%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COM019+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n011.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 : Fri Sep 25 01:04:20 PM UTC 2026
% Result : Theorem 59.81s 10.08s
% Output : CNFRefutation 59.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 14
% Syntax : Number of formulae : 164 ( 46 unt; 0 def)
% Number of atoms : 782 ( 36 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 1123 ( 505 ~; 508 |; 86 &)
% ( 12 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 2 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-3 aty)
% Number of variables : 330 ( 0 sgn 313 !; 17 ?; 157 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] :
( ( aRewritingSystem0(X1)
& aElement0(X0) )
=> ! [X2] :
( aReductOfIn0(X2,X0,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mTCRTrans) ).
fof(f12,axiom,
! [X0] :
( aRewritingSystem0(X0)
=> ( isTerminating0(X0)
<=> ! [X1,X2] :
( ( aElement0(X2)
& aElement0(X1) )
=> ( sdtmndtplgtdt0(X1,X0,X2)
=> iLess0(X2,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTermin) ).
fof(f13,axiom,
! [X0,X1] :
( ( aRewritingSystem0(X1)
& aElement0(X0) )
=> ! [X2] :
( aNormalFormOfIn0(X2,X0,X1)
<=> ( ~ ? [X3] : aReductOfIn0(X3,X2,X1)
& sdtmndtasgtdt0(X0,X1,X2)
& aElement0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNFRDef) ).
fof(f15,axiom,
aRewritingSystem0(xR),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__656) ).
fof(f16,axiom,
( isTerminating0(xR)
& isLocallyConfluent0(xR) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__656_01) ).
fof(f17,axiom,
( aElement0(xc)
& aElement0(xb)
& aElement0(xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__731) ).
fof(f18,axiom,
! [X0,X1,X2] :
( ( sdtmndtasgtdt0(X0,xR,X2)
& sdtmndtasgtdt0(X0,xR,X1)
& aElement0(X2)
& aElement0(X1)
& aElement0(X0) )
=> ( iLess0(X0,xa)
=> ? [X3] :
( sdtmndtasgtdt0(X2,xR,X3)
& sdtmndtasgtdt0(X1,xR,X3)
& aElement0(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__715) ).
fof(f20,axiom,
( sdtmndtasgtdt0(xu,xR,xb)
& aReductOfIn0(xu,xa,xR)
& aElement0(xu) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__755) ).
fof(f22,axiom,
( sdtmndtasgtdt0(xv,xR,xw)
& sdtmndtasgtdt0(xu,xR,xw)
& aElement0(xw) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__799) ).
fof(f23,axiom,
aNormalFormOfIn0(xd,xw,xR),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__818) ).
fof(f24,conjecture,
sdtmndtasgtdt0(xb,xR,xd),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f25,negated_conjecture,
~ sdtmndtasgtdt0(xb,xR,xd),
inference(negated_conjecture,[status(cth)],[f24]) ).
fof(f30,plain,
~ sdtmndtasgtdt0(xb,xR,xd),
inference(flattening,[],[f25]) ).
fof(f31,plain,
! [X0,X1] :
( ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ! [X2] :
( ~ aReductOfIn0(X2,X0,X1)
| aElement0(X2) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f32,plain,
! [X0,X1] :
( ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ! [X2] :
( ~ aReductOfIn0(X2,X0,X1)
| aElement0(X2) ) ),
inference(flattening,[],[f31]) ).
fof(f33,plain,
! [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) ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f34,plain,
! [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) ) ) ),
inference(flattening,[],[f33]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ( sdtmndtasgtdt0(X0,X1,X2)
<=> ( sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2 ) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ( sdtmndtasgtdt0(X0,X1,X2)
<=> ( sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2 ) ) ),
inference(flattening,[],[f37]) ).
fof(f39,plain,
! [X0,X1,X2,X3] :
( ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ~ sdtmndtasgtdt0(X2,X1,X3)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| sdtmndtasgtdt0(X0,X1,X3) ),
inference(ennf_transformation,[],[f9]) ).
fof(f40,plain,
! [X0,X1,X2,X3] :
( ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ~ sdtmndtasgtdt0(X2,X1,X3)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| sdtmndtasgtdt0(X0,X1,X3) ),
inference(flattening,[],[f39]) ).
fof(f45,plain,
! [X0] :
( ~ aRewritingSystem0(X0)
| ( isTerminating0(X0)
<=> ! [X1,X2] :
( ~ aElement0(X2)
| ~ aElement0(X1)
| ~ sdtmndtplgtdt0(X1,X0,X2)
| iLess0(X2,X1) ) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f46,plain,
! [X0] :
( ~ aRewritingSystem0(X0)
| ( isTerminating0(X0)
<=> ! [X1,X2] :
( ~ aElement0(X2)
| ~ aElement0(X1)
| ~ sdtmndtplgtdt0(X1,X0,X2)
| iLess0(X2,X1) ) ) ),
inference(flattening,[],[f45]) ).
fof(f47,plain,
! [X0,X1] :
( ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ! [X2] :
( aNormalFormOfIn0(X2,X0,X1)
<=> ( ! [X3] : ~ aReductOfIn0(X3,X2,X1)
& sdtmndtasgtdt0(X0,X1,X2)
& aElement0(X2) ) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f48,plain,
! [X0,X1] :
( ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ! [X2] :
( aNormalFormOfIn0(X2,X0,X1)
<=> ( ! [X3] : ~ aReductOfIn0(X3,X2,X1)
& sdtmndtasgtdt0(X0,X1,X2)
& aElement0(X2) ) ) ),
inference(flattening,[],[f47]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ~ sdtmndtasgtdt0(X0,xR,X2)
| ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ iLess0(X0,xa)
| ? [X3] :
( sdtmndtasgtdt0(X2,xR,X3)
& sdtmndtasgtdt0(X1,xR,X3)
& aElement0(X3) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ~ sdtmndtasgtdt0(X0,xR,X2)
| ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ iLess0(X0,xa)
| ? [X3] :
( sdtmndtasgtdt0(X2,xR,X3)
& sdtmndtasgtdt0(X1,xR,X3)
& aElement0(X3) ) ),
inference(flattening,[],[f51]) ).
fof(f59,plain,
! [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) )
& ( ( ! [X3] :
( ~ sdtmndtplgtdt0(X3,X1,X2)
| ~ aReductOfIn0(X3,X0,X1)
| ~ aElement0(X3) )
& ~ aReductOfIn0(X2,X0,X1) )
| sdtmndtplgtdt0(X0,X1,X2) ) ) ),
inference(nnf_transformation,[],[f34]) ).
fof(f60,plain,
! [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) )
& ( ( ! [X3] :
( ~ sdtmndtplgtdt0(X3,X1,X2)
| ~ aReductOfIn0(X3,X0,X1)
| ~ aElement0(X3) )
& ~ aReductOfIn0(X2,X0,X1) )
| sdtmndtplgtdt0(X0,X1,X2) ) ) ),
inference(flattening,[],[f59]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ( ( ~ sdtmndtplgtdt0(X0,X1,X2)
| ? [X4] :
( sdtmndtplgtdt0(X4,X1,X2)
& aReductOfIn0(X4,X0,X1)
& aElement0(X4) )
| aReductOfIn0(X2,X0,X1) )
& ( ( ! [X3] :
( ~ sdtmndtplgtdt0(X3,X1,X2)
| ~ aReductOfIn0(X3,X0,X1)
| ~ aElement0(X3) )
& ~ aReductOfIn0(X2,X0,X1) )
| sdtmndtplgtdt0(X0,X1,X2) ) ) ),
inference(rectify,[],[f60]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ( ( ~ sdtmndtplgtdt0(X0,X1,X2)
| ( sdtmndtplgtdt0(sK4(X0,X1,X2),X1,X2)
& aReductOfIn0(sK4(X0,X1,X2),X0,X1)
& aElement0(sK4(X0,X1,X2)) )
| aReductOfIn0(X2,X0,X1) )
& ( ( ! [X3] :
( ~ sdtmndtplgtdt0(X3,X1,X2)
| ~ aReductOfIn0(X3,X0,X1)
| ~ aElement0(X3) )
& ~ aReductOfIn0(X2,X0,X1) )
| sdtmndtplgtdt0(X0,X1,X2) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X4,sK4(X0,X1,X2))],[f61]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ( ( ~ sdtmndtasgtdt0(X0,X1,X2)
| sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2 )
& ( ( ~ sdtmndtplgtdt0(X0,X1,X2)
& X0 != X2 )
| sdtmndtasgtdt0(X0,X1,X2) ) ) ),
inference(nnf_transformation,[],[f38]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ( ( ~ sdtmndtasgtdt0(X0,X1,X2)
| sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2 )
& ( ( ~ sdtmndtplgtdt0(X0,X1,X2)
& X0 != X2 )
| sdtmndtasgtdt0(X0,X1,X2) ) ) ),
inference(flattening,[],[f63]) ).
fof(f73,plain,
! [X0] :
( ~ aRewritingSystem0(X0)
| ( ( ~ isTerminating0(X0)
| ! [X1,X2] :
( ~ aElement0(X2)
| ~ aElement0(X1)
| ~ sdtmndtplgtdt0(X1,X0,X2)
| iLess0(X2,X1) ) )
& ( ? [X1,X2] :
( aElement0(X2)
& aElement0(X1)
& sdtmndtplgtdt0(X1,X0,X2)
& ~ iLess0(X2,X1) )
| isTerminating0(X0) ) ) ),
inference(nnf_transformation,[],[f46]) ).
fof(f74,plain,
! [X0] :
( ~ aRewritingSystem0(X0)
| ( ( ~ isTerminating0(X0)
| ! [X3,X4] :
( ~ aElement0(X4)
| ~ aElement0(X3)
| ~ sdtmndtplgtdt0(X3,X0,X4)
| iLess0(X4,X3) ) )
& ( ? [X1,X2] :
( aElement0(X2)
& aElement0(X1)
& sdtmndtplgtdt0(X1,X0,X2)
& ~ iLess0(X2,X1) )
| isTerminating0(X0) ) ) ),
inference(rectify,[],[f73]) ).
fof(f75,plain,
! [X0] :
( ~ aRewritingSystem0(X0)
| ( ( ~ isTerminating0(X0)
| ! [X3,X4] :
( ~ aElement0(X4)
| ~ aElement0(X3)
| ~ sdtmndtplgtdt0(X3,X0,X4)
| iLess0(X4,X3) ) )
& ( ( aElement0(sK14(X0))
& aElement0(sK13(X0))
& sdtmndtplgtdt0(sK13(X0),X0,sK14(X0))
& ~ iLess0(sK14(X0),sK13(X0)) )
| isTerminating0(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14]),skolemize(X1,sK13(X0)),skolemize(X2,sK14(X0))],[f74]) ).
fof(f76,plain,
! [X0,X1] :
( ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ! [X2] :
( ( ~ aNormalFormOfIn0(X2,X0,X1)
| ( ! [X3] : ~ aReductOfIn0(X3,X2,X1)
& sdtmndtasgtdt0(X0,X1,X2)
& aElement0(X2) ) )
& ( ? [X3] : aReductOfIn0(X3,X2,X1)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X2)
| aNormalFormOfIn0(X2,X0,X1) ) ) ),
inference(nnf_transformation,[],[f48]) ).
fof(f77,plain,
! [X0,X1] :
( ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ! [X2] :
( ( ~ aNormalFormOfIn0(X2,X0,X1)
| ( ! [X3] : ~ aReductOfIn0(X3,X2,X1)
& sdtmndtasgtdt0(X0,X1,X2)
& aElement0(X2) ) )
& ( ? [X3] : aReductOfIn0(X3,X2,X1)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X2)
| aNormalFormOfIn0(X2,X0,X1) ) ) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
! [X0,X1] :
( ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ! [X2] :
( ( ~ aNormalFormOfIn0(X2,X0,X1)
| ( ! [X4] : ~ aReductOfIn0(X4,X2,X1)
& sdtmndtasgtdt0(X0,X1,X2)
& aElement0(X2) ) )
& ( ? [X3] : aReductOfIn0(X3,X2,X1)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X2)
| aNormalFormOfIn0(X2,X0,X1) ) ) ),
inference(rectify,[],[f77]) ).
fof(f79,plain,
! [X0,X1] :
( ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ! [X2] :
( ( ~ aNormalFormOfIn0(X2,X0,X1)
| ( ! [X4] : ~ aReductOfIn0(X4,X2,X1)
& sdtmndtasgtdt0(X0,X1,X2)
& aElement0(X2) ) )
& ( aReductOfIn0(sK15(X1,X2),X2,X1)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X2)
| aNormalFormOfIn0(X2,X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(X3,sK15(X1,X2))],[f78]) ).
fof(f81,plain,
! [X0,X1,X2] :
( ~ sdtmndtasgtdt0(X0,xR,X2)
| ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ iLess0(X0,xa)
| ( sdtmndtasgtdt0(X2,xR,sK17(X1,X2))
& sdtmndtasgtdt0(X1,xR,sK17(X1,X2))
& aElement0(sK17(X1,X2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(X3,sK17(X1,X2))],[f52]) ).
fof(f82,plain,
! [X2,X0,X1] :
( ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ~ aReductOfIn0(X2,X0,X1)
| aElement0(X2) ),
inference(cnf_transformation,[],[f32]) ).
fof(f84,plain,
! [X2,X0,X1] :
( ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(X0,X1,X2)
| aReductOfIn0(sK4(X0,X1,X2),X0,X1)
| aReductOfIn0(X2,X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f87,plain,
! [X2,X0,X1] :
( ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ~ aReductOfIn0(X2,X0,X1)
| sdtmndtplgtdt0(X0,X1,X2) ),
inference(cnf_transformation,[],[f62]) ).
fof(f89,plain,
! [X2,X0,X1] :
( ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2 ),
inference(cnf_transformation,[],[f64]) ).
fof(f92,plain,
! [X2,X3,X0,X1] :
( ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ~ sdtmndtasgtdt0(X2,X1,X3)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| sdtmndtasgtdt0(X0,X1,X3) ),
inference(cnf_transformation,[],[f40]) ).
fof(f117,plain,
! [X3,X0,X4] :
( ~ aRewritingSystem0(X0)
| ~ isTerminating0(X0)
| ~ aElement0(X4)
| ~ aElement0(X3)
| ~ sdtmndtplgtdt0(X3,X0,X4)
| iLess0(X4,X3) ),
inference(cnf_transformation,[],[f75]) ).
fof(f122,plain,
! [X2,X0,X1,X4] :
( ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ~ aNormalFormOfIn0(X2,X0,X1)
| ~ aReductOfIn0(X4,X2,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f123,plain,
! [X2,X0,X1] :
( ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ~ aNormalFormOfIn0(X2,X0,X1)
| sdtmndtasgtdt0(X0,X1,X2) ),
inference(cnf_transformation,[],[f79]) ).
fof(f124,plain,
! [X2,X0,X1] :
( ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ~ aNormalFormOfIn0(X2,X0,X1)
| aElement0(X2) ),
inference(cnf_transformation,[],[f79]) ).
fof(f127,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[],[f15]) ).
fof(f128,plain,
isTerminating0(xR),
inference(cnf_transformation,[],[f16]) ).
fof(f131,plain,
aElement0(xb),
inference(cnf_transformation,[],[f17]) ).
fof(f132,plain,
aElement0(xa),
inference(cnf_transformation,[],[f17]) ).
fof(f133,plain,
! [X2,X0,X1] :
( ~ sdtmndtasgtdt0(X0,xR,X2)
| ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ iLess0(X0,xa)
| sdtmndtasgtdt0(X2,xR,sK17(X1,X2)) ),
inference(cnf_transformation,[],[f81]) ).
fof(f134,plain,
! [X2,X0,X1] :
( ~ sdtmndtasgtdt0(X0,xR,X2)
| ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ iLess0(X0,xa)
| sdtmndtasgtdt0(X1,xR,sK17(X1,X2)) ),
inference(cnf_transformation,[],[f81]) ).
fof(f135,plain,
! [X2,X0,X1] :
( ~ sdtmndtasgtdt0(X0,xR,X2)
| ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ iLess0(X0,xa)
| aElement0(sK17(X1,X2)) ),
inference(cnf_transformation,[],[f81]) ).
fof(f138,plain,
sdtmndtasgtdt0(xu,xR,xb),
inference(cnf_transformation,[],[f20]) ).
fof(f139,plain,
aReductOfIn0(xu,xa,xR),
inference(cnf_transformation,[],[f20]) ).
fof(f140,plain,
aElement0(xu),
inference(cnf_transformation,[],[f20]) ).
fof(f145,plain,
sdtmndtasgtdt0(xu,xR,xw),
inference(cnf_transformation,[],[f22]) ).
fof(f146,plain,
aElement0(xw),
inference(cnf_transformation,[],[f22]) ).
fof(f147,plain,
aNormalFormOfIn0(xd,xw,xR),
inference(cnf_transformation,[],[f23]) ).
fof(f148,plain,
~ sdtmndtasgtdt0(xb,xR,xd),
inference(cnf_transformation,[],[f30]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElement0(X0)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X1)
| ~ aReductOfIn0(X0,X1,X2) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtmndtplgtdt0(X1,X2,X0)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ aReductOfIn0(X0,X1,X2) ),
inference(cnf_transformation,[],[f87]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( aReductOfIn0(X2,X0,X1)
| aReductOfIn0(sK4(X0,X1,X2),X0,X1)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(X0,X1,X2) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtmndtplgtdt0(X0,X1,X2)
| ( X0 = X2 )
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2)
| ~ aElement0(X0)
| ~ sdtmndtasgtdt0(X0,X1,X2) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdtmndtasgtdt0(X3,X1,X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X0)
| ~ sdtmndtasgtdt0(X3,X1,X0)
| ~ sdtmndtasgtdt0(X0,X1,X2) ),
inference(cnf_transformation,[],[f92]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i,X2: $i] :
( iLess0(X2,X0)
| ~ isTerminating0(X1)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(X0,X1,X2) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElement0(X0)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X1)
| ~ aNormalFormOfIn0(X0,X1,X2) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtmndtasgtdt0(X1,X2,X0)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X1)
| ~ aNormalFormOfIn0(X0,X1,X2) ),
inference(cnf_transformation,[],[f123]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ aRewritingSystem0(X2)
| ~ aElement0(X3)
| ~ aNormalFormOfIn0(X1,X3,X2)
| ~ aReductOfIn0(X0,X1,X2) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_94,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[],[f127]) ).
tcf(c_96,plain,
isTerminating0(xR),
inference(cnf_transformation,[],[f128]) ).
tcf(c_97,plain,
aElement0(xa),
inference(cnf_transformation,[],[f132]) ).
tcf(c_98,plain,
aElement0(xb),
inference(cnf_transformation,[],[f131]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElement0(sK17(X2,X1))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ iLess0(X0,xa)
| ~ sdtmndtasgtdt0(X0,xR,X2)
| ~ sdtmndtasgtdt0(X0,xR,X1) ),
inference(cnf_transformation,[],[f135]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtmndtasgtdt0(X2,xR,sK17(X2,X1))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ iLess0(X0,xa)
| ~ sdtmndtasgtdt0(X0,xR,X2)
| ~ sdtmndtasgtdt0(X0,xR,X1) ),
inference(cnf_transformation,[],[f134]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtmndtasgtdt0(X1,xR,sK17(X2,X1))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ iLess0(X0,xa)
| ~ sdtmndtasgtdt0(X0,xR,X2)
| ~ sdtmndtasgtdt0(X0,xR,X1) ),
inference(cnf_transformation,[],[f133]) ).
tcf(c_105,plain,
aElement0(xu),
inference(cnf_transformation,[],[f140]) ).
tcf(c_106,plain,
aReductOfIn0(xu,xa,xR),
inference(cnf_transformation,[],[f139]) ).
tcf(c_107,plain,
sdtmndtasgtdt0(xu,xR,xb),
inference(cnf_transformation,[],[f138]) ).
tcf(c_111,plain,
aElement0(xw),
inference(cnf_transformation,[],[f146]) ).
tcf(c_112,plain,
sdtmndtasgtdt0(xu,xR,xw),
inference(cnf_transformation,[],[f145]) ).
tcf(c_114,plain,
aNormalFormOfIn0(xd,xw,xR),
inference(cnf_transformation,[],[f147]) ).
tcf(c_115,negated_conjecture,
~ sdtmndtasgtdt0(xb,xR,xd),
inference(cnf_transformation,[],[f148]) ).
tcf(c_149,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtmndtplgtdt0(X1,X2,X0)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X1)
| ~ aReductOfIn0(X0,X1,X2) ),
inference(global_subsumption_just,[status(thm)],[c_50,c_49,c_50]) ).
tcf(c_1016,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtmndtasgtdt0(X1,X2,X0)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X1)
| ( X2 != xR )
| ( X1 != xw )
| ( X0 != xd ) ),
inference(resolution_lifted,[status(thm)],[c_91,c_114]) ).
tcf(c_1017,plain,
( sdtmndtasgtdt0(xw,xR,xd)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xw) ),
inference(unflattening,[status(thm)],[c_1016]) ).
tcf(c_1018,plain,
sdtmndtasgtdt0(xw,xR,xd),
inference(global_subsumption_just,[status(thm)],[c_1017,c_111,c_94,c_1017]) ).
tcf(c_1023,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElement0(X0)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X1)
| ( X2 != xR )
| ( X1 != xw )
| ( X0 != xd ) ),
inference(resolution_lifted,[status(thm)],[c_90,c_114]) ).
tcf(c_1024,plain,
( aElement0(xd)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xw) ),
inference(unflattening,[status(thm)],[c_1023]) ).
tcf(c_1025,plain,
aElement0(xd),
inference(global_subsumption_just,[status(thm)],[c_1024,c_111,c_94,c_1024]) ).
tcf(c_1066,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ aRewritingSystem0(X1)
| ~ aElement0(X2)
| ~ aReductOfIn0(X3,X0,X1)
| ( X2 != xw )
| ( X1 != xR )
| ( X0 != xd ) ),
inference(resolution_lifted,[status(thm)],[c_92,c_114]) ).
tcf(c_1067,plain,
! [X0: $i] :
( ~ aRewritingSystem0(xR)
| ~ aElement0(xw)
| ~ aReductOfIn0(X0,xd,xR) ),
inference(unflattening,[status(thm)],[c_1066]) ).
tcf(c_1069,plain,
! [X0: $i] : ~ aReductOfIn0(X0,xd,xR),
inference(global_subsumption_just,[status(thm)],[c_1067,c_111,c_94,c_1067]) ).
tcf(c_1131,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtmndtplgtdt0(X2,X0,X1)
| ~ aElement0(X2)
| ~ aReductOfIn0(X1,X2,X0)
| ( X0 != xR ) ),
inference(resolution_lifted,[status(thm)],[c_149,c_94]) ).
tcf(c_1132,plain,
! [X0: $i,X1: $i] :
( sdtmndtplgtdt0(X1,xR,X0)
| ~ aElement0(X1)
| ~ aReductOfIn0(X0,X1,xR) ),
inference(unflattening,[status(thm)],[c_1131]) ).
tcf(c_1190,plain,
! [X0: $i,X1: $i,X2: $i] :
( iLess0(X2,X1)
| ~ isTerminating0(X0)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ sdtmndtplgtdt0(X1,X0,X2)
| ( X0 != xR ) ),
inference(resolution_lifted,[status(thm)],[c_88,c_94]) ).
tcf(c_1191,plain,
! [X0: $i,X1: $i] :
( iLess0(X1,X0)
| ~ isTerminating0(xR)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(X0,xR,X1) ),
inference(unflattening,[status(thm)],[c_1190]) ).
tcf(c_1193,plain,
! [X0: $i,X1: $i] :
( iLess0(X1,X0)
| ~ sdtmndtplgtdt0(X0,xR,X1)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(global_subsumption_just,[status(thm)],[c_1191,c_96,c_1191]) ).
tcf(c_1194,plain,
! [X0: $i,X1: $i] :
( iLess0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(X0,xR,X1) ),
inference(renaming,[status(thm)],[c_1193]) ).
tcf(c_1208,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdtmndtasgtdt0(X3,X0,X2)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ sdtmndtasgtdt0(X3,X0,X1)
| ~ sdtmndtasgtdt0(X1,X0,X2)
| ( X0 != xR ) ),
inference(resolution_lifted,[status(thm)],[c_59,c_94]) ).
tcf(c_1209,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtmndtasgtdt0(X2,xR,X1)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ sdtmndtasgtdt0(X2,xR,X0)
| ~ sdtmndtasgtdt0(X0,xR,X1) ),
inference(unflattening,[status(thm)],[c_1208]) ).
tcf(c_1228,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtmndtplgtdt0(X1,X0,X2)
| ( X1 = X2 )
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ sdtmndtasgtdt0(X1,X0,X2)
| ( X0 != xR ) ),
inference(resolution_lifted,[status(thm)],[c_58,c_94]) ).
tcf(c_1229,plain,
! [X0: $i,X1: $i] :
( sdtmndtplgtdt0(X0,xR,X1)
| ( X0 = X1 )
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ sdtmndtasgtdt0(X0,xR,X1) ),
inference(unflattening,[status(thm)],[c_1228]) ).
tcf(c_1308,plain,
! [X0: $i,X1: $i,X2: $i] :
( aReductOfIn0(X2,X1,X0)
| aReductOfIn0(sK4(X1,X0,X2),X1,X0)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ sdtmndtplgtdt0(X1,X0,X2)
| ( X0 != xR ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_94]) ).
tcf(c_1309,plain,
! [X0: $i,X1: $i] :
( aReductOfIn0(X1,X0,xR)
| aReductOfIn0(sK4(X0,xR,X1),X0,xR)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(X0,xR,X1) ),
inference(unflattening,[status(thm)],[c_1308]) ).
tcf(c_1416,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sdtmndtasgtdt0(X3,xR,sK17(X4,X3))
| ~ aElement0(X4)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ sdtmndtasgtdt0(X0,xR,X4)
| ~ sdtmndtasgtdt0(X0,xR,X3)
| ~ sdtmndtplgtdt0(X2,xR,X1)
| ( X2 != xa )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_102,c_1194]) ).
tcf(c_1417,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtmndtasgtdt0(X1,xR,sK17(X2,X1))
| ~ aElement0(xa)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(xa,xR,X0)
| ~ sdtmndtasgtdt0(X0,xR,X2)
| ~ sdtmndtasgtdt0(X0,xR,X1) ),
inference(unflattening,[status(thm)],[c_1416]) ).
tcf(c_1419,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtmndtasgtdt0(X1,xR,sK17(X2,X1))
| ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ sdtmndtasgtdt0(X0,xR,X2)
| ~ sdtmndtplgtdt0(xa,xR,X0)
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(global_subsumption_just,[status(thm)],[c_1417,c_97,c_1417]) ).
tcf(c_1420,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtmndtasgtdt0(X1,xR,sK17(X2,X1))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(xa,xR,X0)
| ~ sdtmndtasgtdt0(X0,xR,X2)
| ~ sdtmndtasgtdt0(X0,xR,X1) ),
inference(renaming,[status(thm)],[c_1419]) ).
tcf(c_1443,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sdtmndtasgtdt0(X4,xR,sK17(X4,X3))
| ~ aElement0(X4)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ sdtmndtasgtdt0(X0,xR,X4)
| ~ sdtmndtasgtdt0(X0,xR,X3)
| ~ sdtmndtplgtdt0(X2,xR,X1)
| ( X2 != xa )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_101,c_1194]) ).
tcf(c_1444,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtmndtasgtdt0(X2,xR,sK17(X2,X1))
| ~ aElement0(xa)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(xa,xR,X0)
| ~ sdtmndtasgtdt0(X0,xR,X2)
| ~ sdtmndtasgtdt0(X0,xR,X1) ),
inference(unflattening,[status(thm)],[c_1443]) ).
tcf(c_1445,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtmndtasgtdt0(X2,xR,sK17(X2,X1))
| ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ sdtmndtasgtdt0(X0,xR,X2)
| ~ sdtmndtplgtdt0(xa,xR,X0)
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(global_subsumption_just,[status(thm)],[c_1444,c_97,c_1444]) ).
tcf(c_1446,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtmndtasgtdt0(X2,xR,sK17(X2,X1))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(xa,xR,X0)
| ~ sdtmndtasgtdt0(X0,xR,X2)
| ~ sdtmndtasgtdt0(X0,xR,X1) ),
inference(renaming,[status(thm)],[c_1445]) ).
tcf(c_1468,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( aElement0(sK17(X4,X3))
| ~ aElement0(X4)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ sdtmndtasgtdt0(X0,xR,X4)
| ~ sdtmndtasgtdt0(X0,xR,X3)
| ~ sdtmndtplgtdt0(X2,xR,X1)
| ( X2 != xa )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_100,c_1194]) ).
tcf(c_1469,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElement0(sK17(X2,X1))
| ~ aElement0(xa)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(xa,xR,X0)
| ~ sdtmndtasgtdt0(X0,xR,X2)
| ~ sdtmndtasgtdt0(X0,xR,X1) ),
inference(unflattening,[status(thm)],[c_1468]) ).
tcf(c_1471,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElement0(sK17(X2,X1))
| ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ sdtmndtasgtdt0(X0,xR,X2)
| ~ sdtmndtplgtdt0(xa,xR,X0)
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(global_subsumption_just,[status(thm)],[c_1469,c_97,c_1469]) ).
tcf(c_1472,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElement0(sK17(X2,X1))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(xa,xR,X0)
| ~ sdtmndtasgtdt0(X0,xR,X2)
| ~ sdtmndtasgtdt0(X0,xR,X1) ),
inference(renaming,[status(thm)],[c_1471]) ).
tcf(c_4427,plain,
! [X0_iProver_sdtmndtplgtdt0_3: iProver_sdtmndtplgtdt0_3,X1_iProver_sdtmndtplgtdt0_3: iProver_sdtmndtplgtdt0_3,X2_iProver_sdtmndtplgtdt0_3: iProver_sdtmndtplgtdt0_3] :
( aElement0(sK17(X2_iProver_sdtmndtplgtdt0_3,X1_iProver_sdtmndtplgtdt0_3))
| ~ aElement0(X2_iProver_sdtmndtplgtdt0_3)
| ~ aElement0(X1_iProver_sdtmndtplgtdt0_3)
| ~ aElement0(X0_iProver_sdtmndtplgtdt0_3)
| ~ sdtmndtplgtdt0(xa,xR,X0_iProver_sdtmndtplgtdt0_3)
| ~ sdtmndtasgtdt0(X0_iProver_sdtmndtplgtdt0_3,xR,X2_iProver_sdtmndtplgtdt0_3)
| ~ sdtmndtasgtdt0(X0_iProver_sdtmndtplgtdt0_3,xR,X1_iProver_sdtmndtplgtdt0_3) ),
inference(subtyping,[status(esa)],[c_1472]) ).
tcf(c_4428,plain,
! [X0_iProver_sdtmndtplgtdt0_3: iProver_sdtmndtplgtdt0_3,X1_iProver_sdtmndtplgtdt0_3: iProver_sdtmndtplgtdt0_3,X2_iProver_sdtmndtplgtdt0_3: iProver_sdtmndtplgtdt0_3] :
( sdtmndtasgtdt0(X2_iProver_sdtmndtplgtdt0_3,xR,sK17(X2_iProver_sdtmndtplgtdt0_3,X1_iProver_sdtmndtplgtdt0_3))
| ~ aElement0(X2_iProver_sdtmndtplgtdt0_3)
| ~ aElement0(X1_iProver_sdtmndtplgtdt0_3)
| ~ aElement0(X0_iProver_sdtmndtplgtdt0_3)
| ~ sdtmndtplgtdt0(xa,xR,X0_iProver_sdtmndtplgtdt0_3)
| ~ sdtmndtasgtdt0(X0_iProver_sdtmndtplgtdt0_3,xR,X2_iProver_sdtmndtplgtdt0_3)
| ~ sdtmndtasgtdt0(X0_iProver_sdtmndtplgtdt0_3,xR,X1_iProver_sdtmndtplgtdt0_3) ),
inference(subtyping,[status(esa)],[c_1446]) ).
tcf(c_4429,plain,
! [X0_iProver_sdtmndtplgtdt0_3: iProver_sdtmndtplgtdt0_3,X1_iProver_sdtmndtplgtdt0_3: iProver_sdtmndtplgtdt0_3,X2_iProver_sdtmndtplgtdt0_3: iProver_sdtmndtplgtdt0_3] :
( sdtmndtasgtdt0(X1_iProver_sdtmndtplgtdt0_3,xR,sK17(X2_iProver_sdtmndtplgtdt0_3,X1_iProver_sdtmndtplgtdt0_3))
| ~ aElement0(X2_iProver_sdtmndtplgtdt0_3)
| ~ aElement0(X1_iProver_sdtmndtplgtdt0_3)
| ~ aElement0(X0_iProver_sdtmndtplgtdt0_3)
| ~ sdtmndtplgtdt0(xa,xR,X0_iProver_sdtmndtplgtdt0_3)
| ~ sdtmndtasgtdt0(X0_iProver_sdtmndtplgtdt0_3,xR,X2_iProver_sdtmndtplgtdt0_3)
| ~ sdtmndtasgtdt0(X0_iProver_sdtmndtplgtdt0_3,xR,X1_iProver_sdtmndtplgtdt0_3) ),
inference(subtyping,[status(esa)],[c_1420]) ).
tcf(c_4431,plain,
! [X0_iProver_sdtmndtplgtdt0_3: iProver_sdtmndtplgtdt0_3,X1_iProver_sdtmndtplgtdt0_3: iProver_sdtmndtplgtdt0_3] :
( aReductOfIn0(X1_iProver_sdtmndtplgtdt0_3,X0_iProver_sdtmndtplgtdt0_3,xR)
| aReductOfIn0(sK4(X0_iProver_sdtmndtplgtdt0_3,xR,X1_iProver_sdtmndtplgtdt0_3),X0_iProver_sdtmndtplgtdt0_3,xR)
| ~ aElement0(X1_iProver_sdtmndtplgtdt0_3)
| ~ aElement0(X0_iProver_sdtmndtplgtdt0_3)
| ~ sdtmndtplgtdt0(X0_iProver_sdtmndtplgtdt0_3,xR,X1_iProver_sdtmndtplgtdt0_3) ),
inference(subtyping,[status(esa)],[c_1309]) ).
tcf(c_4436,plain,
! [X0_iProver_sdtmndtplgtdt0_3: iProver_sdtmndtplgtdt0_3,X1_iProver_sdtmndtplgtdt0_3: iProver_sdtmndtplgtdt0_3] :
( sdtmndtplgtdt0(X0_iProver_sdtmndtplgtdt0_3,xR,X1_iProver_sdtmndtplgtdt0_3)
| ( X0_iProver_sdtmndtplgtdt0_3 = X1_iProver_sdtmndtplgtdt0_3 )
| ~ aElement0(X1_iProver_sdtmndtplgtdt0_3)
| ~ aElement0(X0_iProver_sdtmndtplgtdt0_3)
| ~ sdtmndtasgtdt0(X0_iProver_sdtmndtplgtdt0_3,xR,X1_iProver_sdtmndtplgtdt0_3) ),
inference(subtyping,[status(esa)],[c_1229]) ).
tcf(c_4437,plain,
! [X0_iProver_sdtmndtplgtdt0_3: iProver_sdtmndtplgtdt0_3,X1_iProver_sdtmndtplgtdt0_3: iProver_sdtmndtplgtdt0_3,X2_iProver_sdtmndtplgtdt0_3: iProver_sdtmndtplgtdt0_3] :
( sdtmndtasgtdt0(X2_iProver_sdtmndtplgtdt0_3,xR,X1_iProver_sdtmndtplgtdt0_3)
| ~ aElement0(X2_iProver_sdtmndtplgtdt0_3)
| ~ aElement0(X1_iProver_sdtmndtplgtdt0_3)
| ~ aElement0(X0_iProver_sdtmndtplgtdt0_3)
| ~ sdtmndtasgtdt0(X2_iProver_sdtmndtplgtdt0_3,xR,X0_iProver_sdtmndtplgtdt0_3)
| ~ sdtmndtasgtdt0(X0_iProver_sdtmndtplgtdt0_3,xR,X1_iProver_sdtmndtplgtdt0_3) ),
inference(subtyping,[status(esa)],[c_1209]) ).
tcf(c_4442,plain,
! [X0_iProver_sdtmndtplgtdt0_3: iProver_sdtmndtplgtdt0_3,X1_iProver_sdtmndtplgtdt0_3: iProver_sdtmndtplgtdt0_3] :
( sdtmndtplgtdt0(X1_iProver_sdtmndtplgtdt0_3,xR,X0_iProver_sdtmndtplgtdt0_3)
| ~ aElement0(X1_iProver_sdtmndtplgtdt0_3)
| ~ aReductOfIn0(X0_iProver_sdtmndtplgtdt0_3,X1_iProver_sdtmndtplgtdt0_3,xR) ),
inference(subtyping,[status(esa)],[c_1132]) ).
tcf(c_4445,plain,
! [X0_iProver_sdtmndtplgtdt0_3: iProver_sdtmndtplgtdt0_3] : ~ aReductOfIn0(X0_iProver_sdtmndtplgtdt0_3,xd,xR),
inference(subtyping,[status(esa)],[c_1069]) ).
tcf(c_4446,plain,
aElement0(xd),
inference(subtyping,[status(esa)],[c_1025]) ).
tcf(c_4447,plain,
sdtmndtasgtdt0(xw,xR,xd),
inference(subtyping,[status(esa)],[c_1018]) ).
tcf(c_4449,negated_conjecture,
~ sdtmndtasgtdt0(xb,xR,xd),
inference(subtyping,[status(esa)],[c_115]) ).
tcf(c_4451,plain,
sdtmndtasgtdt0(xu,xR,xw),
inference(subtyping,[status(esa)],[c_112]) ).
tcf(c_4452,plain,
aElement0(xw),
inference(subtyping,[status(esa)],[c_111]) ).
tcf(c_4456,plain,
sdtmndtasgtdt0(xu,xR,xb),
inference(subtyping,[status(esa)],[c_107]) ).
tcf(c_4457,plain,
aReductOfIn0(xu,xa,xR),
inference(subtyping,[status(esa)],[c_106]) ).
tcf(c_4458,plain,
aElement0(xu),
inference(subtyping,[status(esa)],[c_105]) ).
tcf(c_4462,plain,
aElement0(xb),
inference(subtyping,[status(esa)],[c_98]) ).
tcf(c_4463,plain,
aElement0(xa),
inference(subtyping,[status(esa)],[c_97]) ).
tcf(c_5376,plain,
( sdtmndtplgtdt0(xa,xR,xu)
| ~ aElement0(xa) ),
inference(superposition,[status(thm)],[c_4457,c_4442]) ).
tcf(c_5378,plain,
sdtmndtplgtdt0(xa,xR,xu),
inference(forward_subsumption_resolution,[status(thm)],[c_5376,c_4463]) ).
tcf(c_8420,plain,
! [X0_iProver_sdtmndtplgtdt0_3: iProver_sdtmndtplgtdt0_3] :
( sdtmndtasgtdt0(X0_iProver_sdtmndtplgtdt0_3,xR,xd)
| ~ aElement0(xd)
| ~ aElement0(xw)
| ~ aElement0(X0_iProver_sdtmndtplgtdt0_3)
| ~ sdtmndtasgtdt0(X0_iProver_sdtmndtplgtdt0_3,xR,xw) ),
inference(superposition,[status(thm)],[c_4447,c_4437]) ).
tcf(c_8422,plain,
! [X0_iProver_sdtmndtplgtdt0_3: iProver_sdtmndtplgtdt0_3] :
( sdtmndtasgtdt0(X0_iProver_sdtmndtplgtdt0_3,xR,xd)
| ~ aElement0(X0_iProver_sdtmndtplgtdt0_3)
| ~ sdtmndtasgtdt0(X0_iProver_sdtmndtplgtdt0_3,xR,xw) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8420,c_4446,c_4452]) ).
tcf(c_8492,plain,
! [X0_iProver_sdtmndtplgtdt0_3: iProver_sdtmndtplgtdt0_3] :
( aReductOfIn0(X0_iProver_sdtmndtplgtdt0_3,xd,xR)
| ~ aElement0(xd)
| ~ aElement0(X0_iProver_sdtmndtplgtdt0_3)
| ~ sdtmndtplgtdt0(xd,xR,X0_iProver_sdtmndtplgtdt0_3) ),
inference(superposition,[status(thm)],[c_4431,c_4445]) ).
tcf(c_8493,plain,
! [X0_iProver_sdtmndtplgtdt0_3: iProver_sdtmndtplgtdt0_3] :
( ~ aElement0(X0_iProver_sdtmndtplgtdt0_3)
| ~ sdtmndtplgtdt0(xd,xR,X0_iProver_sdtmndtplgtdt0_3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8492,c_4445,c_4446]) ).
tcf(c_8526,plain,
! [X0_iProver_sdtmndtplgtdt0_3: iProver_sdtmndtplgtdt0_3] :
( sdtmndtasgtdt0(xb,xR,sK17(X0_iProver_sdtmndtplgtdt0_3,xb))
| ~ aElement0(xu)
| ~ aElement0(xb)
| ~ aElement0(X0_iProver_sdtmndtplgtdt0_3)
| ~ sdtmndtplgtdt0(xa,xR,xu)
| ~ sdtmndtasgtdt0(xu,xR,X0_iProver_sdtmndtplgtdt0_3) ),
inference(superposition,[status(thm)],[c_4456,c_4429]) ).
tcf(c_8527,plain,
! [X0_iProver_sdtmndtplgtdt0_3: iProver_sdtmndtplgtdt0_3] :
( sdtmndtasgtdt0(X0_iProver_sdtmndtplgtdt0_3,xR,sK17(X0_iProver_sdtmndtplgtdt0_3,xb))
| ~ aElement0(xu)
| ~ aElement0(xb)
| ~ aElement0(X0_iProver_sdtmndtplgtdt0_3)
| ~ sdtmndtplgtdt0(xa,xR,xu)
| ~ sdtmndtasgtdt0(xu,xR,X0_iProver_sdtmndtplgtdt0_3) ),
inference(superposition,[status(thm)],[c_4456,c_4428]) ).
tcf(c_8528,plain,
! [X0_iProver_sdtmndtplgtdt0_3: iProver_sdtmndtplgtdt0_3] :
( aElement0(sK17(X0_iProver_sdtmndtplgtdt0_3,xb))
| ~ aElement0(xu)
| ~ aElement0(xb)
| ~ aElement0(X0_iProver_sdtmndtplgtdt0_3)
| ~ sdtmndtplgtdt0(xa,xR,xu)
| ~ sdtmndtasgtdt0(xu,xR,X0_iProver_sdtmndtplgtdt0_3) ),
inference(superposition,[status(thm)],[c_4456,c_4427]) ).
tcf(c_8531,plain,
! [X0_iProver_sdtmndtplgtdt0_3: iProver_sdtmndtplgtdt0_3] :
( aElement0(sK17(X0_iProver_sdtmndtplgtdt0_3,xb))
| ~ aElement0(X0_iProver_sdtmndtplgtdt0_3)
| ~ sdtmndtplgtdt0(xa,xR,xu)
| ~ sdtmndtasgtdt0(xu,xR,X0_iProver_sdtmndtplgtdt0_3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8528,c_4458,c_4462]) ).
tcf(c_8532,plain,
! [X0_iProver_sdtmndtplgtdt0_3: iProver_sdtmndtplgtdt0_3] :
( sdtmndtasgtdt0(X0_iProver_sdtmndtplgtdt0_3,xR,sK17(X0_iProver_sdtmndtplgtdt0_3,xb))
| ~ aElement0(X0_iProver_sdtmndtplgtdt0_3)
| ~ sdtmndtplgtdt0(xa,xR,xu)
| ~ sdtmndtasgtdt0(xu,xR,X0_iProver_sdtmndtplgtdt0_3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8527,c_4458,c_4462]) ).
tcf(c_8533,plain,
! [X0_iProver_sdtmndtplgtdt0_3: iProver_sdtmndtplgtdt0_3] :
( sdtmndtasgtdt0(xb,xR,sK17(X0_iProver_sdtmndtplgtdt0_3,xb))
| ~ aElement0(X0_iProver_sdtmndtplgtdt0_3)
| ~ sdtmndtplgtdt0(xa,xR,xu)
| ~ sdtmndtasgtdt0(xu,xR,X0_iProver_sdtmndtplgtdt0_3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8526,c_4458,c_4462]) ).
tcf(c_8909,plain,
( sdtmndtasgtdt0(xu,xR,xd)
| ~ aElement0(xu) ),
inference(superposition,[status(thm)],[c_4451,c_8422]) ).
tcf(c_8914,plain,
sdtmndtasgtdt0(xu,xR,xd),
inference(forward_subsumption_resolution,[status(thm)],[c_8909,c_4458]) ).
tcf(c_9673,plain,
( aElement0(sK17(xd,xb))
| ~ aElement0(xd)
| ~ sdtmndtplgtdt0(xa,xR,xu) ),
inference(superposition,[status(thm)],[c_8914,c_8531]) ).
tcf(c_9674,plain,
aElement0(sK17(xd,xb)),
inference(forward_subsumption_resolution,[status(thm)],[c_9673,c_4446,c_5378]) ).
tcf(c_9695,plain,
! [X0_iProver_sdtmndtplgtdt0_3: iProver_sdtmndtplgtdt0_3] :
( sdtmndtplgtdt0(X0_iProver_sdtmndtplgtdt0_3,xR,sK17(X0_iProver_sdtmndtplgtdt0_3,xb))
| ( sK17(X0_iProver_sdtmndtplgtdt0_3,xb) = X0_iProver_sdtmndtplgtdt0_3 )
| ~ aElement0(X0_iProver_sdtmndtplgtdt0_3)
| ~ sdtmndtplgtdt0(xa,xR,xu)
| ~ sdtmndtasgtdt0(xu,xR,X0_iProver_sdtmndtplgtdt0_3)
| ~ aElement0(sK17(X0_iProver_sdtmndtplgtdt0_3,xb)) ),
inference(superposition,[status(thm)],[c_8532,c_4436]) ).
tcf(c_9714,plain,
! [X0_iProver_sdtmndtplgtdt0_3: iProver_sdtmndtplgtdt0_3] :
( sdtmndtplgtdt0(X0_iProver_sdtmndtplgtdt0_3,xR,sK17(X0_iProver_sdtmndtplgtdt0_3,xb))
| ( sK17(X0_iProver_sdtmndtplgtdt0_3,xb) = X0_iProver_sdtmndtplgtdt0_3 )
| ~ aElement0(X0_iProver_sdtmndtplgtdt0_3)
| ~ sdtmndtasgtdt0(xu,xR,X0_iProver_sdtmndtplgtdt0_3)
| ~ aElement0(sK17(X0_iProver_sdtmndtplgtdt0_3,xb)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9695,c_5378]) ).
tcf(c_28043,plain,
( ( sK17(xd,xb) = xd )
| ~ aElement0(xd)
| ~ sdtmndtasgtdt0(xu,xR,xd)
| ~ aElement0(sK17(xd,xb)) ),
inference(superposition,[status(thm)],[c_9714,c_8493]) ).
tcf(c_28045,plain,
sK17(xd,xb) = xd,
inference(forward_subsumption_resolution,[status(thm)],[c_28043,c_4446,c_8914,c_9674]) ).
tcf(c_28595,plain,
( sdtmndtasgtdt0(xb,xR,xd)
| ~ aElement0(xd)
| ~ sdtmndtasgtdt0(xu,xR,xd)
| ~ sdtmndtplgtdt0(xa,xR,xu) ),
inference(superposition,[status(thm)],[c_28045,c_8533]) ).
tcf(c_28610,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_28595,c_4449,c_4446,c_8914,c_5378]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM019+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n011.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 07:48:44 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/0.43 Running first-order theorem proving
% 0.15/0.43 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.45
% 0.15/0.45 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.45
% 0.15/0.45 % Detected problem language: tptp
% 0.15/0.47 % Proving...
% 59.81/10.08 % SZS status Started for theBenchmark.p
% 59.81/10.08 % SZS status Theorem for theBenchmark.p
% 59.81/10.08
% 59.81/10.08 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 59.81/10.08
% 59.81/10.08 % ------ iProver source info
% 59.81/10.08
% 59.81/10.08 % git: date: 2026-07-19 20:42:38 +0200
% 59.81/10.08 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 59.81/10.08 % git: non_committed_changes: false
% 59.81/10.08
% 59.81/10.08 % ------ Parsing...
% 59.81/10.08 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 59.81/10.08
% 59.81/10.08 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 0 sf_s rm: 6 0s sf_e pe_s pe_e %
% 59.81/10.08
% 59.81/10.08 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 59.81/10.08
% 59.81/10.08 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 59.81/10.08 % ------ Proving...
% 59.81/10.08 % ------ Problem Properties
% 59.81/10.08
% 59.81/10.08 %
% 59.81/10.08 % clauses 55
% 59.81/10.08 % conjectures 1
% 59.81/10.08 % EPR 27
% 59.81/10.08 % Horn 41
% 59.81/10.08 % unary 19
% 59.81/10.08 % binary 14
% 59.81/10.08 % lits 170
% 59.81/10.08 % lits eq 1
% 59.81/10.08 % fd_pure 0
% 59.81/10.08 % fd_pseudo 0
% 59.81/10.08 % fd_cond 0
% 59.81/10.08 % fd_pseudo_cond 1
% 59.81/10.08 % AC symbols 0
% 59.81/10.08
% 59.81/10.08 % ------ Input Options Time Limit: Unbounded
% 59.81/10.08
% 59.81/10.08
% 59.81/10.08 % ------
% 59.81/10.08 % Current options:
% 59.81/10.08 % ------
% 59.81/10.08
% 59.81/10.08
% 59.81/10.08 %
% 59.81/10.08
% 59.81/10.08 % ------ Proving...
% 59.81/10.08 %
% 59.81/10.08
% 59.81/10.08 % SZS status Theorem for theBenchmark.p
% 59.81/10.08
% 59.81/10.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 59.81/10.08
% 59.81/10.08
%------------------------------------------------------------------------------