%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUN056+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 : n002.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 19.25s 2.84s
% Output : CNFRefutation 19.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 60 ( 25 unt; 0 def)
% Number of atoms : 213 ( 48 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 263 ( 110 ~; 89 |; 64 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 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 : 198 ( 7 sgn 35 !; 44 ?)
% 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_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(oneplustwoeqthree,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('theBenchmark.p',oneplustwoeqthree) ).
fof(oneplustwoeqthree_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(assume_negation,[status(cth)],[oneplustwoeqthree]) ).
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(V9,V8)
| ~ r1(V9)
| ~ r2(V8,V6)
| ~ r2(V7,F)
| ~ r1(V7)
| ~ r3(F,V6,A)
| ~ r2(E,D)
| ~ r1(E)
| ~ r2(D,C)
| ~ r2(C,B)
| A != B ),
inference(clausify,[status(thm)],[oneplustwoeqthree_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]) ).
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,sK11(X2,X9))
& r3(sK11(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,sK11]),skolemize(Y2,sK10(X2,X9)),skolemize(Y3,sK9(X2,X9)),skolemize(Y14,sK8(X2,X9)),skolemize(Y6,sK11(X2,X9))],[nnf_6]) ).
cnf(c_38,plain,
r2(A,sK8(B,A)),
inference(split_conjunct,[status(thm)],[sk_axiom_2a]) ).
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_3029,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_3029]) ).
cnf(c_68,negated_conjecture,
( sK0(V6,V8) != A
| ~ r2(V9,V7)
| ~ r1(V9)
| ~ r2(V7,V8)
| ~ r2(F,V6)
| ~ r1(F)
| ~ r2(E,D)
| ~ r1(E)
| ~ r2(D,C)
| ~ r2(C,B)
| A != B ),
inference(resolve,[status(thm)],[c_19,c_13]) ).
cnf(c_69,negated_conjecture,
( sK3(V6,V8) != A
| ~ r2(V9,V7)
| ~ r1(V9)
| ~ r2(V7,V8)
| ~ r2(F,V6)
| ~ r1(F)
| ~ r2(E,D)
| ~ r1(E)
| ~ r2(D,C)
| ~ r2(C,B)
| A != B ),
inference(paramod,[status(thm)],[c_57,c_68]) ).
cnf(c_3030,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_3030]) ).
cnf(c_3031,plain,
( ~ r2(V7,V6)
| ~ r1(V7)
| ~ r2(V6,B)
| ~ r2(F,A)
| ~ r1(F)
| ~ r2(E,D)
| ~ r1(E)
| ~ r2(D,C)
| ~ r2(C,sK3(A,B))
| sK3(A,B) != sK3(A,B) ),
inference(factor,[status(thm)],[c_69]) ).
cnf(c_129,plain,
( ~ r2(V7,V6)
| ~ r1(V7)
| ~ r2(V6,C)
| ~ r2(F,B)
| ~ r1(F)
| ~ r2(E,D)
| ~ r1(E)
| ~ r2(D,A)
| ~ r2(A,sK3(B,C)) ),
inference(copy,[status(thm)],[c_3031]) ).
cnf(c_403,plain,
( ~ r2(V6,F)
| ~ r1(V6)
| ~ r2(F,C)
| ~ r2(E,B)
| ~ r2(E,D)
| ~ r1(E)
| ~ r2(D,A)
| ~ r2(A,sK3(B,C)) ),
inference(factor,[status(thm)],[c_129]) ).
cnf(c_869,plain,
( ~ r2(E,F)
| ~ r2(F,C)
| ~ r2(E,B)
| ~ r2(E,D)
| ~ r1(E)
| ~ r2(D,A)
| ~ r2(A,sK3(B,C)) ),
inference(factor,[status(thm)],[c_403]) ).
cnf(c_1239,plain,
r1(sK6),
inference(xxres,[status(thm)],[c_31]) ).
cnf(c_3032,plain,
sK6 = sK4(A),
inference(resolve,[status(thm)],[c_42,c_30]) ).
cnf(c_1249,plain,
sK4(A) = sK6,
inference(copy,[status(thm)],[c_3032]) ).
cnf(c_1317,plain,
sK3(A,sK6) = A,
inference(paramod,[status(thm)],[c_1249,c_61]) ).
cnf(c_3033,plain,
( ~ r2(D,E)
| ~ r2(E,sK1(B,C))
| ~ r2(D,B)
| ~ r2(D,A)
| ~ r1(D)
| ~ r2(A,sK3(B,C)) ),
inference(resolve,[status(thm)],[c_869,c_72]) ).
cnf(c_3034,plain,
( ~ r2(A,D)
| ~ r2(D,sK1(B,sK1(B,C)))
| ~ r2(A,B)
| ~ r2(A,sK3(B,C))
| ~ r1(A) ),
inference(resolve,[status(thm)],[c_3033,c_72]) ).
cnf(c_3035,plain,
( ~ r2(sK6,C)
| ~ r2(C,sK1(A,sK1(A,B)))
| ~ r2(sK6,A)
| ~ r2(sK6,sK3(A,B)) ),
inference(resolve,[status(thm)],[c_3034,c_1239]) ).
cnf(c_3036,plain,
( ~ r2(sK6,C)
| ~ r2(C,sK1(sK8(A,sK6),sK1(sK8(A,sK6),B)))
| ~ r2(sK6,sK3(sK8(A,sK6),B)) ),
inference(resolve,[status(thm)],[c_3035,c_38]) ).
cnf(c_3037,plain,
( ~ r2(sK6,sK1(sK8(A,sK6),B))
| ~ r2(sK6,sK3(sK8(A,sK6),B)) ),
inference(resolve,[status(thm)],[c_3036,c_34]) ).
cnf(c_3038,plain,
~ r2(sK6,sK3(sK8(A,sK6),sK6)),
inference(resolve,[status(thm)],[c_3037,c_34]) ).
cnf(c_3039,plain,
~ r2(sK6,sK8(A,sK6)),
inference(paramod,[status(thm)],[c_1317,c_3038]) ).
cnf(c_3028,plain,
$false,
inference(resolve,[status(thm)],[c_38,c_3039]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN056+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n002.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 26 04:30:35 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 826016 was started by sandbox on n002,
% 0.07/0.35 % Sat Sep 26 04:30:35 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/0.35
% 0.07/0.35 % From the command line: assign(max_seconds, 300).
% 19.25/2.84
% 19.25/2.84 % SZS status Theorem for theBenchmark
% 19.25/2.84
% 19.25/2.84 % Proof 1 at 2.05 (+ 0.37) seconds.
% 19.25/2.84 % Length of proof is 36.
% 19.25/2.84 % Level of proof is 7.
% 19.25/2.84 % Maximum clause weight is 36.000.
% 19.25/2.84 % Given clauses 132.
% 19.25/2.84
% 19.25/2.84 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------