%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUN055+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 : n016.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 08:19:18 AM UTC 2026
% Result : Theorem 3.08s 0.88s
% Output : CNFRefutation 3.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 54 ( 24 unt; 0 def)
% Number of atoms : 168 ( 47 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 199 ( 85 ~; 66 |; 48 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 156 ( 9 sgn 29 !; 32 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_1,axiom,
? [Y24] :
! [X19] :
( ( X19 = Y24
& r1(X19) )
| ( X19 != Y24
& ~ r1(X19) ) ),
file('theBenchmark.p',axiom_1) ).
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(zeroplustwoeqtwo,conjecture,
? [Y1] :
( ? [Y3] :
( ? [Y5] :
( ? [Y8] :
( r2(Y8,Y5)
& r1(Y8) )
& r2(Y5,Y3) )
& Y1 = Y3 )
& ? [Y2] :
( ? [Y7] :
( r3(Y7,Y2,Y1)
& r1(Y7) )
& ? [Y4] :
( ? [Y6] :
( r2(Y6,Y4)
& r1(Y6) )
& r2(Y4,Y2) ) ) ),
file('theBenchmark.p',zeroplustwoeqtwo) ).
fof(zeroplustwoeqtwo_neg,negated_conjecture,
~ ? [Y1] :
( ? [Y3] :
( ? [Y5] :
( ? [Y8] :
( r2(Y8,Y5)
& r1(Y8) )
& r2(Y5,Y3) )
& Y1 = Y3 )
& ? [Y2] :
( ? [Y7] :
( r3(Y7,Y2,Y1)
& r1(Y7) )
& ? [Y4] :
( ? [Y6] :
( r2(Y6,Y4)
& r1(Y6) )
& r2(Y4,Y2) ) ) ),
inference(assume_negation,[status(cth)],[zeroplustwoeqtwo]) ).
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] :
( ( sK0(X13,X14) = X15
& r3(X13,X14,X15) )
| ( sK0(X13,X14) != X15
& ~ r3(X13,X14,X15) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(Y22,sK0(X13,X14))],[nnf_3]) ).
fof(sk_axiom_3,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( r3(VAR_0,VAR_1,VAR_2)
| sK0(VAR_0,VAR_1) != VAR_2 )
& ! [VAR_0,VAR_1,VAR_2] :
( sK0(VAR_0,VAR_1) = VAR_2
| ~ r3(VAR_0,VAR_1,VAR_2) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_3_sk]) ).
cnf(c_13,plain,
( r3(A,B,C)
| sK0(A,B) != C ),
inference(split_conjunct,[status(thm)],[sk_axiom_3]) ).
cnf(c_14,plain,
( sK0(A,B) = C
| ~ r3(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_axiom_3]) ).
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,sK3(X1,X8))
& r2(sK3(X1,X8),sK7(X1,X8))
& sK7(X1,X8) = sK2(X1,X8)
& r3(X1,sK1(X1,X8),sK2(X1,X8))
& r2(X8,sK1(X1,X8)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK7,sK3]),skolemize(Y4,sK7(X1,X8)),skolemize(Y5,sK2(X1,X8)),skolemize(Y15,sK1(X1,X8)),skolemize(Y7,sK3(X1,X8))],[nnf_5]) ).
cnf(c_15,plain,
r3(A,sK1(A,B),sK2(A,B)),
inference(split_conjunct,[status(thm)],[sk_axiom_1a]) ).
cnf(c_16,plain,
r3(A,B,sK3(A,B)),
inference(split_conjunct,[status(thm)],[sk_axiom_1a]) ).
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] :
( sK5(X4) = X4
& r3(X4,sK4(X4),sK5(X4))
& r1(sK4(X4)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(Y9,sK5(X4)),skolemize(Y16,sK4(X4))],[nnf_8]) ).
cnf(c_18,plain,
r3(A,sK4(A),sK5(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
cnf(c_19,negated_conjecture,
( ~ r2(V7,V6)
| ~ r1(V7)
| ~ r2(V6,F)
| E != F
| ~ r3(D,B,E)
| ~ r1(D)
| ~ r2(C,A)
| ~ r1(C)
| ~ r2(A,B) ),
inference(clausify,[status(thm)],[zeroplustwoeqtwo_neg]) ).
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_30,plain,
( sK6 = A
| ~ r1(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_1]) ).
cnf(c_31,plain,
( r1(A)
| sK6 != A ),
inference(split_conjunct,[status(thm)],[sk_axiom_1]) ).
cnf(c_34,plain,
r2(A,sK1(B,A)),
inference(split_conjunct,[status(thm)],[sk_axiom_1a]) ).
cnf(c_35,plain,
sK7(A,B) = sK2(A,B),
inference(split_conjunct,[status(thm)],[sk_axiom_1a]) ).
cnf(c_36,plain,
r2(sK3(A,B),sK7(A,B)),
inference(split_conjunct,[status(thm)],[sk_axiom_1a]) ).
cnf(c_37,plain,
r2(sK3(A,B),sK2(A,B)),
inference(paramod,[status(thm)],[c_35,c_36]) ).
cnf(c_42,plain,
r1(sK4(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
cnf(c_43,plain,
sK5(A) = A,
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
cnf(c_55,plain,
sK0(A,sK1(A,B)) = sK2(A,B),
inference(resolve,[status(thm)],[c_15,c_14]) ).
cnf(c_56,plain,
sK2(A,B) = sK0(A,sK1(A,B)),
inference(copy,[status(thm)],[c_55]) ).
cnf(c_57,plain,
sK0(A,B) = sK3(A,B),
inference(resolve,[status(thm)],[c_16,c_14]) ).
cnf(c_60,plain,
sK0(A,sK4(A)) = sK5(A),
inference(resolve,[status(thm)],[c_18,c_14]) ).
cnf(c_975,plain,
sK3(A,sK4(A)) = sK5(A),
inference(paramod,[status(thm)],[c_57,c_60]) ).
cnf(c_61,plain,
sK3(A,sK4(A)) = A,
inference(paramod,[status(thm)],[c_43,c_975]) ).
cnf(c_68,negated_conjecture,
( sK0(D,B) != E
| ~ r2(V7,V6)
| ~ r1(V7)
| ~ r2(V6,F)
| E != F
| ~ r1(D)
| ~ r2(C,A)
| ~ r1(C)
| ~ r2(A,B) ),
inference(resolve,[status(thm)],[c_19,c_13]) ).
cnf(c_69,negated_conjecture,
( sK3(D,B) != E
| ~ r2(V7,V6)
| ~ r1(V7)
| ~ r2(V6,F)
| E != F
| ~ r1(D)
| ~ r2(C,A)
| ~ r1(C)
| ~ r2(A,B) ),
inference(paramod,[status(thm)],[c_57,c_68]) ).
cnf(c_976,plain,
r2(sK3(A,B),sK0(A,sK1(A,B))),
inference(paramod,[status(thm)],[c_56,c_37]) ).
cnf(c_72,plain,
r2(sK3(A,B),sK3(A,sK1(A,B))),
inference(paramod,[status(thm)],[c_57,c_976]) ).
cnf(c_106,plain,
( sK3(C,B) != D
| ~ r2(V6,F)
| ~ r1(V6)
| ~ r2(F,E)
| D != E
| ~ r2(C,A)
| ~ r1(C)
| ~ r2(A,B) ),
inference(factor,[status(thm)],[c_69]) ).
cnf(c_977,plain,
( ~ r2(E,D)
| ~ r1(E)
| ~ r2(D,sK3(C,B))
| sK3(C,B) != sK3(C,B)
| ~ r2(C,A)
| ~ r1(C)
| ~ r2(A,B) ),
inference(factor,[status(thm)],[c_106]) ).
cnf(c_185,plain,
( ~ r2(E,D)
| ~ r1(E)
| ~ r2(D,sK3(C,B))
| ~ r2(C,A)
| ~ r1(C)
| ~ r2(A,B) ),
inference(copy,[status(thm)],[c_977]) ).
cnf(c_260,plain,
r1(sK6),
inference(xxres,[status(thm)],[c_31]) ).
cnf(c_978,plain,
sK6 = sK4(A),
inference(resolve,[status(thm)],[c_42,c_30]) ).
cnf(c_270,plain,
sK4(A) = sK6,
inference(copy,[status(thm)],[c_978]) ).
cnf(c_293,plain,
sK3(A,sK6) = A,
inference(paramod,[status(thm)],[c_270,c_61]) ).
cnf(c_979,plain,
( ~ r2(E,C)
| ~ r1(E)
| ~ r2(C,sK3(A,sK1(D,B)))
| ~ r2(A,B)
| ~ r1(A) ),
inference(resolve,[status(thm)],[c_185,c_34]) ).
cnf(c_980,plain,
( ~ r2(D,B)
| ~ r1(D)
| ~ r2(B,sK3(sK6,sK1(C,A)))
| ~ r2(sK6,A) ),
inference(resolve,[status(thm)],[c_979,c_260]) ).
cnf(c_981,plain,
( ~ r2(D,A)
| ~ r1(D)
| ~ r2(A,sK3(sK6,sK1(B,sK1(C,sK6)))) ),
inference(resolve,[status(thm)],[c_980,c_34]) ).
cnf(c_982,plain,
( ~ r2(A,sK3(sK6,sK1(B,sK6)))
| ~ r1(A) ),
inference(resolve,[status(thm)],[c_981,c_72]) ).
cnf(c_983,plain,
~ r1(sK3(sK6,sK6)),
inference(resolve,[status(thm)],[c_982,c_72]) ).
cnf(c_984,plain,
~ r1(sK6),
inference(paramod,[status(thm)],[c_293,c_983]) ).
cnf(c_974,plain,
$false,
inference(resolve,[status(thm)],[c_260,c_984]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUN055+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.40 % Computer : n016.cluster.edu
% 0.16/0.40 % Model : x86_64 x86_64
% 0.16/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.40 % Memory : 8046.5625MB
% 0.16/0.40 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sat Sep 26 04:32:44 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.41 % Process 4180112 was started by sandbox on n016,
% 0.16/0.41 % Sat Sep 26 04:32:44 2026
% 0.16/0.41 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.42
% 0.16/0.42 % From the command line: assign(max_seconds, 300).
% 3.08/0.88
% 3.08/0.88 % SZS status Theorem for theBenchmark
% 3.08/0.88
% 3.08/0.88 % Proof 1 at 0.35 (+ 0.09) seconds.
% 3.08/0.88 % Length of proof is 33.
% 3.08/0.88 % Level of proof is 6.
% 3.08/0.88 % Maximum clause weight is 30.000.
% 3.08/0.88 % Given clauses 49.
% 3.08/0.88
% 3.08/0.88 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------