%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUN076+2 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 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 : Sun Sep 27 08:19:22 AM UTC 2026
% Result : Theorem 0.14s 5.68s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 66 ( 29 unt; 0 def)
% Number of atoms : 186 ( 81 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 201 ( 81 ~; 60 |; 60 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 1 con; 0-2 aty)
% Number of variables : 179 ( 23 sgn 42 !; 40 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_1,axiom,
? [Y24] :
! [X19] :
( ( X19 = Y24
& r1(X19) )
| ( X19 != Y24
& ~ r1(X19) ) ),
file('theBenchmark.p',axiom_1) ).
fof(axiom_2,axiom,
! [X11] :
? [Y21] :
! [X12] :
( ( X12 = Y21
& r2(X11,X12) )
| ( X12 != Y21
& ~ r2(X11,X12) ) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3,axiom,
! [X13,X14] :
? [Y22] :
! [X15] :
( ( X15 = Y22
& r3(X13,X14,X15) )
| ( X15 != Y22
& ~ r3(X13,X14,X15) ) ),
file('theBenchmark.p',axiom_3) ).
fof(axiom_1a,axiom,
! [X1,X8] :
? [Y4] :
( ? [Y7] :
( r3(X1,X8,Y7)
& r2(Y7,Y4) )
& ? [Y5] :
( Y5 = Y4
& ? [Y15] :
( r3(X1,Y15,Y5)
& r2(X8,Y15) ) ) ),
file('theBenchmark.p',axiom_1a) ).
fof(axiom_4a,axiom,
! [X4] :
? [Y9] :
( Y9 = X4
& ? [Y16] :
( r3(X4,Y16,Y9)
& r1(Y16) ) ),
file('theBenchmark.p',axiom_4a) ).
fof(axiom_5a,axiom,
! [X5] :
? [Y8] :
( ? [Y18] :
( Y8 = Y18
& r1(Y18) )
& ? [Y17] :
( r4(X5,Y17,Y8)
& r1(Y17) ) ),
file('theBenchmark.p',axiom_5a) ).
fof(thereexistsanevennumber,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('theBenchmark.p',thereexistsanevennumber) ).
fof(thereexistsanevennumber_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(assume_negation,[status(cth)],[thereexistsanevennumber]) ).
fof(nnf_1,plain,
? [Y24] :
! [X19] :
( ( Y24 = X19
& r1(X19) )
| ( Y24 != X19
& ~ r1(X19) ) ),
inference(fof_nnf,[status(thm)],[axiom_1]) ).
fof(sk_axiom_1_sk,plain,
! [X19] :
( ( sK0 = X19
& r1(X19) )
| ( sK0 != X19
& ~ r1(X19) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(Y24,sK0)],[nnf_1]) ).
fof(sk_axiom_1,plain,
( ! [VAR_0] :
( r1(VAR_0)
| sK0 != VAR_0 )
& ! [VAR_0] :
( sK0 = VAR_0
| ~ r1(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_1_sk]) ).
cnf(c_14,plain,
( sK0 = A
| ~ r1(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_1]) ).
fof(nnf_8,plain,
! [X4] :
? [Y9] :
( Y9 = X4
& ? [Y16] :
( r3(X4,Y16,Y9)
& r1(Y16) ) ),
inference(fof_nnf,[status(thm)],[axiom_4a]) ).
fof(sk_axiom_4a,plain,
! [X4] :
( sK4(X4) = X4
& r3(X4,sK1(X4),sK4(X4))
& r1(sK1(X4)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK4]),skolemize(Y9,sK4(X4)),skolemize(Y16,sK1(X4))],[nnf_8]) ).
cnf(c_15,plain,
r1(sK1(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
fof(nnf_9,plain,
! [X5] :
? [Y8] :
( ? [Y18] :
( Y18 = Y8
& r1(Y18) )
& ? [Y17] :
( r4(X5,Y17,Y8)
& r1(Y17) ) ),
inference(fof_nnf,[status(thm)],[axiom_5a]) ).
fof(sk_axiom_5a,plain,
! [X5] :
( sK3(X5) = sK8(X5)
& r1(sK3(X5))
& r4(X5,sK2(X5),sK8(X5))
& r1(sK2(X5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK8,sK3]),skolemize(Y8,sK8(X5)),skolemize(Y17,sK2(X5)),skolemize(Y18,sK3(X5))],[nnf_9]) ).
cnf(c_16,plain,
r1(sK2(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_17,plain,
r1(sK3(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_21,negated_conjecture,
( A != V7
| ~ r3(D,V6,V7)
| ~ r2(F,E)
| ~ r1(F)
| ~ r2(E,C)
| ~ r4(C,D,B)
| A != B ),
inference(clausify,[status(thm)],[thereexistsanevennumber_neg]) ).
cnf(c_22,plain,
r3(A,sK1(A),sK4(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
cnf(c_25,negated_conjecture,
( A != V7
| ~ r3(D,V6,V7)
| ~ r2(sK3(F),E)
| ~ r2(E,C)
| ~ r4(C,D,B)
| A != B ),
inference(resolve,[status(thm)],[c_21,c_17]) ).
fof(nnf_5,plain,
! [X1,X8] :
? [Y4] :
( ? [Y7] :
( r3(X1,X8,Y7)
& r2(Y7,Y4) )
& ? [Y5] :
( Y4 = Y5
& ? [Y15] :
( r3(X1,Y15,Y5)
& r2(X8,Y15) ) ) ),
inference(fof_nnf,[status(thm)],[axiom_1a]) ).
fof(sk_axiom_1a,plain,
! [X1,X8] :
( r3(X1,X8,sK5(X1,X8))
& r2(sK5(X1,X8),sK11(X1,X8))
& sK11(X1,X8) = sK10(X1,X8)
& r3(X1,sK9(X1,X8),sK10(X1,X8))
& r2(X8,sK9(X1,X8)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK5]),skolemize(Y4,sK11(X1,X8)),skolemize(Y5,sK10(X1,X8)),skolemize(Y15,sK9(X1,X8)),skolemize(Y7,sK5(X1,X8))],[nnf_5]) ).
cnf(c_30,plain,
r3(A,B,sK5(A,B)),
inference(split_conjunct,[status(thm)],[sk_axiom_1a]) ).
fof(nnf_3,plain,
! [X13,X14] :
? [Y22] :
! [X15] :
( ( Y22 = X15
& r3(X13,X14,X15) )
| ( Y22 != X15
& ~ r3(X13,X14,X15) ) ),
inference(fof_nnf,[status(thm)],[axiom_3]) ).
fof(sk_axiom_3_sk,plain,
! [X13,X14,X15] :
( ( sK6(X13,X14) = X15
& r3(X13,X14,X15) )
| ( sK6(X13,X14) != X15
& ~ r3(X13,X14,X15) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(Y22,sK6(X13,X14))],[nnf_3]) ).
fof(sk_axiom_3,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( r3(VAR_0,VAR_1,VAR_2)
| sK6(VAR_0,VAR_1) != VAR_2 )
& ! [VAR_0,VAR_1,VAR_2] :
( sK6(VAR_0,VAR_1) = VAR_2
| ~ r3(VAR_0,VAR_1,VAR_2) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_3_sk]) ).
cnf(c_32,plain,
( r3(A,B,C)
| sK6(A,B) != C ),
inference(split_conjunct,[status(thm)],[sk_axiom_3]) ).
cnf(c_33,plain,
( sK6(A,B) = C
| ~ r3(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_axiom_3]) ).
cnf(c_34,plain,
sK6(A,sK1(A)) = sK4(A),
inference(resolve,[status(thm)],[c_33,c_22]) ).
cnf(c_35,plain,
sK4(A) = sK6(A,sK1(A)),
inference(copy,[status(thm)],[c_34]) ).
cnf(c_38,plain,
sK6(A,B) = sK5(A,B),
inference(resolve,[status(thm)],[c_33,c_30]) ).
cnf(c_47,negated_conjecture,
( D != C
| ~ r2(sK3(V7),V6)
| ~ r2(V6,F)
| ~ r4(F,A,E)
| D != E
| sK6(A,B) != C ),
inference(resolve,[status(thm)],[c_32,c_25]) ).
cnf(c_48,negated_conjecture,
( D != C
| ~ r2(sK3(V7),V6)
| ~ r2(V6,F)
| ~ r4(F,A,E)
| D != E
| sK5(A,B) != C ),
inference(paramod,[status(thm)],[c_38,c_47]) ).
fof(nnf_2,plain,
! [X11] :
? [Y21] :
! [X12] :
( ( Y21 = X12
& r2(X11,X12) )
| ( Y21 != X12
& ~ r2(X11,X12) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X11,X12] :
( ( sK7(X11) = X12
& r2(X11,X12) )
| ( sK7(X11) != X12
& ~ r2(X11,X12) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(Y21,sK7(X11))],[nnf_2]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1] :
( r2(VAR_0,VAR_1)
| sK7(VAR_0) != VAR_1 )
& ! [VAR_0,VAR_1] :
( sK7(VAR_0) = VAR_1
| ~ r2(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_90,plain,
( r2(A,B)
| sK7(A) != B ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_104,plain,
sK4(A) = A,
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
cnf(c_263,plain,
sK6(A,sK1(A)) = A,
inference(paramod,[status(thm)],[c_35,c_104]) ).
cnf(c_105,plain,
sK5(A,sK1(A)) = A,
inference(paramod,[status(thm)],[c_38,c_263]) ).
cnf(c_106,plain,
r4(A,sK2(A),sK8(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_107,plain,
sK3(A) = sK8(A),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_112,plain,
sK0 = sK1(A),
inference(resolve,[status(thm)],[c_15,c_14]) ).
cnf(c_113,plain,
sK1(A) = sK0,
inference(copy,[status(thm)],[c_112]) ).
cnf(c_114,plain,
sK0 = sK2(A),
inference(resolve,[status(thm)],[c_16,c_14]) ).
cnf(c_115,plain,
sK2(A) = sK0,
inference(copy,[status(thm)],[c_114]) ).
cnf(c_116,plain,
sK0 = sK3(A),
inference(resolve,[status(thm)],[c_17,c_14]) ).
cnf(c_264,plain,
sK0 = sK8(A),
inference(paramod,[status(thm)],[c_107,c_116]) ).
cnf(c_117,plain,
sK8(A) = sK0,
inference(copy,[status(thm)],[c_264]) ).
cnf(c_265,plain,
sK4(A) = sK6(A,sK0),
inference(paramod,[status(thm)],[c_113,c_35]) ).
cnf(c_132,plain,
sK4(A) = sK5(A,sK0),
inference(paramod,[status(thm)],[c_38,c_265]) ).
cnf(c_266,negated_conjecture,
( D != C
| ~ r2(sK8(V7),V6)
| ~ r2(V6,F)
| ~ r4(F,A,E)
| D != E
| sK5(A,B) != C ),
inference(paramod,[status(thm)],[c_107,c_48]) ).
cnf(c_159,negated_conjecture,
( D != C
| ~ r2(sK0,V6)
| ~ r2(V6,F)
| ~ r4(F,A,E)
| D != E
| sK5(A,B) != C ),
inference(paramod,[status(thm)],[c_117,c_266]) ).
cnf(c_160,plain,
sK5(A,sK0) = A,
inference(paramod,[status(thm)],[c_113,c_105]) ).
cnf(c_267,plain,
r4(A,sK0,sK8(A)),
inference(paramod,[status(thm)],[c_115,c_106]) ).
cnf(c_161,plain,
r4(A,sK0,sK0),
inference(paramod,[status(thm)],[c_117,c_267]) ).
cnf(c_170,plain,
sK4(A) = A,
inference(paramod,[status(thm)],[c_160,c_132]) ).
cnf(c_171,plain,
r2(A,sK7(A)),
inference(xxres,[status(thm)],[c_90]) ).
cnf(c_268,negated_conjecture,
( A != D
| ~ r2(sK0,E)
| ~ r2(E,C)
| ~ r4(C,D,B)
| A != B ),
inference(resolve,[status(thm)],[c_159,c_160]) ).
cnf(c_269,negated_conjecture,
( sK4(C) != B
| ~ r2(sK0,D)
| ~ r2(D,A)
| ~ r4(A,B,C) ),
inference(resolve,[status(thm)],[c_268,c_170]) ).
cnf(c_270,negated_conjecture,
( sK4(sK0) != sK0
| ~ r2(sK0,A)
| ~ r2(A,B) ),
inference(resolve,[status(thm)],[c_269,c_161]) ).
cnf(c_271,negated_conjecture,
( sK4(sK0) != sK0
| ~ r2(sK0,A) ),
inference(resolve,[status(thm)],[c_270,c_171]) ).
cnf(c_272,negated_conjecture,
sK4(sK0) != sK0,
inference(resolve,[status(thm)],[c_271,c_171]) ).
cnf(c_262,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_272,c_170]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN076+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.58 % Computer : n010.cluster.edu
% 0.09/5.58 % Model : x86_64 x86_64
% 0.09/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.58 % Memory : 8046.5625MB
% 0.09/5.58 % OS : Linux 6.8.0-71-generic
% 0.09/5.58 % CPULimit : 300
% 0.09/5.58 % WCLimit : 300
% 0.09/5.58 % DateTime : Sat Sep 26 04:30:59 UTC 2026
% 0.09/5.58 % CPUTime :
% 0.09/5.59 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.59 % Process 2487388 was started by sandbox on n010,
% 0.09/5.59 % Sat Sep 26 04:30:59 2026
% 0.09/5.59 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/5.59
% 0.09/5.59 % From the command line: assign(max_seconds, 300).
% 0.14/5.68
% 0.14/5.68 % SZS status Theorem for theBenchmark
% 0.14/5.68
% 0.14/5.68 % Proof 1 at 0.07 (+ 0.01) seconds.
% 0.14/5.68 % Length of proof is 40.
% 0.14/5.68 % Level of proof is 7.
% 0.14/5.68 % Maximum clause weight is 32.000.
% 0.14/5.68 % Given clauses 56.
% 0.14/5.68
% 0.14/5.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------