) ) )
| ~ aRewritingSystem0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f37,plain,
! [X0] :
( ( isTerminating0(X0)
<=> ! [X1,X2] :
( iLess0(X2,X1)
| ~ sdtmndtplgtdt0(X1,X0,X2)
| ~ aElement0(X1)
| ~ aElement0(X2) ) )
| ~ aRewritingSystem0(X0) ),
inference(flattening,[],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( ! [X2] :
( aNormalFormOfIn0(X2,X0,X1)
<=> ( aElement0(X2)
& sdtmndtasgtdt0(X0,X1,X2)
& ! [X3] : ~ aReductOfIn0(X3,X2,X1) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f39,plain,
! [X0,X1] :
( ! [X2] :
( aNormalFormOfIn0(X2,X0,X1)
<=> ( aElement0(X2)
& sdtmndtasgtdt0(X0,X1,X2)
& ! [X3] : ~ aReductOfIn0(X3,X2,X1) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(flattening,[],[f38]) ).
fof(f40,plain,
? [X0] :
( ! [X3] : ~ aNormalFormOfIn0(X3,X0,xR)
& ! [X1] :
( ? [X2] : aNormalFormOfIn0(X2,X1,xR)
| ~ iLess0(X1,X0)
| ~ aElement0(X1) )
& aElement0(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f41,plain,
? [X0] :
( ! [X3] : ~ aNormalFormOfIn0(X3,X0,xR)
& ! [X1] :
( ? [X2] : aNormalFormOfIn0(X2,X1,xR)
| ~ iLess0(X1,X0)
| ~ aElement0(X1) )
& aElement0(X0) ),
inference(flattening,[],[f40]) ).
fof(f48,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,[],[f25]) ).
fof(f49,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,[],[f48]) ).
fof(f50,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,[],[f49]) ).
fof(f51,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(sK4(X0,X1,X2))
& aReductOfIn0(sK4(X0,X1,X2),X0,X1)
& sdtmndtplgtdt0(sK4(X0,X1,X2),X1,X2) )
| ~ sdtmndtplgtdt0(X0,X1,X2) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X4,sK4(X0,X1,X2))],[f50]) ).
fof(f52,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,[],[f29]) ).
fof(f53,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,[],[f52]) ).
fof(f62,plain,
! [X0] :
( ( ( isTerminating0(X0)
| ? [X1,X2] :
( ~ iLess0(X2,X1)
& sdtmndtplgtdt0(X1,X0,X2)
& aElement0(X1)
& aElement0(X2) ) )
& ( ! [X1,X2] :
( iLess0(X2,X1)
| ~ sdtmndtplgtdt0(X1,X0,X2)
| ~ aElement0(X1)
| ~ aElement0(X2) )
| ~ isTerminating0(X0) ) )
| ~ aRewritingSystem0(X0) ),
inference(nnf_transformation,[],[f37]) ).
fof(f63,plain,
! [X0] :
( ( ( isTerminating0(X0)
| ? [X1,X2] :
( ~ iLess0(X2,X1)
& sdtmndtplgtdt0(X1,X0,X2)
& aElement0(X1)
& aElement0(X2) ) )
& ( ! [X3,X4] :
( iLess0(X4,X3)
| ~ sdtmndtplgtdt0(X3,X0,X4)
| ~ aElement0(X3)
| ~ aElement0(X4) )
| ~ isTerminating0(X0) ) )
| ~ aRewritingSystem0(X0) ),
inference(rectify,[],[f62]) ).
fof(f64,plain,
! [X0] :
( ( ( isTerminating0(X0)
| ( ~ iLess0(sK14(X0),sK13(X0))
& sdtmndtplgtdt0(sK13(X0),X0,sK14(X0))
& aElement0(sK13(X0))
& aElement0(sK14(X0)) ) )
& ( ! [X3,X4] :
( iLess0(X4,X3)
| ~ sdtmndtplgtdt0(X3,X0,X4)
| ~ aElement0(X3)
| ~ aElement0(X4) )
| ~ isTerminating0(X0) ) )
| ~ aRewritingSystem0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14]),skolemize(X1,sK13(X0)),skolemize(X2,sK14(X0))],[f63]) ).
fof(f65,plain,
! [X0,X1] :
( ! [X2] :
( ( aNormalFormOfIn0(X2,X0,X1)
| ~ aElement0(X2)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| ? [X3] : aReductOfIn0(X3,X2,X1) )
& ( ( aElement0(X2)
& sdtmndtasgtdt0(X0,X1,X2)
& ! [X3] : ~ aReductOfIn0(X3,X2,X1) )
| ~ aNormalFormOfIn0(X2,X0,X1) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(nnf_transformation,[],[f39]) ).
fof(f66,plain,
! [X0,X1] :
( ! [X2] :
( ( aNormalFormOfIn0(X2,X0,X1)
| ~ aElement0(X2)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| ? [X3] : aReductOfIn0(X3,X2,X1) )
& ( ( aElement0(X2)
& sdtmndtasgtdt0(X0,X1,X2)
& ! [X3] : ~ aReductOfIn0(X3,X2,X1) )
| ~ aNormalFormOfIn0(X2,X0,X1) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
! [X0,X1] :
( ! [X2] :
( ( aNormalFormOfIn0(X2,X0,X1)
| ~ aElement0(X2)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| ? [X3] : aReductOfIn0(X3,X2,X1) )
& ( ( aElement0(X2)
& sdtmndtasgtdt0(X0,X1,X2)
& ! [X4] : ~ aReductOfIn0(X4,X2,X1) )
| ~ aNormalFormOfIn0(X2,X0,X1) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(rectify,[],[f66]) ).
fof(f68,plain,
! [X0,X1] :
( ! [X2] :
( ( aNormalFormOfIn0(X2,X0,X1)
| ~ aElement0(X2)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| aReductOfIn0(sK15(X1,X2),X2,X1) )
& ( ( aElement0(X2)
& sdtmndtasgtdt0(X0,X1,X2)
& ! [X4] : ~ aReductOfIn0(X4,X2,X1) )
| ~ aNormalFormOfIn0(X2,X0,X1) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(X3,sK15(X1,X2))],[f67]) ).
fof(f69,plain,
? [X0] :
( ! [X1] : ~ aNormalFormOfIn0(X1,X0,xR)
& ! [X2] :
( ? [X3] : aNormalFormOfIn0(X3,X2,xR)
| ~ iLess0(X2,X0)
| ~ aElement0(X2) )
& aElement0(X0) ),
inference(rectify,[],[f41]) ).
fof(f70,plain,
( ! [X1] : ~ aNormalFormOfIn0(X1,sK16,xR)
& ! [X2] :
( aNormalFormOfIn0(sK17(X2),X2,xR)
| ~ iLess0(X2,sK16)
| ~ aElement0(X2) )
& aElement0(sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16,sK17]),skolemize(X0,sK16),skolemize(X3,sK17(X2))],[f69]) ).
fof(f71,plain,
! [X2,X0,X1] :
( ~ aReductOfIn0(X2,X0,X1)
| aElement0(X2)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f76,plain,
! [X2,X0,X1] :
( sdtmndtplgtdt0(X0,X1,X2)
| ~ aReductOfIn0(X2,X0,X1)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(cnf_transformation,[],[f51]) ).
fof(f79,plain,
! [X2,X0,X1] :
( ~ sdtmndtplgtdt0(X0,X1,X2)
| sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(cnf_transformation,[],[f53]) ).
fof(f80,plain,
! [X2,X0,X1] :
( sdtmndtasgtdt0(X0,X1,X2)
| X0 != X2
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(cnf_transformation,[],[f53]) ).
fof(f81,plain,
! [X2,X3,X0,X1] :
( ~ aRewritingSystem0(X1)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| ~ sdtmndtasgtdt0(X2,X1,X3)
| ~ aElement0(X0)
| sdtmndtasgtdt0(X0,X1,X3)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(cnf_transformation,[],[f31]) ).
fof(f106,plain,
! [X3,X0,X4] :
( iLess0(X4,X3)
| ~ sdtmndtplgtdt0(X3,X0,X4)
| ~ aElement0(X3)
| ~ aElement0(X4)
| ~ isTerminating0(X0)
| ~ aRewritingSystem0(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f111,plain,
! [X2,X0,X1,X4] :
( ~ aNormalFormOfIn0(X2,X0,X1)
| ~ aReductOfIn0(X4,X2,X1)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f112,plain,
! [X2,X0,X1] :
( ~ aNormalFormOfIn0(X2,X0,X1)
| sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f113,plain,
! [X2,X0,X1] :
( ~ aNormalFormOfIn0(X2,X0,X1)
| aElement0(X2)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f114,plain,
! [X2,X0,X1] :
( aNormalFormOfIn0(X2,X0,X1)
| ~ aElement0(X2)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| aReductOfIn0(sK15(X1,X2),X2,X1)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f115,plain,
isTerminating0(xR),
inference(cnf_transformation,[],[f14]) ).
fof(f116,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[],[f14]) ).
fof(f117,plain,
aElement0(sK16),
inference(cnf_transformation,[],[f70]) ).
fof(f118,plain,
! [X2] :
( ~ iLess0(X2,sK16)
| aNormalFormOfIn0(sK17(X2),X2,xR)
| ~ aElement0(X2) ),
inference(cnf_transformation,[],[f70]) ).
fof(f119,plain,
! [X1] : ~ aNormalFormOfIn0(X1,sK16,xR),
inference(cnf_transformation,[],[f70]) ).
fof(f120,plain,
! [X2,X1] :
( sdtmndtasgtdt0(X2,X1,X2)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(equality_resolution,[],[f80]) ).
fof(f125,plain,
! [X2,X1] :
( ~ aRewritingSystem0(X1)
| ~ aElement0(X2)
| sdtmndtasgtdt0(X2,X1,X2) ),
inference(duplicate_literal_removal,[],[f120]) ).
fof(f130,plain,
! [X0] :
( sdtmndtasgtdt0(X0,xR,X0)
| ~ aElement0(X0) ),
inference(resolution,[],[f125,f116]) ).
fof(f131,plain,
! [X2,X0,X1] :
( sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2)
| ~ aReductOfIn0(X2,X0,X1)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(resolution,[],[f79,f76]) ).
fof(f132,plain,
! [X2,X0,X1] :
( ~ aReductOfIn0(X2,X0,X1)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2)
| sdtmndtasgtdt0(X0,X1,X2) ),
inference(duplicate_literal_removal,[],[f131]) ).
fof(f133,plain,
! [X0,X1] :
( ~ sdtmndtplgtdt0(sK16,X0,X1)
| ~ aElement0(sK16)
| ~ aElement0(X1)
| ~ isTerminating0(X0)
| ~ aRewritingSystem0(X0)
| aNormalFormOfIn0(sK17(X1),X1,xR)
| ~ aElement0(X1) ),
inference(resolution,[],[f106,f118]) ).
fof(f135,plain,
! [X0,X1] :
( ~ sdtmndtplgtdt0(sK16,X0,X1)
| ~ aElement0(sK16)
| ~ aElement0(X1)
| ~ isTerminating0(X0)
| ~ aRewritingSystem0(X0)
| aNormalFormOfIn0(sK17(X1),X1,xR) ),
inference(duplicate_literal_removal,[],[f133]) ).
fof(f137,definition,
( spl19_1
<=> aElement0(sK16) ),
introduced(definition,[new_symbols(definition,[spl19_1])],[avatar_definition]) ).
fof(f138,plain,
( ~ aElement0(sK16)
| spl19_1 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f140,definition,
( spl19_2
<=> ! [X0,X1] :
( ~ sdtmndtplgtdt0(sK16,X0,X1)
| aNormalFormOfIn0(sK17(X1),X1,xR)
| ~ aRewritingSystem0(X0)
| ~ isTerminating0(X0)
| ~ aElement0(X1) ) ),
introduced(definition,[new_symbols(definition,[spl19_2])],[avatar_definition]) ).
fof(f141,plain,
( ! [X0,X1] :
( aNormalFormOfIn0(sK17(X1),X1,xR)
| ~ sdtmndtplgtdt0(sK16,X0,X1)
| ~ aRewritingSystem0(X0)
| ~ isTerminating0(X0)
| ~ aElement0(X1) )
| ~ spl19_2 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f142,plain,
( ~ spl19_1
| spl19_2 ),
inference(avatar_split_clause,[],[f135,f140,f137]) ).
fof(f143,plain,
( $false
| spl19_1 ),
inference(resolution,[],[f138,f117]) ).
fof(f144,plain,
spl19_1,
inference(avatar_contradiction_clause,[],[f143]) ).
fof(f146,plain,
( ! [X0,X1] :
( ~ sdtmndtplgtdt0(sK16,X0,X1)
| ~ aRewritingSystem0(X0)
| ~ isTerminating0(X0)
| ~ aElement0(X1)
| sdtmndtasgtdt0(X1,xR,sK17(X1))
| ~ aElement0(X1)
| ~ aRewritingSystem0(xR) )
| ~ spl19_2 ),
inference(resolution,[],[f141,f112]) ).
fof(f147,plain,
( ! [X2,X0,X1] :
( ~ sdtmndtplgtdt0(sK16,X0,X1)
| ~ aRewritingSystem0(X0)
| ~ isTerminating0(X0)
| ~ aElement0(X1)
| ~ aReductOfIn0(X2,sK17(X1),xR)
| ~ aElement0(X1)
| ~ aRewritingSystem0(xR) )
| ~ spl19_2 ),
inference(resolution,[],[f141,f111]) ).
fof(f148,plain,
( ! [X0,X1] :
( ~ sdtmndtplgtdt0(sK16,X0,X1)
| ~ aRewritingSystem0(X0)
| ~ isTerminating0(X0)
| ~ aElement0(X1)
| aElement0(sK17(X1))
| ~ aElement0(X1)
| ~ aRewritingSystem0(xR) )
| ~ spl19_2 ),
inference(resolution,[],[f141,f113]) ).
fof(f149,plain,
( ! [X0,X1] :
( ~ sdtmndtplgtdt0(sK16,X0,X1)
| ~ aRewritingSystem0(X0)
| ~ isTerminating0(X0)
| ~ aElement0(X1)
| aElement0(sK17(X1))
| ~ aRewritingSystem0(xR) )
| ~ spl19_2 ),
inference(duplicate_literal_removal,[],[f148]) ).
fof(f150,plain,
( ! [X2,X0,X1] :
( ~ sdtmndtplgtdt0(sK16,X0,X1)
| ~ aRewritingSystem0(X0)
| ~ isTerminating0(X0)
| ~ aElement0(X1)
| ~ aReductOfIn0(X2,sK17(X1),xR)
| ~ aRewritingSystem0(xR) )
| ~ spl19_2 ),
inference(duplicate_literal_removal,[],[f147]) ).
fof(f151,plain,
( ! [X0,X1] :
( ~ sdtmndtplgtdt0(sK16,X0,X1)
| ~ aRewritingSystem0(X0)
| ~ isTerminating0(X0)
| ~ aElement0(X1)
| sdtmndtasgtdt0(X1,xR,sK17(X1))
| ~ aRewritingSystem0(xR) )
| ~ spl19_2 ),
inference(duplicate_literal_removal,[],[f146]) ).
fof(f153,definition,
( spl19_3
<=> aRewritingSystem0(xR) ),
introduced(definition,[new_symbols(definition,[spl19_3])],[avatar_definition]) ).
fof(f154,plain,
( ~ aRewritingSystem0(xR)
| spl19_3 ),
inference(avatar_component_clause,[],[f153]) ).
fof(f156,definition,
( spl19_4
<=> ! [X0,X1] :
( ~ sdtmndtplgtdt0(sK16,X0,X1)
| aElement0(sK17(X1))
| ~ aElement0(X1)
| ~ isTerminating0(X0)
| ~ aRewritingSystem0(X0) ) ),
introduced(definition,[new_symbols(definition,[spl19_4])],[avatar_definition]) ).
fof(f157,plain,
( ! [X0,X1] :
( ~ isTerminating0(X0)
| aElement0(sK17(X1))
| ~ aElement0(X1)
| ~ sdtmndtplgtdt0(sK16,X0,X1)
| ~ aRewritingSystem0(X0) )
| ~ spl19_4 ),
inference(avatar_component_clause,[],[f156]) ).
fof(f158,plain,
( ~ spl19_3
| spl19_4
| ~ spl19_2 ),
inference(avatar_split_clause,[],[f149,f140,f156,f153]) ).
fof(f160,definition,
( spl19_5
<=> ! [X2,X0,X1] :
( ~ sdtmndtplgtdt0(sK16,X0,X1)
| ~ aReductOfIn0(X2,sK17(X1),xR)
| ~ aElement0(X1)
| ~ isTerminating0(X0)
| ~ aRewritingSystem0(X0) ) ),
introduced(definition,[new_symbols(definition,[spl19_5])],[avatar_definition]) ).
fof(f161,plain,
( ! [X2,X0,X1] :
( ~ isTerminating0(X0)
| ~ aReductOfIn0(X2,sK17(X1),xR)
| ~ aElement0(X1)
| ~ sdtmndtplgtdt0(sK16,X0,X1)
| ~ aRewritingSystem0(X0) )
| ~ spl19_5 ),
inference(avatar_component_clause,[],[f160]) ).
fof(f162,plain,
( ~ spl19_3
| spl19_5
| ~ spl19_2 ),
inference(avatar_split_clause,[],[f150,f140,f160,f153]) ).
fof(f164,definition,
( spl19_6
<=> ! [X0,X1] :
( ~ sdtmndtplgtdt0(sK16,X0,X1)
| sdtmndtasgtdt0(X1,xR,sK17(X1))
| ~ aElement0(X1)
| ~ isTerminating0(X0)
| ~ aRewritingSystem0(X0) ) ),
introduced(definition,[new_symbols(definition,[spl19_6])],[avatar_definition]) ).
fof(f165,plain,
( ! [X0,X1] :
( ~ isTerminating0(X0)
| sdtmndtasgtdt0(X1,xR,sK17(X1))
| ~ aElement0(X1)
| ~ sdtmndtplgtdt0(sK16,X0,X1)
| ~ aRewritingSystem0(X0) )
| ~ spl19_6 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f166,plain,
( ~ spl19_3
| spl19_6
| ~ spl19_2 ),
inference(avatar_split_clause,[],[f151,f140,f164,f153]) ).
fof(f171,plain,
( $false
| spl19_3 ),
inference(resolution,[],[f154,f116]) ).
fof(f172,plain,
spl19_3,
inference(avatar_contradiction_clause,[],[f171]) ).
fof(f190,plain,
( ! [X0] :
( aElement0(sK17(X0))
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(sK16,xR,X0)
| ~ aRewritingSystem0(xR) )
| ~ spl19_4 ),
inference(resolution,[],[f157,f115]) ).
fof(f198,definition,
( spl19_10
<=> ! [X0] :
( aElement0(sK17(X0))
| ~ sdtmndtplgtdt0(sK16,xR,X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[spl19_10])],[avatar_definition]) ).
fof(f199,plain,
( ! [X0] :
( ~ sdtmndtplgtdt0(sK16,xR,X0)
| aElement0(sK17(X0))
| ~ aElement0(X0) )
| ~ spl19_10 ),
inference(avatar_component_clause,[],[f198]) ).
fof(f200,plain,
( ~ spl19_3
| spl19_10
| ~ spl19_4 ),
inference(avatar_split_clause,[],[f190,f156,f198,f153]) ).
fof(f201,plain,
( ! [X0,X1] :
( ~ aReductOfIn0(X0,sK17(X1),xR)
| ~ aElement0(X1)
| ~ sdtmndtplgtdt0(sK16,xR,X1)
| ~ aRewritingSystem0(xR) )
| ~ spl19_5 ),
inference(resolution,[],[f161,f115]) ).
fof(f209,definition,
( spl19_11
<=> ! [X0,X1] :
( ~ aReductOfIn0(X0,sK17(X1),xR)
| ~ sdtmndtplgtdt0(sK16,xR,X1)
| ~ aElement0(X1) ) ),
introduced(definition,[new_symbols(definition,[spl19_11])],[avatar_definition]) ).
fof(f210,plain,
( ! [X0,X1] :
( ~ sdtmndtplgtdt0(sK16,xR,X1)
| ~ aReductOfIn0(X0,sK17(X1),xR)
| ~ aElement0(X1) )
| ~ spl19_11 ),
inference(avatar_component_clause,[],[f209]) ).
fof(f211,plain,
( ~ spl19_3
| spl19_11
| ~ spl19_5 ),
inference(avatar_split_clause,[],[f201,f160,f209,f153]) ).
fof(f218,plain,
( ! [X0] :
( sdtmndtasgtdt0(X0,xR,sK17(X0))
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(sK16,xR,X0)
| ~ aRewritingSystem0(xR) )
| ~ spl19_6 ),
inference(resolution,[],[f165,f115]) ).
fof(f226,definition,
( spl19_13
<=> ! [X0] :
( sdtmndtasgtdt0(X0,xR,sK17(X0))
| ~ sdtmndtplgtdt0(sK16,xR,X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[spl19_13])],[avatar_definition]) ).
fof(f227,plain,
( ! [X0] :
( ~ sdtmndtplgtdt0(sK16,xR,X0)
| sdtmndtasgtdt0(X0,xR,sK17(X0))
| ~ aElement0(X0) )
| ~ spl19_13 ),
inference(avatar_component_clause,[],[f226]) ).
fof(f228,plain,
( ~ spl19_3
| spl19_13
| ~ spl19_6 ),
inference(avatar_split_clause,[],[f218,f164,f226,f153]) ).
fof(f235,plain,
( ! [X0] :
( aElement0(sK17(X0))
| ~ aElement0(X0)
| ~ aReductOfIn0(X0,sK16,xR)
| ~ aElement0(sK16)
| ~ aRewritingSystem0(xR)
| ~ aElement0(X0) )
| ~ spl19_10 ),
inference(resolution,[],[f199,f76]) ).
fof(f236,plain,
( ! [X0] :
( aElement0(sK17(X0))
| ~ aElement0(X0)
| ~ aReductOfIn0(X0,sK16,xR)
| ~ aElement0(sK16)
| ~ aRewritingSystem0(xR) )
| ~ spl19_10 ),
inference(duplicate_literal_removal,[],[f235]) ).
fof(f238,definition,
( spl19_15
<=> ! [X0] :
( aElement0(sK17(X0))
| ~ aReductOfIn0(X0,sK16,xR)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[spl19_15])],[avatar_definition]) ).
fof(f239,plain,
( ! [X0] :
( ~ aReductOfIn0(X0,sK16,xR)
| aElement0(sK17(X0))
| ~ aElement0(X0) )
| ~ spl19_15 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f240,plain,
( ~ spl19_3
| ~ spl19_1
| spl19_15
| ~ spl19_10 ),
inference(avatar_split_clause,[],[f236,f198,f238,f137,f153]) ).
fof(f241,plain,
( ! [X0,X1] :
( ~ aReductOfIn0(X0,sK17(X1),xR)
| ~ aElement0(X1)
| ~ aReductOfIn0(X1,sK16,xR)
| ~ aElement0(sK16)
| ~ aRewritingSystem0(xR)
| ~ aElement0(X1) )
| ~ spl19_11 ),
inference(resolution,[],[f210,f76]) ).
fof(f242,plain,
( ! [X0,X1] :
( ~ aReductOfIn0(X0,sK17(X1),xR)
| ~ aElement0(X1)
| ~ aReductOfIn0(X1,sK16,xR)
| ~ aElement0(sK16)
| ~ aRewritingSystem0(xR) )
| ~ spl19_11 ),
inference(duplicate_literal_removal,[],[f241]) ).
fof(f244,definition,
( spl19_16
<=> ! [X0,X1] :
( ~ aReductOfIn0(X0,sK17(X1),xR)
| ~ aReductOfIn0(X1,sK16,xR)
| ~ aElement0(X1) ) ),
introduced(definition,[new_symbols(definition,[spl19_16])],[avatar_definition]) ).
fof(f245,plain,
( ! [X0,X1] :
( ~ aReductOfIn0(X0,sK17(X1),xR)
| ~ aReductOfIn0(X1,sK16,xR)
| ~ aElement0(X1) )
| ~ spl19_16 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f246,plain,
( ~ spl19_3
| ~ spl19_1
| spl19_16
| ~ spl19_11 ),
inference(avatar_split_clause,[],[f242,f209,f244,f137,f153]) ).
fof(f247,plain,
( ! [X0] :
( sdtmndtasgtdt0(X0,xR,sK17(X0))
| ~ aElement0(X0)
| ~ aReductOfIn0(X0,sK16,xR)
| ~ aElement0(sK16)
| ~ aRewritingSystem0(xR)
| ~ aElement0(X0) )
| ~ spl19_13 ),
inference(resolution,[],[f227,f76]) ).
fof(f248,plain,
( ! [X0] :
( sdtmndtasgtdt0(X0,xR,sK17(X0))
| ~ aElement0(X0)
| ~ aReductOfIn0(X0,sK16,xR)
| ~ aElement0(sK16)
| ~ aRewritingSystem0(xR) )
| ~ spl19_13 ),
inference(duplicate_literal_removal,[],[f247]) ).
fof(f250,definition,
( spl19_17
<=> ! [X0] :
( sdtmndtasgtdt0(X0,xR,sK17(X0))
| ~ aReductOfIn0(X0,sK16,xR)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[spl19_17])],[avatar_definition]) ).
fof(f251,plain,
( ! [X0] :
( ~ aReductOfIn0(X0,sK16,xR)
| sdtmndtasgtdt0(X0,xR,sK17(X0))
| ~ aElement0(X0) )
| ~ spl19_17 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f252,plain,
( ~ spl19_3
| ~ spl19_1
| spl19_17
| ~ spl19_13 ),
inference(avatar_split_clause,[],[f248,f226,f250,f137,f153]) ).
fof(f996,plain,
! [X2,X0,X1] :
( sdtmndtasgtdt0(X0,xR,X2)
| ~ sdtmndtasgtdt0(X1,xR,X2)
| ~ aElement0(X0)
| ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(resolution,[],[f81,f116]) ).
fof(f1262,plain,
! [X0] :
( ~ aElement0(X0)
| ~ sdtmndtasgtdt0(sK16,xR,X0)
| aReductOfIn0(sK15(xR,X0),X0,xR)
| ~ aElement0(sK16)
| ~ aRewritingSystem0(xR) ),
inference(resolution,[],[f114,f119]) ).
fof(f1270,definition,
( spl19_138
<=> ! [X0] :
( ~ aElement0(X0)
| aReductOfIn0(sK15(xR,X0),X0,xR)
| ~ sdtmndtasgtdt0(sK16,xR,X0) ) ),
introduced(definition,[new_symbols(definition,[spl19_138])],[avatar_definition]) ).
fof(f1271,plain,
( ! [X0] :
( aReductOfIn0(sK15(xR,X0),X0,xR)
| ~ aElement0(X0)
| ~ sdtmndtasgtdt0(sK16,xR,X0) )
| ~ spl19_138 ),
inference(avatar_component_clause,[],[f1270]) ).
fof(f1272,plain,
( ~ spl19_3
| ~ spl19_1
| spl19_138 ),
inference(avatar_split_clause,[],[f1262,f1270,f137,f153]) ).
fof(f1275,plain,
( ! [X0] :
( ~ aElement0(X0)
| ~ sdtmndtasgtdt0(sK16,xR,X0)
| ~ aElement0(X0)
| ~ aRewritingSystem0(xR)
| ~ aElement0(sK15(xR,X0))
| sdtmndtasgtdt0(X0,xR,sK15(xR,X0)) )
| ~ spl19_138 ),
inference(resolution,[],[f1271,f132]) ).
fof(f1276,plain,
( ! [X0] :
( ~ aElement0(X0)
| ~ sdtmndtasgtdt0(sK16,xR,X0)
| aElement0(sK15(xR,X0))
| ~ aElement0(X0)
| ~ aRewritingSystem0(xR) )
| ~ spl19_138 ),
inference(resolution,[],[f1271,f71]) ).
fof(f1280,plain,
( ~ aElement0(sK16)
| ~ sdtmndtasgtdt0(sK16,xR,sK16)
| sdtmndtasgtdt0(sK15(xR,sK16),xR,sK17(sK15(xR,sK16)))
| ~ aElement0(sK15(xR,sK16))
| ~ spl19_17
| ~ spl19_138 ),
inference(resolution,[],[f1271,f251]) ).
fof(f1281,plain,
( ~ aElement0(sK16)
| ~ sdtmndtasgtdt0(sK16,xR,sK16)
| aElement0(sK17(sK15(xR,sK16)))
| ~ aElement0(sK15(xR,sK16))
| ~ spl19_15
| ~ spl19_138 ),
inference(resolution,[],[f1271,f239]) ).
fof(f1289,plain,
( ! [X0] :
( ~ aReductOfIn0(X0,sK16,xR)
| ~ sdtmndtasgtdt0(sK16,xR,sK17(X0))
| ~ aElement0(sK17(X0))
| ~ aElement0(X0) )
| ~ spl19_16
| ~ spl19_138 ),
inference(resolution,[],[f1271,f245]) ).
fof(f1290,plain,
( ! [X0] :
( ~ aElement0(X0)
| ~ sdtmndtasgtdt0(sK16,xR,X0)
| aElement0(sK15(xR,X0))
| ~ aRewritingSystem0(xR) )
| ~ spl19_138 ),
inference(duplicate_literal_removal,[],[f1276]) ).
fof(f1291,plain,
( ! [X0] :
( ~ aElement0(X0)
| ~ sdtmndtasgtdt0(sK16,xR,X0)
| ~ aRewritingSystem0(xR)
| ~ aElement0(sK15(xR,X0))
| sdtmndtasgtdt0(X0,xR,sK15(xR,X0)) )
| ~ spl19_138 ),
inference(duplicate_literal_removal,[],[f1275]) ).
fof(f1295,definition,
( spl19_139
<=> aElement0(sK17(sK15(xR,sK16))) ),
introduced(definition,[new_symbols(definition,[spl19_139])],[avatar_definition]) ).
fof(f1301,definition,
( spl19_141
<=> aElement0(sK15(xR,sK16)) ),
introduced(definition,[new_symbols(definition,[spl19_141])],[avatar_definition]) ).
fof(f1304,definition,
( spl19_142
<=> sdtmndtasgtdt0(sK16,xR,sK16) ),
introduced(definition,[new_symbols(definition,[spl19_142])],[avatar_definition]) ).
fof(f1305,plain,
( ~ sdtmndtasgtdt0(sK16,xR,sK16)
| spl19_142 ),
inference(avatar_component_clause,[],[f1304]) ).
fof(f1312,definition,
( spl19_144
<=> sdtmndtasgtdt0(sK15(xR,sK16),xR,sK17(sK15(xR,sK16))) ),
introduced(definition,[new_symbols(definition,[spl19_144])],[avatar_definition]) ).
fof(f1313,plain,
( sdtmndtasgtdt0(sK15(xR,sK16),xR,sK17(sK15(xR,sK16)))
| ~ spl19_144 ),
inference(avatar_component_clause,[],[f1312]) ).
fof(f1323,plain,
( ~ spl19_141
| spl19_139
| ~ spl19_142
| ~ spl19_1
| ~ spl19_15
| ~ spl19_138 ),
inference(avatar_split_clause,[],[f1281,f1270,f238,f137,f1304,f1295,f1301]) ).
fof(f1324,plain,
( ~ spl19_141
| spl19_144
| ~ spl19_142
| ~ spl19_1
| ~ spl19_17
| ~ spl19_138 ),
inference(avatar_split_clause,[],[f1280,f1270,f250,f137,f1304,f1312,f1301]) ).
fof(f1338,definition,
( spl19_149
<=> ! [X0] :
( ~ aElement0(X0)
| aElement0(sK15(xR,X0))
| ~ sdtmndtasgtdt0(sK16,xR,X0) ) ),
introduced(definition,[new_symbols(definition,[spl19_149])],[avatar_definition]) ).
fof(f1339,plain,
( ! [X0] :
( ~ sdtmndtasgtdt0(sK16,xR,X0)
| aElement0(sK15(xR,X0))
| ~ aElement0(X0) )
| ~ spl19_149 ),
inference(avatar_component_clause,[],[f1338]) ).
fof(f1340,plain,
( ~ spl19_3
| spl19_149
| ~ spl19_138 ),
inference(avatar_split_clause,[],[f1290,f1270,f1338,f153]) ).
fof(f1342,definition,
( spl19_150
<=> ! [X0] :
( ~ aElement0(X0)
| sdtmndtasgtdt0(X0,xR,sK15(xR,X0))
| ~ aElement0(sK15(xR,X0))
| ~ sdtmndtasgtdt0(sK16,xR,X0) ) ),
introduced(definition,[new_symbols(definition,[spl19_150])],[avatar_definition]) ).
fof(f1343,plain,
( ! [X0] :
( sdtmndtasgtdt0(X0,xR,sK15(xR,X0))
| ~ aElement0(X0)
| ~ aElement0(sK15(xR,X0))
| ~ sdtmndtasgtdt0(sK16,xR,X0) )
| ~ spl19_150 ),
inference(avatar_component_clause,[],[f1342]) ).
fof(f1344,plain,
( ~ spl19_3
| spl19_150
| ~ spl19_138 ),
inference(avatar_split_clause,[],[f1291,f1270,f1342,f153]) ).
fof(f1345,plain,
( aElement0(sK15(xR,sK16))
| ~ aElement0(sK16)
| ~ aElement0(sK16)
| ~ spl19_149 ),
inference(resolution,[],[f1339,f130]) ).
fof(f1354,plain,
( aElement0(sK15(xR,sK16))
| ~ aElement0(sK16)
| ~ spl19_149 ),
inference(duplicate_literal_removal,[],[f1345]) ).
fof(f1360,plain,
( ~ spl19_1
| spl19_141
| ~ spl19_149 ),
inference(avatar_split_clause,[],[f1354,f1338,f1301,f137]) ).
fof(f1367,plain,
( ~ aElement0(sK16)
| spl19_142 ),
inference(resolution,[],[f1305,f130]) ).
fof(f1374,plain,
( ~ spl19_1
| spl19_142 ),
inference(avatar_split_clause,[],[f1367,f1304,f137]) ).
fof(f1377,definition,
( spl19_154
<=> sdtmndtasgtdt0(sK16,xR,sK15(xR,sK16)) ),
introduced(definition,[new_symbols(definition,[spl19_154])],[avatar_definition]) ).
fof(f1378,plain,
( ~ sdtmndtasgtdt0(sK16,xR,sK15(xR,sK16))
| spl19_154 ),
inference(avatar_component_clause,[],[f1377]) ).
fof(f1384,plain,
( ~ sdtmndtasgtdt0(sK16,xR,sK17(sK15(xR,sK16)))
| ~ aElement0(sK17(sK15(xR,sK16)))
| ~ aElement0(sK15(xR,sK16))
| ~ aElement0(sK16)
| ~ sdtmndtasgtdt0(sK16,xR,sK16)
| ~ spl19_16
| ~ spl19_138 ),
inference(resolution,[],[f1289,f1271]) ).
fof(f1387,definition,
( spl19_156
<=> sdtmndtasgtdt0(sK16,xR,sK17(sK15(xR,sK16))) ),
introduced(definition,[new_symbols(definition,[spl19_156])],[avatar_definition]) ).
fof(f1388,plain,
( ~ sdtmndtasgtdt0(sK16,xR,sK17(sK15(xR,sK16)))
| spl19_156 ),
inference(avatar_component_clause,[],[f1387]) ).
fof(f1389,plain,
( ~ spl19_142
| ~ spl19_1
| ~ spl19_141
| ~ spl19_139
| ~ spl19_156
| ~ spl19_16
| ~ spl19_138 ),
inference(avatar_split_clause,[],[f1384,f1270,f244,f1387,f1295,f1301,f137,f1304]) ).
fof(f1390,plain,
( ~ aElement0(sK16)
| ~ aElement0(sK15(xR,sK16))
| ~ sdtmndtasgtdt0(sK16,xR,sK16)
| ~ spl19_150
| spl19_154 ),
inference(resolution,[],[f1378,f1343]) ).
fof(f1396,plain,
( ~ spl19_142
| ~ spl19_141
| ~ spl19_1
| ~ spl19_150
| spl19_154 ),
inference(avatar_split_clause,[],[f1390,f1377,f1342,f137,f1301,f1304]) ).
fof(f1398,plain,
( ! [X0] :
( ~ sdtmndtasgtdt0(X0,xR,sK17(sK15(xR,sK16)))
| ~ aElement0(sK16)
| ~ sdtmndtasgtdt0(sK16,xR,X0)
| ~ aElement0(X0)
| ~ aElement0(sK17(sK15(xR,sK16))) )
| spl19_156 ),
inference(resolution,[],[f1388,f996]) ).
fof(f1400,definition,
( spl19_158
<=> ! [X0] :
( ~ sdtmndtasgtdt0(X0,xR,sK17(sK15(xR,sK16)))
| ~ aElement0(X0)
| ~ sdtmndtasgtdt0(sK16,xR,X0) ) ),
introduced(definition,[new_symbols(definition,[spl19_158])],[avatar_definition]) ).
fof(f1401,plain,
( ! [X0] :
( ~ sdtmndtasgtdt0(X0,xR,sK17(sK15(xR,sK16)))
| ~ aElement0(X0)
| ~ sdtmndtasgtdt0(sK16,xR,X0) )
| ~ spl19_158 ),
inference(avatar_component_clause,[],[f1400]) ).
fof(f1402,plain,
( ~ spl19_139
| ~ spl19_1
| spl19_158
| spl19_156 ),
inference(avatar_split_clause,[],[f1398,f1387,f1400,f137,f1295]) ).
fof(f1592,plain,
( ~ aElement0(sK15(xR,sK16))
| ~ sdtmndtasgtdt0(sK16,xR,sK15(xR,sK16))
| ~ spl19_144
| ~ spl19_158 ),
inference(resolution,[],[f1401,f1313]) ).
fof(f1602,plain,
( ~ spl19_154
| ~ spl19_141
| ~ spl19_144
| ~ spl19_158 ),
inference(avatar_split_clause,[],[f1592,f1400,f1312,f1301,f1377]) ).
cnf(s1,plain,
( ~ spl19_1
| spl19_2 ),
inference(sat_conversion,[],[f142]) ).
cnf(s2,plain,
spl19_1,
inference(sat_conversion,[],[f144]) ).
cnf(s3,plain,
( ~ spl19_2
| ~ spl19_3
| spl19_4 ),
inference(sat_conversion,[],[f158]) ).
cnf(s4,plain,
( ~ spl19_2
| ~ spl19_3
| spl19_5 ),
inference(sat_conversion,[],[f162]) ).
cnf(s5,plain,
( ~ spl19_2
| ~ spl19_3
| spl19_6 ),
inference(sat_conversion,[],[f166]) ).
cnf(s7,plain,
spl19_3,
inference(sat_conversion,[],[f172]) ).
cnf(s10,plain,
( ~ spl19_3
| ~ spl19_4
| spl19_10 ),
inference(sat_conversion,[],[f200]) ).
cnf(s11,plain,
( ~ spl19_3
| ~ spl19_5
| spl19_11 ),
inference(sat_conversion,[],[f211]) ).
cnf(s13,plain,
( ~ spl19_3
| ~ spl19_6
| spl19_13 ),
inference(sat_conversion,[],[f228]) ).
cnf(s15,plain,
( ~ spl19_1
| ~ spl19_3
| ~ spl19_10
| spl19_15 ),
inference(sat_conversion,[],[f240]) ).
cnf(s16,plain,
( ~ spl19_1
| ~ spl19_3
| ~ spl19_11
| spl19_16 ),
inference(sat_conversion,[],[f246]) ).
cnf(s17,plain,
( ~ spl19_1
| ~ spl19_3
| ~ spl19_13
| spl19_17 ),
inference(sat_conversion,[],[f252]) ).
cnf(s161,plain,
( ~ spl19_1
| ~ spl19_3
| spl19_138 ),
inference(sat_conversion,[],[f1272]) ).
cnf(s168,plain,
( ~ spl19_1
| ~ spl19_15
| ~ spl19_138
| spl19_139
| ~ spl19_141
| ~ spl19_142 ),
inference(sat_conversion,[],[f1323]) ).
cnf(s169,plain,
( ~ spl19_1
| ~ spl19_17
| ~ spl19_138
| ~ spl19_141
| ~ spl19_142
| spl19_144 ),
inference(sat_conversion,[],[f1324]) ).
cnf(s173,plain,
( ~ spl19_3
| ~ spl19_138
| spl19_149 ),
inference(sat_conversion,[],[f1340]) ).
cnf(s174,plain,
( ~ spl19_3
| ~ spl19_138
| spl19_150 ),
inference(sat_conversion,[],[f1344]) ).
cnf(s176,plain,
( ~ spl19_1
| spl19_141
| ~ spl19_149 ),
inference(sat_conversion,[],[f1360]) ).
cnf(s179,plain,
( ~ spl19_1
| spl19_142 ),
inference(sat_conversion,[],[f1374]) ).
cnf(s181,plain,
( ~ spl19_1
| ~ spl19_16
| ~ spl19_138
| ~ spl19_139
| ~ spl19_141
| ~ spl19_142
| ~ spl19_156 ),
inference(sat_conversion,[],[f1389]) ).
cnf(s183,plain,
( ~ spl19_1
| ~ spl19_141
| ~ spl19_142
| ~ spl19_150
| spl19_154 ),
inference(sat_conversion,[],[f1396]) ).
cnf(s184,plain,
( ~ spl19_1
| ~ spl19_139
| spl19_156
| spl19_158 ),
inference(sat_conversion,[],[f1402]) ).
cnf(s208,plain,
( ~ spl19_141
| ~ spl19_144
| ~ spl19_154
| ~ spl19_158 ),
inference(sat_conversion,[],[f1602]) ).
cnf(s217,plain,
( ~ spl19_2
| spl19_6 ),
inference(rat,[],[s5,s7]) ).
cnf(s218,plain,
( ~ spl19_2
| spl19_5 ),
inference(rat,[],[s4,s7]) ).
cnf(s219,plain,
( ~ spl19_2
| spl19_4 ),
inference(rat,[],[s3,s7]) ).
cnf(s220,plain,
spl19_142,
inference(rat,[],[s179,s2]) ).
cnf(s221,plain,
spl19_138,
inference(rat,[],[s161,s7,s2]) ).
cnf(s222,plain,
spl19_150,
inference(rat,[],[s174,s7,s221]) ).
cnf(s223,plain,
spl19_149,
inference(rat,[],[s173,s7,s221]) ).
cnf(s225,plain,
spl19_141,
inference(rat,[],[s176,s2,s223]) ).
cnf(s226,plain,
spl19_154,
inference(rat,[],[s183,s222,s220,s2,s225]) ).
cnf(s228,plain,
spl19_2,
inference(rat,[],[s1,s2]) ).
cnf(s230,plain,
spl19_6,
inference(rat,[],[s217,s228]) ).
cnf(s231,plain,
spl19_5,
inference(rat,[],[s218,s228]) ).
cnf(s232,plain,
spl19_4,
inference(rat,[],[s219,s228]) ).
cnf(s260,plain,
spl19_13,
inference(rat,[],[s13,s7,s230]) ).
cnf(s274,plain,
spl19_11,
inference(rat,[],[s11,s7,s231]) ).
cnf(s288,plain,
spl19_10,
inference(rat,[],[s10,s7,s232]) ).
cnf(s303,plain,
spl19_17,
inference(rat,[],[s17,s2,s7,s260]) ).
cnf(s306,plain,
spl19_16,
inference(rat,[],[s16,s2,s7,s274]) ).
cnf(s309,plain,
spl19_15,
inference(rat,[],[s15,s2,s7,s288]) ).
cnf(s325,plain,
spl19_144,
inference(rat,[],[s169,s225,s220,s221,s2,s303]) ).
cnf(s335,plain,
spl19_139,
inference(rat,[],[s168,s220,s225,s221,s2,s309]) ).
cnf(s352,plain,
~ spl19_158,
inference(rat,[],[s208,s226,s225,s325]) ).
cnf(s368,plain,
spl19_156,
inference(rat,[],[s184,s352,s2,s335]) ).
cnf(s369,plain,
$false,
inference(rat,[],[s181,s306,s220,s225,s221,s2,s368,s335]) ).
fof(f1635,plain,
$false,
inference(avatar_sat_refutation,[],[s369]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM013+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n019.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 21:45:18 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.15/0.72 % (308522)Detected formulas, will run a generic FOF schedule.
% 2.15/0.72 % (308533)dis-21_1_sil=8000:lcm=predicate:random_seed=1584959759: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)
% 2.15/0.72 % (308533)First to succeed.
% 2.15/0.72 % (308533)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-308522"
% 2.15/0.72 % (308530)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4278489992:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.15/0.72 % (308531)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=531708912:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.15/0.72 % (308529)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=934259214:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.15/0.72 % (308527)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=2201836871:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.15/0.72 % (308532)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1384260108:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.15/0.72 % (308528)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=3449933555:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.15/0.72 % (308530)Refutation not found, incomplete strategy
% 2.15/0.72 % (308530)------------------------------
% 2.15/0.72 % (308530)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.15/0.72 % (308530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.72 % (308530)CaDiCaL version: 2.1.3
% 2.15/0.72 % (308530)Termination reason: Refutation not found, incomplete strategy
% 2.15/0.72 % (308530)Time elapsed: 0.001 s
% 2.15/0.72 % (308530)Peak memory usage: 87 MB
% 2.15/0.72 % (308532)Also succeeded, but the first one will report.
% 2.15/0.72 % (308531)Instruction limit reached!
% 2.15/0.72 % (308531)------------------------------
% 2.15/0.72 % (308531)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.15/0.72 % (308531)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.72 % (308531)CaDiCaL version: 2.1.3
% 2.15/0.72 % (308531)Termination reason: Instruction limit
% 2.15/0.72 % (308531)Termination phase: Saturation
% 2.15/0.72 % (308531)Time elapsed: 0.050 s
% 2.15/0.72 % (308531)Peak memory usage: 87 MB
% 2.15/0.72 % (308531)Instructions burned: 121 (million)
% 2.15/0.72 % (308533)Refutation found. Thanks to Tanya!
% 2.15/0.72 % SZS status Theorem for theBenchmark
% 2.15/0.72 % SZS output start Proof for theBenchmark
% See solution above
% 2.57/0.91 % (308533)------------------------------
% 2.57/0.91 % (308533)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/0.91 % (308533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/0.91 % (308533)CaDiCaL version: 2.1.3
% 2.57/0.91 % (308533)Termination reason: Refutation
% 2.57/0.91 % (308533)Time elapsed: 0.015 s
% 2.57/0.91 % (308533)Peak memory usage: 90 MB
% 2.57/0.91 % (308533)Instructions burned: 41 (million)
% 2.57/0.91 % (308533)------------------------------
% 2.57/0.91 % (308533)------------------------------
% 2.57/0.91 % (308522)Success in time 0.299 s
% 2.57/0.91 % Vampire exiting
%------------------------------------------------------------------------------