%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUN069+2 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n009.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 02:29:29 PM UTC 2026
% Result : Theorem 4.10s 1.11s
% Output : Proof 4.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 4 unt; 0 def)
% Number of atoms : 49 ( 19 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 58 ( 27 ~; 15 |; 16 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 30 ( 2 sgn 13 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,conjecture,
? [Y1] :
( ? [Y2] :
( r2(Y2,Y1)
& r1(Y2) )
& Y1 = Y1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',oneeqone) ).
fof(f11_neg,negated_conjecture,
~ ? [Y1] :
( ? [Y2] :
( r2(Y2,Y1)
& r1(Y2) )
& Y1 = Y1 ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f11_nnf,plain,
! [Y1] :
( ! [Y2] :
( ~ r2(Y2,Y1)
| ~ r1(Y2) )
| Y1 != Y1 ),
inference(nnf_transformation,[status(thm)],[f11_neg]) ).
fof(f11_sk,plain,
! [Y1,Y2] :
( ~ r2(Y2,Y1)
| ~ r1(Y2)
| Y1 != Y1 ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c39,plain,
( ~ r2(X1,X0)
| ~ r1(X1)
| X0 != X0 ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p73,plain,
( ~ r2(X0,X1)
| ~ r1(X0) ),
inference(equality_resolution,[status(thm)],[c39]) ).
fof(f0,axiom,
? [Y24] :
! [X19] :
( ( X19 = Y24
& r1(X19) )
| ( X19 != Y24
& ~ r1(X19) ) ),
file('/export/starexec/sandbox/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(c2,plain,
( r1(X1)
| X1 != sk0 ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p40,plain,
r1(sk0),
inference(equality_resolution,[status(thm)],[c2]) ).
cnf(p120,plain,
~ r2(sk0,X0),
inference(resolution,[status(thm)],[p73,p40]) ).
fof(f1,axiom,
! [X11] :
? [Y21] :
! [X12] :
( ( X12 = Y21
& r2(X11,X12) )
| ( X12 != Y21
& ~ r2(X11,X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f1_nnf,plain,
! [X11] :
? [Y21] :
! [X12] :
( ( X12 = Y21
& r2(X11,X12) )
| ( X12 != Y21
& ~ r2(X11,X12) ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X11,X12] :
( ( X12 = sk1(X11)
& r2(X11,X12) )
| ( X12 != sk1(X11)
& ~ r2(X11,X12) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f1_nnf]) ).
cnf(c6,plain,
( r2(X0,X2)
| X2 != sk1(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p41,plain,
r2(X0,sk1(X0)),
inference(equality_resolution,[status(thm)],[c6]) ).
cnf(p198,plain,
$false,
inference(resolution,[status(thm)],[p120,p41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN069+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n009.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
% 0.02/0.36 % CPULimit : 300
% 0.02/0.36 % WCLimit : 300
% 0.02/0.36 % DateTime : Thu Sep 24 05:53:58 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.10/1.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.10/1.11 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------