%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COM020+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 : n016.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 1.09s 1.73s
% Output : CNFRefutation 1.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 13
% Syntax : Number of formulae : 128 ( 27 unt; 0 def)
% Number of atoms : 654 ( 15 equ)
% Maximal formula atoms : 13 ( 5 avg)
% Number of connectives : 956 ( 430 ~; 422 |; 84 &)
% ( 9 <=>; 11 =>; 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 : 278 ( 0 sgn 259 !; 19 ?; 126 :)
% 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(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,
? [X0] :
( sdtmndtasgtdt0(xd,xR,X0)
& sdtmndtasgtdt0(xb,xR,X0)
& aElement0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f25,negated_conjecture,
~ ? [X0] :
( sdtmndtasgtdt0(xd,xR,X0)
& sdtmndtasgtdt0(xb,xR,X0)
& aElement0(X0) ),
inference(negated_conjecture,[status(cth)],[f24]) ).
fof(f30,plain,
! [X0,X1] :
( ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ! [X2] :
( ~ aReductOfIn0(X2,X0,X1)
| aElement0(X2) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f31,plain,
! [X0,X1] :
( ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ! [X2] :
( ~ aReductOfIn0(X2,X0,X1)
| aElement0(X2) ) ),
inference(flattening,[],[f30]) ).
fof(f32,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(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(flattening,[],[f32]) ).
fof(f38,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(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(flattening,[],[f38]) ).
fof(f44,plain,
! [X0] :
( ~ aRewritingSystem0(X0)
| ( isTerminating0(X0)
<=> ! [X1,X2] :
( ~ aElement0(X2)
| ~ aElement0(X1)
| ~ sdtmndtplgtdt0(X1,X0,X2)
| iLess0(X2,X1) ) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f45,plain,
! [X0] :
( ~ aRewritingSystem0(X0)
| ( isTerminating0(X0)
<=> ! [X1,X2] :
( ~ aElement0(X2)
| ~ aElement0(X1)
| ~ sdtmndtplgtdt0(X1,X0,X2)
| iLess0(X2,X1) ) ) ),
inference(flattening,[],[f44]) ).
fof(f46,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(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(flattening,[],[f46]) ).
fof(f50,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(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(flattening,[],[f50]) ).
fof(f52,plain,
! [X0] :
( ~ sdtmndtasgtdt0(xd,xR,X0)
| ~ sdtmndtasgtdt0(xb,xR,X0)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f25]) ).
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,[],[f33]) ).
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(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,[],[f45]) ).
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,[],[f47]) ).
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))],[f51]) ).
fof(f82,plain,
! [X2,X0,X1] :
( ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ~ aReductOfIn0(X2,X0,X1)
| aElement0(X2) ),
inference(cnf_transformation,[],[f31]) ).
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(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,[],[f39]) ).
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(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,
! [X0] :
( ~ sdtmndtasgtdt0(xd,xR,X0)
| ~ sdtmndtasgtdt0(xb,xR,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f52]) ).
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_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_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,
! [X0: $i] :
( ~ aElement0(X0)
| ~ sdtmndtasgtdt0(xd,xR,X0)
| ~ sdtmndtasgtdt0(xb,xR,X0) ),
inference(cnf_transformation,[],[f148]) ).
tcf(c_150,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_816,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_817,plain,
( sdtmndtasgtdt0(xw,xR,xd)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xw) ),
inference(unflattening,[status(thm)],[c_816]) ).
tcf(c_818,plain,
sdtmndtasgtdt0(xw,xR,xd),
inference(global_subsumption_just,[status(thm)],[c_817,c_111,c_94,c_817]) ).
tcf(c_823,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_824,plain,
( aElement0(xd)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xw) ),
inference(unflattening,[status(thm)],[c_823]) ).
tcf(c_931,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_150,c_94]) ).
tcf(c_932,plain,
! [X0: $i,X1: $i] :
( sdtmndtplgtdt0(X1,xR,X0)
| ~ aElement0(X1)
| ~ aReductOfIn0(X0,X1,xR) ),
inference(unflattening,[status(thm)],[c_931]) ).
tcf(c_990,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_991,plain,
! [X0: $i,X1: $i] :
( iLess0(X1,X0)
| ~ isTerminating0(xR)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(X0,xR,X1) ),
inference(unflattening,[status(thm)],[c_990]) ).
tcf(c_993,plain,
! [X0: $i,X1: $i] :
( iLess0(X1,X0)
| ~ sdtmndtplgtdt0(X0,xR,X1)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(global_subsumption_just,[status(thm)],[c_991,c_96,c_991]) ).
tcf(c_994,plain,
! [X0: $i,X1: $i] :
( iLess0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(X0,xR,X1) ),
inference(renaming,[status(thm)],[c_993]) ).
tcf(c_1008,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_1009,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_1008]) ).
tcf(c_1216,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_994]) ).
tcf(c_1217,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_1216]) ).
tcf(c_1219,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_1217,c_97,c_1217]) ).
tcf(c_1220,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_1219]) ).
tcf(c_1243,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_994]) ).
tcf(c_1244,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_1243]) ).
tcf(c_1245,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_1244,c_97,c_1244]) ).
tcf(c_1246,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_1245]) ).
tcf(c_1268,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_994]) ).
tcf(c_1269,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_1268]) ).
tcf(c_1271,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_1269,c_97,c_1269]) ).
tcf(c_1272,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_1271]) ).
tcf(c_4082,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_1272]) ).
tcf(c_4083,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_1246]) ).
tcf(c_4084,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_1220]) ).
tcf(c_4092,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_1009]) ).
tcf(c_4097,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_932]) ).
tcf(c_4102,plain,
sdtmndtasgtdt0(xw,xR,xd),
inference(subtyping,[status(esa)],[c_818]) ).
tcf(c_4104,negated_conjecture,
! [X0_iProver_sdtmndtplgtdt0_3: iProver_sdtmndtplgtdt0_3] :
( ~ aElement0(X0_iProver_sdtmndtplgtdt0_3)
| ~ sdtmndtasgtdt0(xd,xR,X0_iProver_sdtmndtplgtdt0_3)
| ~ sdtmndtasgtdt0(xb,xR,X0_iProver_sdtmndtplgtdt0_3) ),
inference(subtyping,[status(esa)],[c_115]) ).
tcf(c_4106,plain,
sdtmndtasgtdt0(xu,xR,xw),
inference(subtyping,[status(esa)],[c_112]) ).
tcf(c_4111,plain,
sdtmndtasgtdt0(xu,xR,xb),
inference(subtyping,[status(esa)],[c_107]) ).
tcf(c_4957,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_4111,c_4083]) ).
tcf(c_4958,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_4111,c_4082]) ).
tcf(c_4960,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(global_subsumption_just,[status(thm)],[c_4958,c_105,c_98,c_4958]) ).
tcf(c_4968,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(global_subsumption_just,[status(thm)],[c_4957,c_105,c_98,c_4957]) ).
tcf(c_5050,plain,
( sdtmndtplgtdt0(xa,xR,xu)
| ~ aElement0(xa)
| ~ aReductOfIn0(xu,xa,xR) ),
inference(instantiation,[status(thm)],[c_4097]) ).
tcf(c_5053,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_4102,c_4092]) ).
tcf(c_5062,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(global_subsumption_just,[status(thm)],[c_5053,c_111,c_94,c_824,c_5053]) ).
tcf(c_5233,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_4111,c_4084]) ).
tcf(c_5260,plain,
! [X0_iProver_sdtmndtplgtdt0_3: iProver_sdtmndtplgtdt0_3] :
( sdtmndtasgtdt0(xb,xR,sK17(X0_iProver_sdtmndtplgtdt0_3,xb))
| ~ aElement0(X0_iProver_sdtmndtplgtdt0_3)
| ~ sdtmndtasgtdt0(xu,xR,X0_iProver_sdtmndtplgtdt0_3) ),
inference(global_subsumption_just,[status(thm)],[c_5233,c_105,c_98,c_97,c_106,c_5050,c_5233]) ).
tcf(c_7564,plain,
! [X0_iProver_sdtmndtplgtdt0_3: iProver_sdtmndtplgtdt0_3] :
( ~ aElement0(X0_iProver_sdtmndtplgtdt0_3)
| ~ sdtmndtasgtdt0(xu,xR,X0_iProver_sdtmndtplgtdt0_3)
| ~ aElement0(sK17(X0_iProver_sdtmndtplgtdt0_3,xb))
| ~ sdtmndtasgtdt0(xd,xR,sK17(X0_iProver_sdtmndtplgtdt0_3,xb)) ),
inference(superposition,[status(thm)],[c_5260,c_4104]) ).
tcf(c_7566,plain,
! [X0_iProver_sdtmndtplgtdt0_3: iProver_sdtmndtplgtdt0_3] :
( ~ aElement0(X0_iProver_sdtmndtplgtdt0_3)
| ~ sdtmndtasgtdt0(xu,xR,X0_iProver_sdtmndtplgtdt0_3)
| ~ sdtmndtasgtdt0(xd,xR,sK17(X0_iProver_sdtmndtplgtdt0_3,xb)) ),
inference(global_subsumption_just,[status(thm)],[c_7564,c_97,c_106,c_4960,c_5050,c_7564]) ).
tcf(c_7772,plain,
( ~ aElement0(xd)
| ~ sdtmndtasgtdt0(xu,xR,xd)
| ~ sdtmndtplgtdt0(xa,xR,xu) ),
inference(superposition,[status(thm)],[c_4968,c_7566]) ).
tcf(c_8937,plain,
( sdtmndtasgtdt0(xu,xR,xd)
| ~ aElement0(xu) ),
inference(superposition,[status(thm)],[c_4106,c_5062]) ).
tcf(c_8938,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_8937,c_7772,c_5050,c_824,c_106,c_94,c_97,c_105,c_111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM020+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n016.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 07:53:13 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.43 % Detected problem language: tptp
% 0.09/0.44 % Proving...
% 1.09/1.73 % SZS status Started for theBenchmark.p
% 1.09/1.73 % SZS status Theorem for theBenchmark.p
% 1.09/1.73
% 1.09/1.73 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.09/1.73
% 1.09/1.73 % ------ iProver source info
% 1.09/1.73
% 1.09/1.73 % git: date: 2026-07-19 20:42:38 +0200
% 1.09/1.73 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.09/1.73 % git: non_committed_changes: false
% 1.09/1.73
% 1.09/1.73 % ------ Parsing...
% 1.09/1.73 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.09/1.73
% 1.09/1.73 % ------ 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 %
% 1.09/1.73
% 1.09/1.73 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.09/1.73
% 1.09/1.73 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.09/1.73 % ------ Proving...
% 1.09/1.73 % ------ Problem Properties
% 1.09/1.73
% 1.09/1.73 %
% 1.09/1.73 % clauses 55
% 1.09/1.73 % conjectures 1
% 1.09/1.73 % EPR 27
% 1.09/1.73 % Horn 41
% 1.09/1.73 % unary 18
% 1.09/1.73 % binary 14
% 1.09/1.73 % lits 172
% 1.09/1.73 % lits eq 1
% 1.09/1.73 % fd_pure 0
% 1.09/1.73 % fd_pseudo 0
% 1.09/1.73 % fd_cond 0
% 1.09/1.73 % fd_pseudo_cond 1
% 1.09/1.73 % AC symbols 0
% 1.09/1.73
% 1.09/1.73 % ------ Input Options Time Limit: Unbounded
% 1.09/1.73
% 1.09/1.73
% 1.09/1.73 % ------
% 1.09/1.73 % Current options:
% 1.09/1.73 % ------
% 1.09/1.73
% 1.09/1.73
% 1.09/1.73 %
% 1.09/1.73
% 1.09/1.73 % ------ Proving...
% 1.09/1.73 %
% 1.09/1.73
% 1.09/1.73 % SZS status Theorem for theBenchmark.p
% 1.09/1.73
% 1.09/1.73 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.09/1.74
% 1.09/1.74
%------------------------------------------------------------------------------