%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUN087+2 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 08:19:25 AM UTC 2026
% Result : Theorem 0.18s 0.47s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 50 ( 26 unt; 0 def)
% Number of atoms : 115 ( 51 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 100 ( 35 ~; 18 |; 47 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 1 con; 0-2 aty)
% Number of variables : 101 ( 15 sgn 32 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_1,axiom,
? [Y24] :
! [X19] :
( ( X19 = Y24
& r1(X19) )
| ( X19 != Y24
& ~ r1(X19) ) ),
file('theBenchmark.p',axiom_1) ).
fof(axiom_4,axiom,
! [X16,X17] :
? [Y23] :
! [X18] :
( ( X18 = Y23
& r4(X16,X17,X18) )
| ( X18 != Y23
& ~ r4(X16,X17,X18) ) ),
file('theBenchmark.p',axiom_4) ).
fof(axiom_2a,axiom,
! [X2,X9] :
? [Y2] :
( ? [Y6] :
( r4(X2,X9,Y6)
& r3(Y6,X2,Y2) )
& ? [Y3] :
( Y3 = Y2
& ? [Y14] :
( r4(X2,Y14,Y3)
& r2(X9,Y14) ) ) ),
file('theBenchmark.p',axiom_2a) ).
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(zerotimeszeroeqzero,conjecture,
? [Y1] :
( ? [Y3] :
( Y1 = Y3
& r1(Y3) )
& ? [Y2] :
( r4(Y2,Y2,Y1)
& r1(Y2) ) ),
file('theBenchmark.p',zerotimeszeroeqzero) ).
fof(zerotimeszeroeqzero_neg,negated_conjecture,
~ ? [Y1] :
( ? [Y3] :
( Y1 = Y3
& r1(Y3) )
& ? [Y2] :
( r4(Y2,Y2,Y1)
& r1(Y2) ) ),
inference(assume_negation,[status(cth)],[zerotimeszeroeqzero]) ).
cnf(c_26,negated_conjecture,
( B != C
| ~ r1(C)
| ~ r4(A,A,B)
| ~ r1(A) ),
inference(clausify,[status(thm)],[zerotimeszeroeqzero_neg]) ).
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] :
( sK0(X5) = sK1(X5)
& r1(sK0(X5))
& r4(X5,sK2(X5),sK1(X5))
& r1(sK2(X5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK1,sK0]),skolemize(Y8,sK1(X5)),skolemize(Y17,sK2(X5)),skolemize(Y18,sK0(X5))],[nnf_9]) ).
cnf(c_34,plain,
sK0(A) = sK1(A),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_35,plain,
r1(sK0(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_36,plain,
r1(sK1(A)),
inference(paramod,[status(thm)],[c_34,c_35]) ).
cnf(c_37,plain,
r4(A,sK2(A),sK1(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_38,plain,
r1(sK2(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
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] :
( sK7(X4) = X4
& r3(X4,sK3(X4),sK7(X4))
& r1(sK3(X4)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK7]),skolemize(Y9,sK7(X4)),skolemize(Y16,sK3(X4))],[nnf_8]) ).
cnf(c_41,plain,
r1(sK3(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
fof(nnf_6,plain,
! [X2,X9] :
? [Y2] :
( ? [Y6] :
( r4(X2,X9,Y6)
& r3(Y6,X2,Y2) )
& ? [Y3] :
( Y2 = Y3
& ? [Y14] :
( r4(X2,Y14,Y3)
& r2(X9,Y14) ) ) ),
inference(fof_nnf,[status(thm)],[axiom_2a]) ).
fof(sk_axiom_2a,plain,
! [X2,X9] :
( r4(X2,X9,sK4(X2,X9))
& r3(sK4(X2,X9),X2,sK10(X2,X9))
& sK10(X2,X9) = sK9(X2,X9)
& r4(X2,sK8(X2,X9),sK9(X2,X9))
& r2(X9,sK8(X2,X9)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK4]),skolemize(Y2,sK10(X2,X9)),skolemize(Y3,sK9(X2,X9)),skolemize(Y14,sK8(X2,X9)),skolemize(Y6,sK4(X2,X9))],[nnf_6]) ).
cnf(c_43,plain,
r4(A,B,sK4(A,B)),
inference(split_conjunct,[status(thm)],[sk_axiom_2a]) ).
fof(nnf_4,plain,
! [X16,X17] :
? [Y23] :
! [X18] :
( ( Y23 = X18
& r4(X16,X17,X18) )
| ( Y23 != X18
& ~ r4(X16,X17,X18) ) ),
inference(fof_nnf,[status(thm)],[axiom_4]) ).
fof(sk_axiom_4_sk,plain,
! [X16,X17,X18] :
( ( sK5(X16,X17) = X18
& r4(X16,X17,X18) )
| ( sK5(X16,X17) != X18
& ~ r4(X16,X17,X18) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(Y23,sK5(X16,X17))],[nnf_4]) ).
fof(sk_axiom_4,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( r4(VAR_0,VAR_1,VAR_2)
| sK5(VAR_0,VAR_1) != VAR_2 )
& ! [VAR_0,VAR_1,VAR_2] :
( sK5(VAR_0,VAR_1) = VAR_2
| ~ r4(VAR_0,VAR_1,VAR_2) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_4_sk]) ).
cnf(c_53,plain,
( sK5(A,B) = C
| ~ r4(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_axiom_4]) ).
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] :
( ( sK6 = X19
& r1(X19) )
| ( sK6 != X19
& ~ r1(X19) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(Y24,sK6)],[nnf_1]) ).
fof(sk_axiom_1,plain,
( ! [VAR_0] :
( r1(VAR_0)
| sK6 != VAR_0 )
& ! [VAR_0] :
( sK6 = VAR_0
| ~ r1(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_1_sk]) ).
cnf(c_57,plain,
( sK6 = A
| ~ r1(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_1]) ).
cnf(c_151,negated_conjecture,
( B != C
| ~ r1(C)
| ~ r4(sK3(A),sK3(A),B) ),
inference(resolve,[status(thm)],[c_26,c_41]) ).
cnf(c_152,negated_conjecture,
( sK4(sK3(B),sK3(B)) != A
| ~ r1(A) ),
inference(resolve,[status(thm)],[c_151,c_43]) ).
cnf(c_153,negated_conjecture,
sK4(sK3(A),sK3(A)) != sK3(B),
inference(resolve,[status(thm)],[c_152,c_41]) ).
cnf(c_83,negated_conjecture,
sK3(A) != sK4(sK3(B),sK3(B)),
inference(copy,[status(thm)],[c_153]) ).
cnf(c_154,plain,
sK5(A,B) = sK4(A,B),
inference(resolve,[status(thm)],[c_53,c_43]) ).
cnf(c_110,plain,
sK4(A,B) = sK5(A,B),
inference(copy,[status(thm)],[c_154]) ).
cnf(c_111,plain,
sK5(A,sK2(A)) = sK1(A),
inference(resolve,[status(thm)],[c_53,c_37]) ).
cnf(c_121,negated_conjecture,
sK3(A) != sK5(sK3(B),sK3(B)),
inference(paramod,[status(thm)],[c_110,c_83]) ).
cnf(c_155,plain,
sK6 = sK3(A),
inference(resolve,[status(thm)],[c_57,c_41]) ).
cnf(c_138,plain,
sK3(A) = sK6,
inference(copy,[status(thm)],[c_155]) ).
cnf(c_156,plain,
sK6 = sK2(A),
inference(resolve,[status(thm)],[c_57,c_38]) ).
cnf(c_139,plain,
sK2(A) = sK6,
inference(copy,[status(thm)],[c_156]) ).
cnf(c_157,plain,
sK6 = sK1(A),
inference(resolve,[status(thm)],[c_57,c_36]) ).
cnf(c_140,plain,
sK1(A) = sK6,
inference(copy,[status(thm)],[c_157]) ).
cnf(c_158,negated_conjecture,
sK6 != sK5(sK3(B),sK3(B)),
inference(paramod,[status(thm)],[c_138,c_121]) ).
cnf(c_159,negated_conjecture,
sK6 != sK5(sK6,sK3(B)),
inference(paramod,[status(thm)],[c_138,c_158]) ).
cnf(c_160,negated_conjecture,
sK6 != sK5(sK6,sK6),
inference(paramod,[status(thm)],[c_138,c_159]) ).
cnf(c_143,negated_conjecture,
sK5(sK6,sK6) != sK6,
inference(copy,[status(thm)],[c_160]) ).
cnf(c_161,plain,
sK5(A,sK6) = sK1(A),
inference(paramod,[status(thm)],[c_139,c_111]) ).
cnf(c_149,plain,
sK5(A,sK6) = sK6,
inference(paramod,[status(thm)],[c_140,c_161]) ).
cnf(c_150,plain,
$false,
inference(resolve,[status(thm)],[c_149,c_143]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUN087+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n026.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sat Sep 26 04:35:10 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.43 % Process 76348 was started by sandbox2 on n026,
% 0.18/0.43 % Sat Sep 26 04:35:10 2026
% 0.18/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.44
% 0.18/0.44 % From the command line: assign(max_seconds, 300).
% 0.18/0.47
% 0.18/0.47 % SZS status Theorem for theBenchmark
% 0.18/0.47
% 0.18/0.47 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.18/0.47 % Length of proof is 26.
% 0.18/0.47 % Level of proof is 5.
% 0.18/0.47 % Maximum clause weight is 11.000.
% 0.18/0.47 % Given clauses 27.
% 0.18/0.47
% 0.18/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------