%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COM021+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 : n010.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 01:03:31 PM UTC 2026
% Result : Theorem 16.51s 7.82s
% Output : Proof 16.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 6 unt; 0 def)
% Number of atoms : 114 ( 16 equ)
% Maximal formula atoms : 15 ( 6 avg)
% Number of connectives : 116 ( 20 ~; 33 |; 63 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 8 con; 0-0 aty)
% Number of variables : 14 ( 1 sgn 4 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f23,hypothesis,
( sdtmndtasgtdt0(xd,xR,xx)
& ( ( sdtmndtplgtdt0(xd,xR,xx)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xx)
& aReductOfIn0(W0,xd,xR)
& aElement0(W0) )
| aReductOfIn0(xx,xd,xR) ) )
| xd = xx )
& sdtmndtasgtdt0(xb,xR,xx)
& ( ( sdtmndtplgtdt0(xb,xR,xx)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xx)
& aReductOfIn0(W0,xb,xR)
& aElement0(W0) )
| aReductOfIn0(xx,xb,xR) ) )
| xb = xx )
& aElement0(xx) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__850) ).
fof(f23_nnf,plain,
( sdtmndtasgtdt0(xd,xR,xx)
& ( ( sdtmndtplgtdt0(xd,xR,xx)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xx)
& aReductOfIn0(W0,xd,xR)
& aElement0(W0) )
| aReductOfIn0(xx,xd,xR) ) )
| xd = xx )
& sdtmndtasgtdt0(xb,xR,xx)
& ( ( sdtmndtplgtdt0(xb,xR,xx)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xx)
& aReductOfIn0(W0,xb,xR)
& aElement0(W0) )
| aReductOfIn0(xx,xb,xR) ) )
| xb = xx )
& aElement0(xx) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
( sdtmndtasgtdt0(xd,xR,xx)
& ( ( sdtmndtplgtdt0(xd,xR,xx)
& ( ( sdtmndtplgtdt0(sk27,xR,xx)
& aReductOfIn0(sk27,xd,xR)
& aElement0(sk27) )
| aReductOfIn0(xx,xd,xR) ) )
| xd = xx )
& sdtmndtasgtdt0(xb,xR,xx)
& ( ( sdtmndtplgtdt0(xb,xR,xx)
& ( ( sdtmndtplgtdt0(sk26,xR,xx)
& aReductOfIn0(sk26,xb,xR)
& aElement0(sk26) )
| aReductOfIn0(xx,xb,xR) ) )
| xb = xx )
& aElement0(xx) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk26,sk27])],[f23_nnf]) ).
cnf(c386,plain,
( aReductOfIn0(sk27,xd,xR)
| aReductOfIn0(xx,xd,xR)
| xd = xx ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
fof(f22,hypothesis,
( aNormalFormOfIn0(xd,xw,xR)
& ~ ? [W0] : aReductOfIn0(W0,xd,xR)
& sdtmndtasgtdt0(xw,xR,xd)
& ( ( sdtmndtplgtdt0(xw,xR,xd)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xd)
& aReductOfIn0(W0,xw,xR)
& aElement0(W0) )
| aReductOfIn0(xd,xw,xR) ) )
| xw = xd )
& aElement0(xd) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__818) ).
fof(f22_nnf,plain,
( aNormalFormOfIn0(xd,xw,xR)
& ! [W0] : ~ aReductOfIn0(W0,xd,xR)
& sdtmndtasgtdt0(xw,xR,xd)
& ( ( sdtmndtplgtdt0(xw,xR,xd)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xd)
& aReductOfIn0(W0,xw,xR)
& aElement0(W0) )
| aReductOfIn0(xd,xw,xR) ) )
| xw = xd )
& aElement0(xd) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [W0] :
( aNormalFormOfIn0(xd,xw,xR)
& ~ aReductOfIn0(W0,xd,xR)
& sdtmndtasgtdt0(xw,xR,xd)
& ( ( sdtmndtplgtdt0(xw,xR,xd)
& ( ( sdtmndtplgtdt0(sk25,xR,xd)
& aReductOfIn0(sk25,xw,xR)
& aElement0(sk25) )
| aReductOfIn0(xd,xw,xR) ) )
| xw = xd )
& aElement0(xd) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk25])],[f22_nnf]) ).
cnf(c377,plain,
~ aReductOfIn0(X0,xd,xR),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p460,plain,
( aReductOfIn0(xx,xd,xR)
| xd = xx ),
inference(resolution,[status(thm)],[c386,c377]) ).
cnf(p461,plain,
xd = xx,
inference(resolution,[status(thm)],[p460,c377]) ).
cnf(c384,plain,
sdtmndtasgtdt0(xb,xR,xx),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(p462,plain,
sdtmndtasgtdt0(xb,xR,xd),
inference(superposition,[status(thm)],[p461,c384]) ).
fof(f24,conjecture,
( sdtmndtasgtdt0(xb,xR,xd)
| sdtmndtplgtdt0(xb,xR,xd)
| ? [W0] :
( sdtmndtplgtdt0(W0,xR,xd)
& aReductOfIn0(W0,xb,xR)
& aElement0(W0) )
| aReductOfIn0(xd,xb,xR)
| xb = xd ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f24_neg,negated_conjecture,
~ ( sdtmndtasgtdt0(xb,xR,xd)
| sdtmndtplgtdt0(xb,xR,xd)
| ? [W0] :
( sdtmndtplgtdt0(W0,xR,xd)
& aReductOfIn0(W0,xb,xR)
& aElement0(W0) )
| aReductOfIn0(xd,xb,xR)
| xb = xd ),
inference(negated_conjecture,[status(cth)],[f24]) ).
fof(f24_nnf,plain,
( ~ sdtmndtasgtdt0(xb,xR,xd)
& ~ sdtmndtplgtdt0(xb,xR,xd)
& ! [W0] :
( ~ sdtmndtplgtdt0(W0,xR,xd)
| ~ aReductOfIn0(W0,xb,xR)
| ~ aElement0(W0) )
& ~ aReductOfIn0(xd,xb,xR)
& xb != xd ),
inference(nnf_transformation,[status(thm)],[f24_neg]) ).
fof(f24_sk,plain,
! [W0] :
( ~ sdtmndtasgtdt0(xb,xR,xd)
& ~ sdtmndtplgtdt0(xb,xR,xd)
& ( ~ sdtmndtplgtdt0(W0,xR,xd)
| ~ aReductOfIn0(W0,xb,xR)
| ~ aElement0(W0) )
& ~ aReductOfIn0(xd,xb,xR)
& xb != xd ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c394,plain,
~ sdtmndtasgtdt0(xb,xR,xd),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p468,plain,
$false,
inference(resolution,[status(thm)],[p462,c394]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM021+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/5.37 % Computer : n010.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Fri Sep 25 07:48:34 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 16.51/7.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.51/7.82 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------