%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUN056+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 : 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 02:29:25 PM UTC 2026
% Result : Theorem 18.15s 2.75s
% Output : Proof 18.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 58 ( 21 unt; 0 def)
% Number of atoms : 210 ( 45 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 273 ( 121 ~; 96 |; 56 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 190 ( 4 sgn 47 !; 38 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X4] :
? [Y9] :
( Y9 = X4
& ? [Y16] :
( r3(X4,Y16,Y9)
& r1(Y16) ) ),
file('/export/starexec/sandbox2/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(c27,plain,
r1(sk13(X0)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
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(p203,plain,
sk13(X0) = sk0,
inference(resolution,[status(thm)],[c27,c1]) ).
cnf(c28,plain,
r3(X0,sk13(X0),sk12(X0)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p204,plain,
r3(X0,sk0,sk12(X0)),
inference(demodulation,[status(thm)],[p203,c28]) ).
fof(f2,axiom,
! [X13,X14] :
? [Y22] :
! [X15] :
( ( X15 = Y22
& r3(X13,X14,X15) )
| ( X15 != Y22
& ~ r3(X13,X14,X15) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
fof(f2_nnf,plain,
! [X13,X14] :
? [Y22] :
! [X15] :
( ( X15 = Y22
& r3(X13,X14,X15) )
| ( X15 != Y22
& ~ r3(X13,X14,X15) ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X13,X14,X15] :
( ( X15 = sk2(X13,X14)
& r3(X13,X14,X15) )
| ( X15 != sk2(X13,X14)
& ~ r3(X13,X14,X15) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f2_nnf]) ).
cnf(c9,plain,
( X3 = sk2(X0,X1)
| ~ r3(X0,X1,X3) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p602,plain,
X0 = sk2(X0,sk0),
inference(resolution,[status(thm)],[p204,c9]) ).
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/sandbox2/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(c20,plain,
r3(X0,X1,sk7(X0,X1)),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p168,plain,
sk7(X0,X1) = sk2(X0,X1),
inference(resolution,[status(thm)],[c20,c9]) ).
cnf(p1453,plain,
sk2(X0,sk0) = X0,
inference(superposition,[status(thm)],[p602,p168]) ).
cnf(c16,plain,
r2(X1,sk6(X0,X1)),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f1,axiom,
! [X11] :
? [Y21] :
! [X12] :
( ( X12 = Y21
& r2(X11,X12) )
| ( X12 != Y21
& ~ r2(X11,X12) ) ),
file('/export/starexec/sandbox2/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(c5,plain,
( X2 = sk1(X0)
| ~ r2(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p154,plain,
sk6(X0,X1) = sk1(X1),
inference(resolution,[status(thm)],[c16,c5]) ).
cnf(c17,plain,
r3(X0,sk6(X0,X1),sk5(X0,X1)),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p155,plain,
r3(X0,sk1(X1),sk5(X0,X1)),
inference(demodulation,[status(thm)],[p154,c17]) ).
cnf(p480,plain,
sk4(X0,X1) = sk2(X0,sk1(X1)),
inference(resolution,[status(thm)],[p155,c9]) ).
cnf(p1224,plain,
sk2(X0,sk1(X1)) = sk4(X0,X1),
inference(superposition,[status(thm)],[p480,p168]) ).
fof(f11,conjecture,
? [Y1] :
( ? [Y4] :
( ? [Y7] :
( ? [Y10] :
( r2(Y10,Y7)
& r1(Y10) )
& r2(Y7,Y4) )
& ? [Y6] :
( ? [Y9] :
( r2(Y9,Y6)
& r1(Y9) )
& r3(Y6,Y4,Y1) ) )
& ? [Y2] :
( ? [Y3] :
( ? [Y5] :
( ? [Y8] :
( r2(Y8,Y5)
& r1(Y8) )
& r2(Y5,Y3) )
& r2(Y3,Y2) )
& Y1 = Y2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oneplustwoeqthree) ).
fof(f11_neg,negated_conjecture,
~ ? [Y1] :
( ? [Y4] :
( ? [Y7] :
( ? [Y10] :
( r2(Y10,Y7)
& r1(Y10) )
& r2(Y7,Y4) )
& ? [Y6] :
( ? [Y9] :
( r2(Y9,Y6)
& r1(Y9) )
& r3(Y6,Y4,Y1) ) )
& ? [Y2] :
( ? [Y3] :
( ? [Y5] :
( ? [Y8] :
( r2(Y8,Y5)
& r1(Y8) )
& r2(Y5,Y3) )
& r2(Y3,Y2) )
& Y1 = Y2 ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f11_nnf,plain,
! [Y1] :
( ! [Y4] :
( ! [Y7] :
( ! [Y10] :
( ~ r2(Y10,Y7)
| ~ r1(Y10) )
| ~ r2(Y7,Y4) )
| ! [Y6] :
( ! [Y9] :
( ~ r2(Y9,Y6)
| ~ r1(Y9) )
| ~ r3(Y6,Y4,Y1) ) )
| ! [Y2] :
( ! [Y3] :
( ! [Y5] :
( ! [Y8] :
( ~ r2(Y8,Y5)
| ~ r1(Y8) )
| ~ r2(Y5,Y3) )
| ~ r2(Y3,Y2) )
| Y1 != Y2 ) ),
inference(nnf_transformation,[status(thm)],[f11_neg]) ).
fof(f11_sk,plain,
! [Y1,Y2,Y3,Y5,Y8,Y6,Y4,Y9,Y7,Y10] :
( ~ r2(Y10,Y7)
| ~ r1(Y10)
| ~ r2(Y7,Y4)
| ~ r2(Y9,Y6)
| ~ r1(Y9)
| ~ r3(Y6,Y4,Y1)
| ~ r2(Y8,Y5)
| ~ r1(Y8)
| ~ r2(Y5,Y3)
| ~ r2(Y3,Y2)
| Y1 != Y2 ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c39,plain,
( ~ r2(X9,X8)
| ~ r1(X9)
| ~ r2(X8,X5)
| ~ r2(X7,X6)
| ~ r1(X7)
| ~ r3(X6,X5,X0)
| ~ r2(X4,X3)
| ~ r1(X4)
| ~ r2(X3,X2)
| ~ r2(X2,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p49,plain,
( ~ r2(X8,X7)
| ~ r1(X8)
| ~ r2(X7,X6)
| ~ r2(X4,X5)
| ~ r3(X5,X6,X0)
| ~ r2(X4,X3)
| ~ r1(X4)
| ~ r2(X3,X2)
| ~ r2(X2,X1)
| X0 != X1 ),
inference(factoring,[status(thm)],[c39]) ).
cnf(p392,plain,
( ~ r2(X7,X6)
| ~ r1(X7)
| ~ r2(X6,X5)
| ~ r3(X3,X5,X0)
| ~ r2(X4,X3)
| ~ r1(X4)
| ~ r2(X3,X2)
| ~ r2(X2,X1)
| X0 != X1 ),
inference(factoring,[status(thm)],[p49]) ).
cnf(p977,plain,
( ~ r1(X4)
| ~ r2(X3,X5)
| ~ r3(X3,X5,X0)
| ~ r2(X4,X3)
| ~ r1(X4)
| ~ r2(X3,X2)
| ~ r2(X2,X1)
| X0 != X1 ),
inference(factoring,[status(thm)],[p392]) ).
cnf(p1120,plain,
( ~ r2(X3,X5)
| ~ r3(X3,X5,X0)
| ~ r2(X4,X3)
| ~ r1(X4)
| ~ r2(X3,X2)
| ~ r2(X2,X1)
| X0 != X1 ),
inference(factoring,[status(thm)],[p977]) ).
cnf(p1121,plain,
( ~ r2(X2,X4)
| ~ r3(X2,X4,X1)
| ~ r2(X3,X2)
| ~ r1(X3)
| ~ r2(X2,X0)
| ~ r2(X0,X1) ),
inference(equality_resolution,[status(thm)],[p1120]) ).
cnf(c19,plain,
r2(sk7(X0,X1),sk4(X0,X1)),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p169,plain,
r2(sk2(X0,X1),sk4(X0,X1)),
inference(demodulation,[status(thm)],[p168,c19]) ).
cnf(p1129,plain,
( ~ r2(X0,X4)
| ~ r3(X0,X4,sk4(X1,X2))
| ~ r2(X3,X0)
| ~ r1(X3)
| ~ r2(X0,sk2(X1,X2)) ),
inference(resolution,[status(thm)],[p1121,p169]) ).
cnf(p3177,plain,
( ~ r2(X0,X4)
| ~ r3(X0,X4,sk4(X1,sk1(X2)))
| ~ r2(X3,X0)
| ~ r1(X3)
| ~ r2(X0,sk4(X1,X2)) ),
inference(superposition,[status(thm)],[p1224,p1129]) ).
cnf(p3247,plain,
( ~ r2(sk2(X1,X2),X3)
| ~ r3(sk2(X1,X2),X3,sk4(X1,sk1(X2)))
| ~ r2(X0,sk2(X1,X2))
| ~ r1(X0) ),
inference(resolution,[status(thm)],[p3177,p169]) ).
cnf(c2,plain,
( r1(X1)
| X1 != sk0 ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p93,plain,
r1(sk0),
inference(equality_resolution,[status(thm)],[c2]) ).
cnf(p3252,plain,
( ~ r2(sk2(X0,X1),X2)
| ~ r3(sk2(X0,X1),X2,sk4(X0,sk1(X1)))
| ~ r2(sk0,sk2(X0,X1)) ),
inference(resolution,[status(thm)],[p3247,p93]) ).
cnf(p3467,plain,
( ~ r2(X0,X1)
| ~ r3(X0,X1,sk4(X0,sk1(sk0)))
| ~ r2(sk0,X0) ),
inference(superposition,[status(thm)],[p1453,p3252]) ).
cnf(c6,plain,
( r2(X0,X2)
| X2 != sk1(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p113,plain,
r2(X0,sk1(X0)),
inference(equality_resolution,[status(thm)],[c6]) ).
cnf(p3484,plain,
( ~ r2(sk1(sk0),X0)
| ~ r3(sk1(sk0),X0,sk4(sk1(sk0),sk1(sk0))) ),
inference(resolution,[status(thm)],[p3467,p113]) ).
cnf(c8,plain,
( r3(X0,X1,X3)
| ~ r3(X0,X1,X3) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p479,plain,
r3(X0,sk1(X1),sk4(X0,X1)),
inference(resolution,[status(thm)],[p155,c8]) ).
cnf(p3485,plain,
~ r2(sk1(sk0),sk1(sk1(sk0))),
inference(resolution,[status(thm)],[p3484,p479]) ).
cnf(p3487,plain,
$false,
inference(resolution,[status(thm)],[p3485,p113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN056+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n018.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 : Thu Sep 24 05:52:33 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 18.15/2.75 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.15/2.75 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------