%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COM013+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p 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 : Fri Sep 25 01:04:18 PM UTC 2026
% Result : Theorem 3.25s 1.47s
% Output : CNFRefutation 3.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of formulae : 96 ( 15 unt; 1 def)
% Number of atoms : 574 ( 35 equ)
% Maximal formula atoms : 23 ( 5 avg)
% Number of connectives : 724 ( 284 ~; 283 |; 133 &)
% ( 6 <=>; 18 =>; 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 : 11 ( 9 usr; 2 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 206 ( 0 sgn 169 !; 37 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] :
( ( aRewritingSystem0(X1)
& aElement0(X0) )
=> ! [X2] :
( aReductOfIn0(X2,X0,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mReduct) ).
fof(f6,axiom,
! [X0,X1,X2] :
( ( aElement0(X2)
& aRewritingSystem0(X1)
& aElement0(X0) )
=> ( sdtmndtplgtdt0(X0,X1,X2)
<=> ( ? [X3] :
( sdtmndtplgtdt0(X3,X1,X2)
& aReductOfIn0(X3,X0,X1)
& aElement0(X3) )
| aReductOfIn0(X2,X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTCDef) ).
fof(f8,axiom,
! [X0,X1,X2] :
( ( aElement0(X2)
& aRewritingSystem0(X1)
& aElement0(X0) )
=> ( sdtmndtasgtdt0(X0,X1,X2)
<=> ( sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTCRDef) ).
fof(f14,axiom,
( isTerminating0(xR)
& ! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> ( ( sdtmndtplgtdt0(X0,xR,X1)
| ? [X2] :
( sdtmndtplgtdt0(X2,xR,X1)
& aReductOfIn0(X2,X0,xR)
& aElement0(X2) )
| aReductOfIn0(X1,X0,xR) )
=> iLess0(X1,X0) ) )
& aRewritingSystem0(xR) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__587) ).
fof(f15,conjecture,
! [X0] :
( aElement0(X0)
=> ( ! [X1] :
( aElement0(X1)
=> ( iLess0(X1,X0)
=> ? [X2] :
( aNormalFormOfIn0(X2,X1,xR)
& ~ ? [X3] : aReductOfIn0(X3,X2,xR)
& sdtmndtasgtdt0(X1,xR,X2)
& ( ( sdtmndtplgtdt0(X1,xR,X2)
& ( ? [X3] :
( sdtmndtplgtdt0(X3,xR,X2)
& aReductOfIn0(X3,X1,xR)
& aElement0(X3) )
| aReductOfIn0(X2,X1,xR) ) )
| X1 = X2 )
& aElement0(X2) ) ) )
=> ? [X1] :
( aNormalFormOfIn0(X1,X0,xR)
| ( ~ ? [X2] : aReductOfIn0(X2,X1,xR)
& ( sdtmndtasgtdt0(X0,xR,X1)
| sdtmndtplgtdt0(X0,xR,X1)
| ? [X2] :
( sdtmndtplgtdt0(X2,xR,X1)
& aReductOfIn0(X2,X0,xR)
& aElement0(X2) )
| aReductOfIn0(X1,X0,xR)
| X0 = X1 )
& aElement0(X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f16,negated_conjecture,
~ ! [X0] :
( aElement0(X0)
=> ( ! [X1] :
( aElement0(X1)
=> ( iLess0(X1,X0)
=> ? [X2] :
( aNormalFormOfIn0(X2,X1,xR)
& ~ ? [X3] : aReductOfIn0(X3,X2,xR)
& sdtmndtasgtdt0(X1,xR,X2)
& ( ( sdtmndtplgtdt0(X1,xR,X2)
& ( ? [X3] :
( sdtmndtplgtdt0(X3,xR,X2)
& aReductOfIn0(X3,X1,xR)
& aElement0(X3) )
| aReductOfIn0(X2,X1,xR) ) )
| X1 = X2 )
& aElement0(X2) ) ) )
=> ? [X1] :
( aNormalFormOfIn0(X1,X0,xR)
| ( ~ ? [X2] : aReductOfIn0(X2,X1,xR)
& ( sdtmndtasgtdt0(X0,xR,X1)
| sdtmndtplgtdt0(X0,xR,X1)
| ? [X2] :
( sdtmndtplgtdt0(X2,xR,X1)
& aReductOfIn0(X2,X0,xR)
& aElement0(X2) )
| aReductOfIn0(X1,X0,xR)
| X0 = X1 )
& aElement0(X1) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f21,plain,
~ ! [X0] :
( aElement0(X0)
=> ( ! [X1] :
( aElement0(X1)
=> ( iLess0(X1,X0)
=> ? [X2] :
( aNormalFormOfIn0(X2,X1,xR)
& ~ ? [X4] : aReductOfIn0(X4,X2,xR)
& sdtmndtasgtdt0(X1,xR,X2)
& ( ( sdtmndtplgtdt0(X1,xR,X2)
& ( ? [X3] :
( sdtmndtplgtdt0(X3,xR,X2)
& aReductOfIn0(X3,X1,xR)
& aElement0(X3) )
| aReductOfIn0(X2,X1,xR) ) )
| X1 = X2 )
& aElement0(X2) ) ) )
=> ? [X5] :
( aNormalFormOfIn0(X5,X0,xR)
| ( ~ ? [X7] : aReductOfIn0(X7,X5,xR)
& ( sdtmndtasgtdt0(X0,xR,X5)
| sdtmndtplgtdt0(X0,xR,X5)
| ? [X6] :
( sdtmndtplgtdt0(X6,xR,X5)
& aReductOfIn0(X6,X0,xR)
& aElement0(X6) )
| aReductOfIn0(X5,X0,xR)
| X0 = X5 )
& aElement0(X5) ) ) ) ),
inference(rectify,[],[f16]) ).
fof(f22,plain,
! [X0,X1] :
( ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ! [X2] :
( ~ aReductOfIn0(X2,X0,X1)
| aElement0(X2) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f23,plain,
! [X0,X1] :
( ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ! [X2] :
( ~ aReductOfIn0(X2,X0,X1)
| aElement0(X2) ) ),
inference(flattening,[],[f22]) ).
fof(f24,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(f25,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,[],[f24]) ).
fof(f28,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(f29,plain,
! [X0,X1,X2] :
( ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ( sdtmndtasgtdt0(X0,X1,X2)
<=> ( sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2 ) ) ),
inference(flattening,[],[f28]) ).
fof(f40,plain,
( isTerminating0(xR)
& ! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| ( ~ sdtmndtplgtdt0(X0,xR,X1)
& ! [X2] :
( ~ sdtmndtplgtdt0(X2,xR,X1)
| ~ aReductOfIn0(X2,X0,xR)
| ~ aElement0(X2) )
& ~ aReductOfIn0(X1,X0,xR) )
| iLess0(X1,X0) )
& aRewritingSystem0(xR) ),
inference(ennf_transformation,[],[f14]) ).
fof(f41,plain,
( isTerminating0(xR)
& ! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| ( ~ sdtmndtplgtdt0(X0,xR,X1)
& ! [X2] :
( ~ sdtmndtplgtdt0(X2,xR,X1)
| ~ aReductOfIn0(X2,X0,xR)
| ~ aElement0(X2) )
& ~ aReductOfIn0(X1,X0,xR) )
| iLess0(X1,X0) )
& aRewritingSystem0(xR) ),
inference(flattening,[],[f40]) ).
fof(f42,plain,
? [X0] :
( aElement0(X0)
& ! [X1] :
( ~ aElement0(X1)
| ~ iLess0(X1,X0)
| ? [X2] :
( aNormalFormOfIn0(X2,X1,xR)
& ! [X4] : ~ aReductOfIn0(X4,X2,xR)
& sdtmndtasgtdt0(X1,xR,X2)
& ( ( sdtmndtplgtdt0(X1,xR,X2)
& ( ? [X3] :
( sdtmndtplgtdt0(X3,xR,X2)
& aReductOfIn0(X3,X1,xR)
& aElement0(X3) )
| aReductOfIn0(X2,X1,xR) ) )
| X1 = X2 )
& aElement0(X2) ) )
& ! [X5] :
( ~ aNormalFormOfIn0(X5,X0,xR)
& ( ? [X7] : aReductOfIn0(X7,X5,xR)
| ( ~ sdtmndtasgtdt0(X0,xR,X5)
& ~ sdtmndtplgtdt0(X0,xR,X5)
& ! [X6] :
( ~ sdtmndtplgtdt0(X6,xR,X5)
| ~ aReductOfIn0(X6,X0,xR)
| ~ aElement0(X6) )
& ~ aReductOfIn0(X5,X0,xR)
& X0 != X5 )
| ~ aElement0(X5) ) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f43,plain,
? [X0] :
( aElement0(X0)
& ! [X1] :
( ~ aElement0(X1)
| ~ iLess0(X1,X0)
| ? [X2] :
( aNormalFormOfIn0(X2,X1,xR)
& ! [X4] : ~ aReductOfIn0(X4,X2,xR)
& sdtmndtasgtdt0(X1,xR,X2)
& ( ( sdtmndtplgtdt0(X1,xR,X2)
& ( ? [X3] :
( sdtmndtplgtdt0(X3,xR,X2)
& aReductOfIn0(X3,X1,xR)
& aElement0(X3) )
| aReductOfIn0(X2,X1,xR) ) )
| X1 = X2 )
& aElement0(X2) ) )
& ! [X5] :
( ~ aNormalFormOfIn0(X5,X0,xR)
& ( ? [X7] : aReductOfIn0(X7,X5,xR)
| ( ~ sdtmndtasgtdt0(X0,xR,X5)
& ~ sdtmndtplgtdt0(X0,xR,X5)
& ! [X6] :
( ~ sdtmndtplgtdt0(X6,xR,X5)
| ~ aReductOfIn0(X6,X0,xR)
| ~ aElement0(X6) )
& ~ aReductOfIn0(X5,X0,xR)
& X0 != X5 )
| ~ aElement0(X5) ) ) ),
inference(flattening,[],[f42]) ).
fof(f50,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,[],[f25]) ).
fof(f51,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,[],[f50]) ).
fof(f52,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,[],[f51]) ).
fof(f53,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))],[f52]) ).
fof(f54,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,[],[f29]) ).
fof(f55,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,[],[f54]) ).
fof(f71,plain,
? [X0] :
( aElement0(X0)
& ! [X4] :
( ~ aElement0(X4)
| ~ iLess0(X4,X0)
| ? [X5] :
( aNormalFormOfIn0(X5,X4,xR)
& ! [X7] : ~ aReductOfIn0(X7,X5,xR)
& sdtmndtasgtdt0(X4,xR,X5)
& ( ( sdtmndtplgtdt0(X4,xR,X5)
& ( ? [X6] :
( sdtmndtplgtdt0(X6,xR,X5)
& aReductOfIn0(X6,X4,xR)
& aElement0(X6) )
| aReductOfIn0(X5,X4,xR) ) )
| X4 = X5 )
& aElement0(X5) ) )
& ! [X1] :
( ~ aNormalFormOfIn0(X1,X0,xR)
& ( ? [X3] : aReductOfIn0(X3,X1,xR)
| ( ~ sdtmndtasgtdt0(X0,xR,X1)
& ~ sdtmndtplgtdt0(X0,xR,X1)
& ! [X2] :
( ~ sdtmndtplgtdt0(X2,xR,X1)
| ~ aReductOfIn0(X2,X0,xR)
| ~ aElement0(X2) )
& ~ aReductOfIn0(X1,X0,xR)
& X0 != X1 )
| ~ aElement0(X1) ) ) ),
inference(rectify,[],[f43]) ).
fof(f72,plain,
( aElement0(sK16)
& ! [X4] :
( ~ aElement0(X4)
| ~ iLess0(X4,sK16)
| ( aNormalFormOfIn0(sK18(X4),X4,xR)
& ! [X7] : ~ aReductOfIn0(X7,sK18(X4),xR)
& sdtmndtasgtdt0(X4,xR,sK18(X4))
& ( ( sdtmndtplgtdt0(X4,xR,sK18(X4))
& ( ( sdtmndtplgtdt0(sK19(X4),xR,sK18(X4))
& aReductOfIn0(sK19(X4),X4,xR)
& aElement0(sK19(X4)) )
| aReductOfIn0(sK18(X4),X4,xR) ) )
| sK18(X4) = X4 )
& aElement0(sK18(X4)) ) )
& ! [X1] :
( ~ aNormalFormOfIn0(X1,sK16,xR)
& ( aReductOfIn0(sK17(X1),X1,xR)
| ( ~ sdtmndtasgtdt0(sK16,xR,X1)
& ~ sdtmndtplgtdt0(sK16,xR,X1)
& ! [X2] :
( ~ sdtmndtplgtdt0(X2,xR,X1)
| ~ aReductOfIn0(X2,sK16,xR)
| ~ aElement0(X2) )
& ~ aReductOfIn0(X1,sK16,xR)
& sK16 != X1 )
| ~ aElement0(X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16,sK17,sK18,sK19]),skolemize(X0,sK16),skolemize(X3,sK17(X1)),skolemize(X5,sK18(X4)),skolemize(X6,sK19(X4))],[f71]) ).
fof(f73,plain,
! [X2,X0,X1] :
( ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ~ aReductOfIn0(X2,X0,X1)
| aElement0(X2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f77,plain,
! [X2,X3,X0,X1] :
( ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(X3,X1,X2)
| ~ aReductOfIn0(X3,X0,X1)
| ~ aElement0(X3)
| sdtmndtplgtdt0(X0,X1,X2) ),
inference(cnf_transformation,[],[f53]) ).
fof(f78,plain,
! [X2,X0,X1] :
( ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ~ aReductOfIn0(X2,X0,X1)
| sdtmndtplgtdt0(X0,X1,X2) ),
inference(cnf_transformation,[],[f53]) ).
fof(f81,plain,
! [X2,X0,X1] :
( ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(X0,X1,X2)
| sdtmndtasgtdt0(X0,X1,X2) ),
inference(cnf_transformation,[],[f55]) ).
fof(f120,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| ~ aReductOfIn0(X1,X0,xR)
| iLess0(X1,X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f121,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[],[f41]) ).
fof(f122,plain,
aElement0(sK16),
inference(cnf_transformation,[],[f72]) ).
fof(f124,plain,
! [X7,X4] :
( ~ aElement0(X4)
| ~ iLess0(X4,sK16)
| ~ aReductOfIn0(X7,sK18(X4),xR) ),
inference(cnf_transformation,[],[f72]) ).
fof(f126,plain,
! [X4] :
( ~ aElement0(X4)
| ~ iLess0(X4,sK16)
| sdtmndtplgtdt0(X4,xR,sK18(X4))
| sK18(X4) = X4 ),
inference(cnf_transformation,[],[f72]) ).
fof(f130,plain,
! [X4] :
( ~ aElement0(X4)
| ~ iLess0(X4,sK16)
| aElement0(sK18(X4)) ),
inference(cnf_transformation,[],[f72]) ).
fof(f132,plain,
! [X1] :
( aReductOfIn0(sK17(X1),X1,xR)
| ~ sdtmndtasgtdt0(sK16,xR,X1)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f133,plain,
! [X1] :
( aReductOfIn0(sK17(X1),X1,xR)
| ~ sdtmndtplgtdt0(sK16,xR,X1)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f136,plain,
! [X1] :
( aReductOfIn0(sK17(X1),X1,xR)
| sK16 != X1
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f138,plain,
( aReductOfIn0(sK17(sK16),sK16,xR)
| ~ aElement0(sK16) ),
inference(equality_resolution,[],[f136]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElement0(X0)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X1)
| ~ aReductOfIn0(X0,X1,X2) ),
inference(cnf_transformation,[],[f73]) ).
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,[],[f78]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdtmndtplgtdt0(X1,X2,X3)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X3)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(X0,X2,X3)
| ~ aReductOfIn0(X0,X1,X2) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtmndtasgtdt0(X0,X1,X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(X0,X1,X2) ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_93,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[],[f121]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i] :
( iLess0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ aReductOfIn0(X0,X1,xR) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_98,negated_conjecture,
( aReductOfIn0(sK17(sK16),sK16,xR)
| ~ aElement0(sK16) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_101,negated_conjecture,
! [X0: $i] :
( aReductOfIn0(sK17(X0),X0,xR)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(sK16,xR,X0) ),
inference(cnf_transformation,[],[f133]) ).
tcf(c_102,negated_conjecture,
! [X0: $i] :
( aReductOfIn0(sK17(X0),X0,xR)
| ~ aElement0(X0)
| ~ sdtmndtasgtdt0(sK16,xR,X0) ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_104,negated_conjecture,
! [X0: $i] :
( aElement0(sK18(X0))
| ~ aElement0(X0)
| ~ iLess0(X0,sK16) ),
inference(cnf_transformation,[],[f130]) ).
tcf(c_108,negated_conjecture,
! [X0: $i] :
( sdtmndtplgtdt0(X0,xR,sK18(X0))
| ( sK18(X0) = X0 )
| ~ aElement0(X0)
| ~ iLess0(X0,sK16) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_110,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ aElement0(X1)
| ~ iLess0(X1,sK16)
| ~ aReductOfIn0(X0,sK18(X1),xR) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_112,negated_conjecture,
aElement0(sK16),
inference(cnf_transformation,[],[f122]) ).
tcf(c_158,negated_conjecture,
aReductOfIn0(sK17(sK16),sK16,xR),
inference(global_subsumption_just,[status(thm)],[c_98,c_112,c_98]) ).
tcf(c_160,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_162,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdtmndtplgtdt0(X1,X2,X3)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X3)
| ~ aElement0(X1)
| ~ aReductOfIn0(X0,X1,X2)
| ~ sdtmndtplgtdt0(X0,X2,X3) ),
inference(global_subsumption_just,[status(thm)],[c_51,c_49,c_51]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdtmndtplgtdt0(X1,X2,X3)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X3)
| ~ aElement0(X1)
| ~ sdtmndtplgtdt0(X0,X2,X3)
| ~ aReductOfIn0(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_162]) ).
tcf(c_1347,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdtmndtplgtdt0(X2,X0,X3)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ sdtmndtplgtdt0(X1,X0,X3)
| ~ aReductOfIn0(X1,X2,X0)
| ( X0 != xR ) ),
inference(resolution_lifted,[status(thm)],[c_163,c_93]) ).
tcf(c_1348,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtmndtplgtdt0(X1,xR,X2)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ sdtmndtplgtdt0(X0,xR,X2)
| ~ aReductOfIn0(X0,X1,xR) ),
inference(unflattening,[status(thm)],[c_1347]) ).
tcf(c_1364,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_160,c_93]) ).
tcf(c_1365,plain,
! [X0: $i,X1: $i] :
( sdtmndtplgtdt0(X1,xR,X0)
| ~ aElement0(X1)
| ~ aReductOfIn0(X0,X1,xR) ),
inference(unflattening,[status(thm)],[c_1364]) ).
tcf(c_1376,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElement0(X1)
| ~ aElement0(X2)
| ~ aReductOfIn0(X1,X2,X0)
| ( X0 != xR ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_93]) ).
tcf(c_1377,plain,
! [X0: $i,X1: $i] :
( aElement0(X0)
| ~ aElement0(X1)
| ~ aReductOfIn0(X0,X1,xR) ),
inference(unflattening,[status(thm)],[c_1376]) ).
tcf(c_1429,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtmndtasgtdt0(X1,X0,X2)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ sdtmndtplgtdt0(X1,X0,X2)
| ( X0 != xR ) ),
inference(resolution_lifted,[status(thm)],[c_57,c_93]) ).
tcf(c_1430,plain,
! [X0: $i,X1: $i] :
( sdtmndtasgtdt0(X0,xR,X1)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(X0,xR,X1) ),
inference(unflattening,[status(thm)],[c_1429]) ).
tcf(c_1551,plain,
! [X0: $i,X1: $i] :
( iLess0(X0,X1)
| ~ aElement0(X1)
| ~ aReductOfIn0(X0,X1,xR) ),
inference(backward_subsumption_resolution,[status(thm)],[c_94,c_1377]) ).
tcf(c_5606,definition,
iPr_def_10 = sK17(sK16),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_5609,negated_conjecture,
aReductOfIn0(iPr_def_10,sK16,xR),
inference(demodulation,[status(thm)],[c_158,c_5606]) ).
tcf(c_5610,negated_conjecture,
aElement0(sK16),
inference(demodulation,[status(thm)],[c_112]) ).
tcf(c_5611,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ aElement0(X1)
| ~ iLess0(X1,sK16)
| ~ aReductOfIn0(X0,sK18(X1),xR) ),
inference(demodulation,[status(thm)],[c_110]) ).
tcf(c_5613,negated_conjecture,
! [X0: $i] :
( sdtmndtplgtdt0(X0,xR,sK18(X0))
| ( sK18(X0) = X0 )
| ~ aElement0(X0)
| ~ iLess0(X0,sK16) ),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_5617,negated_conjecture,
! [X0: $i] :
( aElement0(sK18(X0))
| ~ aElement0(X0)
| ~ iLess0(X0,sK16) ),
inference(demodulation,[status(thm)],[c_104]) ).
tcf(c_5618,negated_conjecture,
! [X0: $i] :
( aReductOfIn0(sK17(X0),X0,xR)
| ~ aElement0(X0)
| ~ sdtmndtasgtdt0(sK16,xR,X0) ),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_5619,negated_conjecture,
! [X0: $i] :
( aReductOfIn0(sK17(X0),X0,xR)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(sK16,xR,X0) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_6529,plain,
! [X0: $i] :
( ~ aElement0(X0)
| ~ iLess0(X0,sK16)
| ~ aElement0(sK18(X0))
| ~ sdtmndtasgtdt0(sK16,xR,sK18(X0)) ),
inference(superposition,[status(thm)],[c_5618,c_5611]) ).
tcf(c_6541,plain,
! [X0: $i] :
( ~ aElement0(X0)
| ~ iLess0(X0,sK16)
| ~ aElement0(sK18(X0))
| ~ sdtmndtplgtdt0(sK16,xR,sK18(X0)) ),
inference(superposition,[status(thm)],[c_5619,c_5611]) ).
tcf(c_6672,plain,
! [X0: $i] :
( ~ aElement0(X0)
| ~ iLess0(X0,sK16)
| ~ sdtmndtasgtdt0(sK16,xR,sK18(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_6529,c_104,c_6529]) ).
tcf(c_6682,plain,
! [X0: $i] :
( ~ aElement0(X0)
| ~ iLess0(X0,sK16)
| ~ sdtmndtplgtdt0(sK16,xR,sK18(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_6541,c_104,c_6541]) ).
tcf(c_6794,plain,
( aElement0(iPr_def_10)
| ~ aElement0(sK16) ),
inference(superposition,[status(thm)],[c_5609,c_1377]) ).
tcf(c_6795,plain,
aElement0(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_6794,c_5610]) ).
tcf(c_6911,plain,
! [X0: $i] :
( sdtmndtplgtdt0(sK16,xR,X0)
| ~ aElement0(sK16)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(iPr_def_10,xR,X0) ),
inference(superposition,[status(thm)],[c_5609,c_1348]) ).
tcf(c_6913,plain,
! [X0: $i] :
( sdtmndtplgtdt0(sK16,xR,X0)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(iPr_def_10,xR,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6911,c_5610]) ).
tcf(c_7073,plain,
( iLess0(iPr_def_10,sK16)
| ~ aElement0(sK16) ),
inference(superposition,[status(thm)],[c_5609,c_1551]) ).
tcf(c_7075,plain,
iLess0(iPr_def_10,sK16),
inference(forward_subsumption_resolution,[status(thm)],[c_7073,c_5610]) ).
tcf(c_7111,plain,
( aElement0(sK18(iPr_def_10))
| ~ aElement0(iPr_def_10) ),
inference(superposition,[status(thm)],[c_7075,c_5617]) ).
tcf(c_7112,plain,
aElement0(sK18(iPr_def_10)),
inference(forward_subsumption_resolution,[status(thm)],[c_7111,c_6795]) ).
tcf(c_7123,plain,
( sdtmndtplgtdt0(sK16,xR,sK18(iPr_def_10))
| ( sK18(iPr_def_10) = iPr_def_10 )
| ~ aElement0(iPr_def_10)
| ~ iLess0(iPr_def_10,sK16)
| ~ aElement0(sK18(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_5613,c_6913]) ).
tcf(c_7124,plain,
( sdtmndtplgtdt0(sK16,xR,sK18(iPr_def_10))
| ( sK18(iPr_def_10) = iPr_def_10 )
| ~ aElement0(sK18(iPr_def_10)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7123,c_6795,c_7075]) ).
tcf(c_7209,plain,
( sdtmndtplgtdt0(sK16,xR,iPr_def_10)
| ~ aElement0(sK16) ),
inference(superposition,[status(thm)],[c_5609,c_1365]) ).
tcf(c_7211,plain,
sdtmndtplgtdt0(sK16,xR,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_7209,c_5610]) ).
tcf(c_8731,plain,
( sdtmndtasgtdt0(sK16,xR,iPr_def_10)
| ~ aElement0(iPr_def_10)
| ~ aElement0(sK16) ),
inference(superposition,[status(thm)],[c_7211,c_1430]) ).
tcf(c_8735,plain,
sdtmndtasgtdt0(sK16,xR,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_8731,c_6795,c_5610]) ).
tcf(c_8993,plain,
( sdtmndtplgtdt0(sK16,xR,sK18(iPr_def_10))
| ( sK18(iPr_def_10) = iPr_def_10 ) ),
inference(global_subsumption_just,[status(thm)],[c_7124,c_7112,c_7124]) ).
tcf(c_9004,plain,
( ( sK18(iPr_def_10) = iPr_def_10 )
| ~ aElement0(iPr_def_10)
| ~ iLess0(iPr_def_10,sK16) ),
inference(superposition,[status(thm)],[c_8993,c_6682]) ).
tcf(c_9005,plain,
sK18(iPr_def_10) = iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_9004,c_6795,c_7075]) ).
tcf(c_9090,plain,
( ~ aElement0(iPr_def_10)
| ~ iLess0(iPr_def_10,sK16)
| ~ sdtmndtasgtdt0(sK16,xR,iPr_def_10) ),
inference(superposition,[status(thm)],[c_9005,c_6672]) ).
tcf(c_9098,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_9090,c_6795,c_7075,c_8735]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM013+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.56 % Computer : n019.cluster.edu
% 0.09/0.56 % Model : x86_64 x86_64
% 0.09/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.56 % Memory : 8046.5625MB
% 0.09/0.56 % OS : Linux 6.8.0-71-generic
% 0.09/0.56 % CPULimit : 300
% 0.09/0.56 % WCLimit : 300
% 0.09/0.56 % DateTime : Fri Sep 25 07:46:23 UTC 2026
% 0.09/0.57 % CPUTime :
% 0.09/0.57 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.60 Running first-order theorem proving
% 0.09/0.60 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.61
% 0.09/0.61 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.61
% 0.09/0.61 % Detected problem language: tptp
% 0.09/0.62 % Proving...
% 3.25/1.47 % SZS status Started for theBenchmark.p
% 3.25/1.47 % SZS status Theorem for theBenchmark.p
% 3.25/1.47
% 3.25/1.47 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.25/1.47
% 3.25/1.47 % ------ iProver source info
% 3.25/1.47
% 3.25/1.47 % git: date: 2026-07-19 20:42:38 +0200
% 3.25/1.47 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.25/1.47 % git: non_committed_changes: false
% 3.25/1.47
% 3.25/1.47 % ------ Parsing...
% 3.25/1.47 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.25/1.47
% 3.25/1.47 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 3.25/1.47
% 3.25/1.47 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.25/1.47
% 3.25/1.47 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.25/1.47 % ------ Proving...
% 3.25/1.47 % ------ Problem Properties
% 3.25/1.47
% 3.25/1.47 %
% 3.25/1.47 % clauses 49
% 3.25/1.47 % conjectures 13
% 3.25/1.47 % EPR 14
% 3.25/1.47 % Horn 31
% 3.25/1.47 % unary 4
% 3.25/1.47 % binary 11
% 3.25/1.47 % lits 185
% 3.25/1.47 % lits eq 6
% 3.25/1.47 % fd_pure 0
% 3.25/1.47 % fd_pseudo 0
% 3.25/1.47 % fd_cond 0
% 3.25/1.47 % fd_pseudo_cond 1
% 3.25/1.47 % AC symbols 0
% 3.25/1.47
% 3.25/1.47 % ------ Schedule dynamic 5 is on
% 3.25/1.47
% 3.25/1.47 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.25/1.47
% 3.25/1.47
% 3.25/1.47 % ------
% 3.25/1.47 % Current options:
% 3.25/1.47 % ------
% 3.25/1.47
% 3.25/1.47
% 3.25/1.47 %
% 3.25/1.47
% 3.25/1.47 % ------ Proving...
% 3.25/1.47 %
% 3.25/1.47
% 3.25/1.47 % SZS status Theorem for theBenchmark.p
% 3.25/1.47
% 3.25/1.47 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.25/1.47
% 3.25/1.47
%------------------------------------------------------------------------------