%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUN076+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 : n018.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 02:29:31 PM UTC 2026
% Result : Theorem 4.77s 1.07s
% Output : Proof 4.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 16 unt; 0 def)
% Number of atoms : 121 ( 31 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 132 ( 50 ~; 37 |; 45 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 1 con; 0-2 aty)
% Number of variables : 114 ( 18 sgn 31 !; 36 ?)
% Comments :
%------------------------------------------------------------------------------
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(c1,plain,
( X1 = sk0
| ~ r1(X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
fof(f8,axiom,
! [X5] :
? [Y8] :
( ? [Y18] :
( Y8 = Y18
& r1(Y18) )
& ? [Y17] :
( r4(X5,Y17,Y8)
& r1(Y17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5a) ).
fof(f8_nnf,plain,
! [X5] :
? [Y8] :
( ? [Y18] :
( Y8 = Y18
& r1(Y18) )
& ? [Y17] :
( r4(X5,Y17,Y8)
& r1(Y17) ) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X5] :
( sk14(X5) = sk16(X5)
& r1(sk16(X5))
& r4(X5,sk15(X5),sk14(X5))
& r1(sk15(X5)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk14,sk15,sk16])],[f8_nnf]) ).
cnf(c30,plain,
r1(sk15(X0)),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p57,plain,
sk15(X0) = sk0,
inference(resolution,[status(thm)],[c1,c30]) ).
cnf(c31,plain,
r4(X0,sk15(X0),sk14(X0)),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p58,plain,
r4(X0,sk0,sk14(X0)),
inference(demodulation,[status(thm)],[p57,c31]) ).
fof(f11,conjecture,
? [Y1,Y2,Y3] :
( ? [Y5] :
( Y5 = Y1
& r3(Y2,Y3,Y5) )
& ? [Y4] :
( ? [Y6] :
( ? [Y7] :
( ? [Y8] :
( r2(Y8,Y7)
& r1(Y8) )
& r2(Y7,Y6) )
& r4(Y6,Y2,Y4) )
& Y4 = Y1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thereexistsanevennumber) ).
fof(f11_neg,negated_conjecture,
~ ? [Y1,Y2,Y3] :
( ? [Y5] :
( Y5 = Y1
& r3(Y2,Y3,Y5) )
& ? [Y4] :
( ? [Y6] :
( ? [Y7] :
( ? [Y8] :
( r2(Y8,Y7)
& r1(Y8) )
& r2(Y7,Y6) )
& r4(Y6,Y2,Y4) )
& Y4 = Y1 ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f11_nnf,plain,
! [Y1,Y2,Y3] :
( ! [Y5] :
( Y5 != Y1
| ~ r3(Y2,Y3,Y5) )
| ! [Y4] :
( ! [Y6] :
( ! [Y7] :
( ! [Y8] :
( ~ r2(Y8,Y7)
| ~ r1(Y8) )
| ~ r2(Y7,Y6) )
| ~ r4(Y6,Y2,Y4) )
| Y4 != Y1 ) ),
inference(nnf_transformation,[status(thm)],[f11_neg]) ).
fof(f11_sk,plain,
! [Y4,Y1,Y6,Y2,Y7,Y8,Y3,Y5] :
( Y5 != Y1
| ~ r3(Y2,Y3,Y5)
| ~ r2(Y8,Y7)
| ~ r1(Y8)
| ~ r2(Y7,Y6)
| ~ r4(Y6,Y2,Y4)
| Y4 != Y1 ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c39,plain,
( X7 != X0
| ~ r3(X1,X2,X7)
| ~ r2(X6,X5)
| ~ r1(X6)
| ~ r2(X5,X4)
| ~ r4(X4,X1,X3)
| X3 != X0 ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p40,plain,
( ~ r3(X3,X6,X0)
| ~ r2(X5,X4)
| ~ r1(X5)
| ~ r2(X4,X2)
| ~ r4(X2,X3,X0)
| X0 != X1 ),
inference(factoring,[status(thm)],[c39]) ).
cnf(p45,plain,
( ~ r3(X1,X5,X2)
| ~ r2(X4,X3)
| ~ r1(X4)
| ~ r2(X3,X0)
| ~ r4(X0,X1,X2) ),
inference(equality_resolution,[status(thm)],[p40]) ).
cnf(p67,plain,
( ~ r3(sk0,X3,sk0)
| ~ r2(X2,X0)
| ~ r1(X2)
| ~ r2(X0,X1) ),
inference(resolution,[status(thm)],[p58,p45]) ).
fof(f4,axiom,
! [X1,X8] :
? [Y4] :
( ? [Y7] :
( r3(X1,X8,Y7)
& r2(Y7,Y4) )
& ? [Y5] :
( Y5 = Y4
& ? [Y15] :
( r3(X1,Y15,Y5)
& r2(X8,Y15) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1a) ).
fof(f4_nnf,plain,
! [X1,X8] :
? [Y4] :
( ? [Y7] :
( r3(X1,X8,Y7)
& r2(Y7,Y4) )
& ? [Y5] :
( Y5 = Y4
& ? [Y15] :
( r3(X1,Y15,Y5)
& r2(X8,Y15) ) ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X8,X1] :
( r3(X1,X8,sk7(X1,X8))
& r2(sk7(X1,X8),sk4(X1,X8))
& sk5(X1,X8) = sk4(X1,X8)
& r3(X1,sk6(X1,X8),sk5(X1,X8))
& r2(X8,sk6(X1,X8)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4,sk5,sk6,sk7])],[f4_nnf]) ).
cnf(c16,plain,
r2(X1,sk6(X0,X1)),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p71,plain,
( ~ r3(sk0,X2,sk0)
| ~ r2(X0,X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[p67,c16]) ).
cnf(c33,plain,
sk14(X0) = sk16(X0),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(c32,plain,
r1(sk16(X0)),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p53,plain,
r1(sk14(X0)),
inference(superposition,[status(thm)],[c33,c32]) ).
cnf(p72,plain,
( ~ r3(sk0,X1,sk0)
| ~ r2(sk0,X0) ),
inference(resolution,[status(thm)],[p71,p53]) ).
cnf(p73,plain,
~ r3(sk0,X0,sk0),
inference(resolution,[status(thm)],[p72,c16]) ).
fof(f7,axiom,
! [X4] :
? [Y9] :
( Y9 = X4
& ? [Y16] :
( r3(X4,Y16,Y9)
& r1(Y16) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4a) ).
fof(f7_nnf,plain,
! [X4] :
? [Y9] :
( Y9 = X4
& ? [Y16] :
( r3(X4,Y16,Y9)
& r1(Y16) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X4] :
( sk12(X4) = X4
& r3(X4,sk13(X4),sk12(X4))
& r1(sk13(X4)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk12,sk13])],[f7_nnf]) ).
cnf(c29,plain,
sk12(X0) = X0,
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(c27,plain,
r1(sk13(X0)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p54,plain,
sk13(X0) = sk0,
inference(resolution,[status(thm)],[c1,c27]) ).
cnf(c28,plain,
r3(X0,sk13(X0),sk12(X0)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p56,plain,
r3(X0,sk0,sk12(X0)),
inference(demodulation,[status(thm)],[p54,c28]) ).
cnf(p65,plain,
r3(X0,sk0,X0),
inference(superposition,[status(thm)],[c29,p56]) ).
cnf(p74,plain,
$false,
inference(resolution,[status(thm)],[p73,p65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN076+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n018.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 05:59:34 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.77/1.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.77/1.07 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------