%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COM018+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 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 01:03:30 PM UTC 2026
% Result : Theorem 5.62s 1.21s
% Output : Proof 5.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 8 unt; 0 def)
% Number of atoms : 204 ( 16 equ)
% Maximal formula atoms : 30 ( 8 avg)
% Number of connectives : 238 ( 58 ~; 76 |; 99 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 49 ( 1 sgn 24 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,axiom,
! [W0] :
( ( isTerminating0(W0)
& aRewritingSystem0(W0) )
=> ! [W1] :
( aElement0(W1)
=> ? [W2] : aNormalFormOfIn0(W2,W1,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTermNF) ).
fof(f13_nnf,plain,
! [W0] :
( ! [W1] :
( ? [W2] : aNormalFormOfIn0(W2,W1,W0)
| ~ aElement0(W1) )
| ~ isTerminating0(W0)
| ~ aRewritingSystem0(W0) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [W0,W1] :
( aNormalFormOfIn0(sk12(W0,W1),W1,W0)
| ~ aElement0(W1)
| ~ isTerminating0(W0)
| ~ aRewritingSystem0(W0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk12])],[f13_nnf]) ).
cnf(c42,plain,
( aNormalFormOfIn0(sk12(X0,X1),X1,X0)
| ~ aElement0(X1)
| ~ isTerminating0(X0)
| ~ aRewritingSystem0(X0) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
fof(f14,hypothesis,
aRewritingSystem0(xR),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656) ).
fof(f14_nnf,plain,
aRewritingSystem0(xR),
inference(nnf_transformation,[status(thm)],[f14]) ).
cnf(c43,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[status(esa)],[f14_nnf]) ).
cnf(p603,plain,
( aNormalFormOfIn0(sk12(xR,X0),X0,xR)
| ~ aElement0(X0)
| ~ isTerminating0(xR) ),
inference(resolution,[status(thm)],[c42,c43]) ).
fof(f15,hypothesis,
( isTerminating0(xR)
& ! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> ( ( sdtmndtplgtdt0(W0,xR,W1)
| ? [W2] :
( sdtmndtplgtdt0(W2,xR,W1)
& aReductOfIn0(W2,W0,xR)
& aElement0(W2) )
| aReductOfIn0(W1,W0,xR) )
=> iLess0(W1,W0) ) )
& isLocallyConfluent0(xR)
& ! [W0,W1,W2] :
( ( aReductOfIn0(W2,W0,xR)
& aReductOfIn0(W1,W0,xR)
& aElement0(W2)
& aElement0(W1)
& aElement0(W0) )
=> ? [W3] :
( sdtmndtasgtdt0(W2,xR,W3)
& ( ( sdtmndtplgtdt0(W2,xR,W3)
& ( ? [W4] :
( sdtmndtplgtdt0(W4,xR,W3)
& aReductOfIn0(W4,W2,xR)
& aElement0(W4) )
| aReductOfIn0(W3,W2,xR) ) )
| W2 = W3 )
& sdtmndtasgtdt0(W1,xR,W3)
& ( ( sdtmndtplgtdt0(W1,xR,W3)
& ( ? [W4] :
( sdtmndtplgtdt0(W4,xR,W3)
& aReductOfIn0(W4,W1,xR)
& aElement0(W4) )
| aReductOfIn0(W3,W1,xR) ) )
| W1 = W3 )
& aElement0(W3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656_01) ).
fof(f15_nnf,plain,
( isTerminating0(xR)
& ! [W0,W1] :
( iLess0(W1,W0)
| ( ~ sdtmndtplgtdt0(W0,xR,W1)
& ! [W2] :
( ~ sdtmndtplgtdt0(W2,xR,W1)
| ~ aReductOfIn0(W2,W0,xR)
| ~ aElement0(W2) )
& ~ aReductOfIn0(W1,W0,xR) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
& isLocallyConfluent0(xR)
& ! [W0,W1,W2] :
( ? [W3] :
( sdtmndtasgtdt0(W2,xR,W3)
& ( ( sdtmndtplgtdt0(W2,xR,W3)
& ( ? [W4] :
( sdtmndtplgtdt0(W4,xR,W3)
& aReductOfIn0(W4,W2,xR)
& aElement0(W4) )
| aReductOfIn0(W3,W2,xR) ) )
| W2 = W3 )
& sdtmndtasgtdt0(W1,xR,W3)
& ( ( sdtmndtplgtdt0(W1,xR,W3)
& ( ? [W4] :
( sdtmndtplgtdt0(W4,xR,W3)
& aReductOfIn0(W4,W1,xR)
& aElement0(W4) )
| aReductOfIn0(W3,W1,xR) ) )
| W1 = W3 )
& aElement0(W3) )
| ~ aReductOfIn0(W2,W0,xR)
| ~ aReductOfIn0(W1,W0,xR)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [W0,W1,W2] :
( isTerminating0(xR)
& ( iLess0(W1,W0)
| ( ~ sdtmndtplgtdt0(W0,xR,W1)
& ( ~ sdtmndtplgtdt0(W2,xR,W1)
| ~ aReductOfIn0(W2,W0,xR)
| ~ aElement0(W2) )
& ~ aReductOfIn0(W1,W0,xR) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
& isLocallyConfluent0(xR)
& ( ( sdtmndtasgtdt0(W2,xR,sk13(W0,W1,W2))
& ( ( sdtmndtplgtdt0(W2,xR,sk13(W0,W1,W2))
& ( ( sdtmndtplgtdt0(sk15(W0,W1,W2),xR,sk13(W0,W1,W2))
& aReductOfIn0(sk15(W0,W1,W2),W2,xR)
& aElement0(sk15(W0,W1,W2)) )
| aReductOfIn0(sk13(W0,W1,W2),W2,xR) ) )
| W2 = sk13(W0,W1,W2) )
& sdtmndtasgtdt0(W1,xR,sk13(W0,W1,W2))
& ( ( sdtmndtplgtdt0(W1,xR,sk13(W0,W1,W2))
& ( ( sdtmndtplgtdt0(sk14(W0,W1,W2),xR,sk13(W0,W1,W2))
& aReductOfIn0(sk14(W0,W1,W2),W1,xR)
& aElement0(sk14(W0,W1,W2)) )
| aReductOfIn0(sk13(W0,W1,W2),W1,xR) ) )
| W1 = sk13(W0,W1,W2) )
& aElement0(sk13(W0,W1,W2)) )
| ~ aReductOfIn0(W2,W0,xR)
| ~ aReductOfIn0(W1,W0,xR)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk13,sk14,sk15])],[f15_nnf]) ).
cnf(c59,plain,
isTerminating0(xR),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p651,plain,
( aNormalFormOfIn0(sk12(xR,X0),X0,xR)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[p603,c59]) ).
fof(f21,hypothesis,
( sdtmndtasgtdt0(xv,xR,xw)
& ( ( sdtmndtplgtdt0(xv,xR,xw)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xw)
& aReductOfIn0(W0,xv,xR)
& aElement0(W0) )
| aReductOfIn0(xw,xv,xR) ) )
| xv = xw )
& sdtmndtasgtdt0(xu,xR,xw)
& ( ( sdtmndtplgtdt0(xu,xR,xw)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xw)
& aReductOfIn0(W0,xu,xR)
& aElement0(W0) )
| aReductOfIn0(xw,xu,xR) ) )
| xu = xw )
& aElement0(xw) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__799) ).
fof(f21_nnf,plain,
( sdtmndtasgtdt0(xv,xR,xw)
& ( ( sdtmndtplgtdt0(xv,xR,xw)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xw)
& aReductOfIn0(W0,xv,xR)
& aElement0(W0) )
| aReductOfIn0(xw,xv,xR) ) )
| xv = xw )
& sdtmndtasgtdt0(xu,xR,xw)
& ( ( sdtmndtplgtdt0(xu,xR,xw)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xw)
& aReductOfIn0(W0,xu,xR)
& aElement0(W0) )
| aReductOfIn0(xw,xu,xR) ) )
| xu = xw )
& aElement0(xw) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
( sdtmndtasgtdt0(xv,xR,xw)
& ( ( sdtmndtplgtdt0(xv,xR,xw)
& ( ( sdtmndtplgtdt0(sk24,xR,xw)
& aReductOfIn0(sk24,xv,xR)
& aElement0(sk24) )
| aReductOfIn0(xw,xv,xR) ) )
| xv = xw )
& sdtmndtasgtdt0(xu,xR,xw)
& ( ( sdtmndtplgtdt0(xu,xR,xw)
& ( ( sdtmndtplgtdt0(sk23,xR,xw)
& aReductOfIn0(sk23,xu,xR)
& aElement0(sk23) )
| aReductOfIn0(xw,xu,xR) ) )
| xu = xw )
& aElement0(xw) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk23,sk24])],[f21_nnf]) ).
cnf(c360,plain,
aElement0(xw),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p657,plain,
aNormalFormOfIn0(sk12(xR,xw),xw,xR),
inference(resolution,[status(thm)],[p651,c360]) ).
fof(f22,conjecture,
? [W0] :
( aNormalFormOfIn0(W0,xw,xR)
| ( ~ ? [W1] : aReductOfIn0(W1,W0,xR)
& ( sdtmndtasgtdt0(xw,xR,W0)
| sdtmndtplgtdt0(xw,xR,W0)
| ? [W1] :
( sdtmndtplgtdt0(W1,xR,W0)
& aReductOfIn0(W1,xw,xR)
& aElement0(W1) )
| aReductOfIn0(W0,xw,xR)
| xw = W0 )
& aElement0(W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f22_neg,negated_conjecture,
~ ? [W0] :
( aNormalFormOfIn0(W0,xw,xR)
| ( ~ ? [W1] : aReductOfIn0(W1,W0,xR)
& ( sdtmndtasgtdt0(xw,xR,W0)
| sdtmndtplgtdt0(xw,xR,W0)
| ? [W1] :
( sdtmndtplgtdt0(W1,xR,W0)
& aReductOfIn0(W1,xw,xR)
& aElement0(W1) )
| aReductOfIn0(W0,xw,xR)
| xw = W0 )
& aElement0(W0) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f22_nnf,plain,
! [W0] :
( ~ aNormalFormOfIn0(W0,xw,xR)
& ( ? [W1] : aReductOfIn0(W1,W0,xR)
| ( ~ sdtmndtasgtdt0(xw,xR,W0)
& ~ sdtmndtplgtdt0(xw,xR,W0)
& ! [W1] :
( ~ sdtmndtplgtdt0(W1,xR,W0)
| ~ aReductOfIn0(W1,xw,xR)
| ~ aElement0(W1) )
& ~ aReductOfIn0(W0,xw,xR)
& xw != W0 )
| ~ aElement0(W0) ) ),
inference(nnf_transformation,[status(thm)],[f22_neg]) ).
fof(f22_sk,plain,
! [W0,W1] :
( ~ aNormalFormOfIn0(W0,xw,xR)
& ( aReductOfIn0(sk25(W0),W0,xR)
| ( ~ sdtmndtasgtdt0(xw,xR,W0)
& ~ sdtmndtplgtdt0(xw,xR,W0)
& ( ~ sdtmndtplgtdt0(W1,xR,W0)
| ~ aReductOfIn0(W1,xw,xR)
| ~ aElement0(W1) )
& ~ aReductOfIn0(W0,xw,xR)
& xw != W0 )
| ~ aElement0(W0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk25])],[f22_nnf]) ).
cnf(c376,plain,
~ aNormalFormOfIn0(X0,xw,xR),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p804,plain,
$false,
inference(resolution,[status(thm)],[p657,c376]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM018+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 07:49:20 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.62/1.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.62/1.21 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------