%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUN089+2 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 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 02:29:33 PM UTC 2026
% Result : Theorem 1.77s 1.19s
% Output : Proof 1.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 6 unt; 0 def)
% Number of atoms : 54 ( 17 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 68 ( 33 ~; 21 |; 14 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 33 ( 3 sgn 20 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( Y20 != Y10
| ~ r1(Y20) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7a) ).
fof(f10_nnf,plain,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( Y20 != Y10
| ~ r1(Y20) ) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [Y20,Y10,X7] :
( ~ r2(X7,Y10)
| Y20 != Y10
| ~ r1(Y20) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c38,plain,
( ~ r2(X0,X1)
| X2 != X1
| ~ r1(X2) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
fof(f11,conjecture,
! [Y1] :
( ! [Y4] :
( ~ r1(Y4)
| Y4 != Y1 )
| ! [Y2] :
( ~ r2(Y2,Y1)
| ! [Y3] :
( ~ r2(Y3,Y2)
| ~ r1(Y3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zerouneqtwo) ).
fof(f11_neg,negated_conjecture,
~ ! [Y1] :
( ! [Y4] :
( ~ r1(Y4)
| Y4 != Y1 )
| ! [Y2] :
( ~ r2(Y2,Y1)
| ! [Y3] :
( ~ r2(Y3,Y2)
| ~ r1(Y3) ) ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f11_nnf,plain,
? [Y1] :
( ? [Y4] :
( r1(Y4)
& Y4 = Y1 )
& ? [Y2] :
( r2(Y2,Y1)
& ? [Y3] :
( r2(Y3,Y2)
& r1(Y3) ) ) ),
inference(nnf_transformation,[status(thm)],[f11_neg]) ).
fof(f11_sk,plain,
( r1(sk23)
& sk23 = sk20
& r2(sk21,sk20)
& r2(sk22,sk21)
& r1(sk22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23])],[f11_nnf]) ).
cnf(c43,plain,
r1(sk23),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p167,plain,
( ~ r2(X1,X0)
| sk0 != X0 ),
inference(resolution,[status(thm)],[c38,c43]) ).
cnf(p168,plain,
~ r2(X0,sk0),
inference(equality_resolution,[status(thm)],[p167]) ).
fof(f0,axiom,
? [Y24] :
! [X19] :
( ( X19 = Y24
& r1(X19) )
| ( X19 != Y24
& ~ r1(X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
fof(f0_nnf,plain,
? [Y24] :
! [X19] :
( ( X19 = Y24
& r1(X19) )
| ( X19 != Y24
& ~ r1(X19) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X19] :
( ( X19 = sk0
& r1(X19) )
| ( X19 != sk0
& ~ r1(X19) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c1,plain,
( X1 = sk0
| ~ r1(X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p48,plain,
sk20 = sk0,
inference(resolution,[status(thm)],[c1,c43]) ).
cnf(c41,plain,
r2(sk21,sk20),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p49,plain,
r2(sk21,sk0),
inference(demodulation,[status(thm)],[p48,c41]) ).
cnf(p172,plain,
$false,
inference(resolution,[status(thm)],[p168,p49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN089+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 06:01:27 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 1.77/1.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.77/1.19 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------