%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUN082+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 : n007.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 08:19:24 AM UTC 2026
% Result : Theorem 0.11s 0.42s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 79 ( 44 unt; 0 def)
% Number of atoms : 180 ( 78 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 154 ( 53 ~; 33 |; 68 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 1 con; 0-2 aty)
% Number of variables : 186 ( 16 sgn 53 !; 42 ?)
% 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_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_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(axiom_5a,axiom,
! [X5] :
? [Y8] :
( ? [Y18] :
( Y8 = Y18
& r1(Y18) )
& ? [Y17] :
( r4(X5,Y17,Y8)
& r1(Y17) ) ),
file('theBenchmark.p',axiom_5a) ).
fof(xtimesoneeqzero,conjecture,
? [Y1,Y2] :
( ? [Y5] :
( Y2 = Y5
& r1(Y5) )
& ? [Y3] :
( ? [Y4] :
( r2(Y4,Y3)
& r1(Y4) )
& r4(Y1,Y3,Y2) ) ),
file('theBenchmark.p',xtimesoneeqzero) ).
fof(xtimesoneeqzero_neg,negated_conjecture,
~ ? [Y1,Y2] :
( ? [Y5] :
( Y2 = Y5
& r1(Y5) )
& ? [Y3] :
( ? [Y4] :
( r2(Y4,Y3)
& r1(Y4) )
& r4(Y1,Y3,Y2) ) ),
inference(assume_negation,[status(cth)],[xtimesoneeqzero]) ).
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_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,sK1(X1,X8))
& r2(sK1(X1,X8),sK15(X1,X8))
& sK15(X1,X8) = sK14(X1,X8)
& r3(X1,sK13(X1,X8),sK14(X1,X8))
& r2(X8,sK13(X1,X8)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK1]),skolemize(Y4,sK15(X1,X8)),skolemize(Y5,sK14(X1,X8)),skolemize(Y15,sK13(X1,X8)),skolemize(Y7,sK1(X1,X8))],[nnf_5]) ).
cnf(c_16,plain,
r3(A,B,sK1(A,B)),
inference(split_conjunct,[status(thm)],[sk_axiom_1a]) ).
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,sK2(X2,X9))
& r3(sK2(X2,X9),X2,sK3(X2,X9))
& sK3(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,sK3,sK2]),skolemize(Y2,sK3(X2,X9)),skolemize(Y3,sK9(X2,X9)),skolemize(Y14,sK8(X2,X9)),skolemize(Y6,sK2(X2,X9))],[nnf_6]) ).
cnf(c_17,plain,
r3(sK2(A,B),A,sK3(A,B)),
inference(split_conjunct,[status(thm)],[sk_axiom_2a]) ).
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]) ).
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] :
( sK12(X5) = sK7(X5)
& r1(sK12(X5))
& r4(X5,sK6(X5),sK7(X5))
& r1(sK6(X5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK12]),skolemize(Y8,sK7(X5)),skolemize(Y17,sK6(X5)),skolemize(Y18,sK12(X5))],[nnf_9]) ).
cnf(c_19,plain,
r4(A,sK6(A),sK7(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_20,negated_conjecture,
( C != E
| ~ r1(E)
| ~ r2(D,B)
| ~ r1(D)
| ~ r4(A,B,C) ),
inference(clausify,[status(thm)],[xtimesoneeqzero_neg]) ).
cnf(c_21,plain,
r4(A,B,sK2(A,B)),
inference(split_conjunct,[status(thm)],[sk_axiom_2a]) ).
cnf(c_22,plain,
r4(A,sK8(A,B),sK9(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] :
( ( sK10(X16,X17) = X18
& r4(X16,X17,X18) )
| ( sK10(X16,X17) != X18
& ~ r4(X16,X17,X18) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(Y23,sK10(X16,X17))],[nnf_4]) ).
fof(sk_axiom_4,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( r4(VAR_0,VAR_1,VAR_2)
| sK10(VAR_0,VAR_1) != VAR_2 )
& ! [VAR_0,VAR_1,VAR_2] :
( sK10(VAR_0,VAR_1) = VAR_2
| ~ r4(VAR_0,VAR_1,VAR_2) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_4_sk]) ).
cnf(c_24,plain,
( sK10(A,B) = C
| ~ r4(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_axiom_4]) ).
cnf(c_25,plain,
sK10(A,sK6(A)) = sK7(A),
inference(resolve,[status(thm)],[c_24,c_19]) ).
cnf(c_26,plain,
sK7(A) = sK10(A,sK6(A)),
inference(copy,[status(thm)],[c_25]) ).
cnf(c_27,plain,
sK10(A,B) = sK2(A,B),
inference(resolve,[status(thm)],[c_24,c_21]) ).
cnf(c_28,plain,
sK10(A,sK8(A,B)) = sK9(A,B),
inference(resolve,[status(thm)],[c_24,c_22]) ).
cnf(c_180,plain,
sK2(A,sK8(A,B)) = sK9(A,B),
inference(paramod,[status(thm)],[c_27,c_28]) ).
cnf(c_29,plain,
sK9(A,B) = sK2(A,sK8(A,B)),
inference(copy,[status(thm)],[c_180]) ).
cnf(c_32,negated_conjecture,
( sK9(B,C) != D
| ~ r1(D)
| ~ r2(A,sK8(B,C))
| ~ r1(A) ),
inference(resolve,[status(thm)],[c_22,c_20]) ).
cnf(c_33,negated_conjecture,
( sK2(B,sK8(B,C)) != D
| ~ r1(D)
| ~ r2(A,sK8(B,C))
| ~ r1(A) ),
inference(paramod,[status(thm)],[c_29,c_32]) ).
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] :
( ( sK11 = X19
& r1(X19) )
| ( sK11 != X19
& ~ r1(X19) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(Y24,sK11)],[nnf_1]) ).
fof(sk_axiom_1,plain,
( ! [VAR_0] :
( r1(VAR_0)
| sK11 != VAR_0 )
& ! [VAR_0] :
( sK11 = VAR_0
| ~ r1(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_1_sk]) ).
cnf(c_36,plain,
( sK11 = A
| ~ r1(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_1]) ).
cnf(c_44,plain,
r2(A,sK8(B,A)),
inference(split_conjunct,[status(thm)],[sk_axiom_2a]) ).
cnf(c_45,plain,
sK3(A,B) = sK9(A,B),
inference(split_conjunct,[status(thm)],[sk_axiom_2a]) ).
cnf(c_46,plain,
sK3(A,B) = sK2(A,sK8(A,B)),
inference(paramod,[status(thm)],[c_29,c_45]) ).
cnf(c_48,plain,
r1(sK4(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
cnf(c_49,plain,
sK5(A) = A,
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
cnf(c_50,plain,
r1(sK6(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_51,plain,
r1(sK12(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_52,plain,
sK12(A) = sK7(A),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_181,plain,
sK12(A) = sK10(A,sK6(A)),
inference(paramod,[status(thm)],[c_26,c_52]) ).
cnf(c_53,plain,
sK12(A) = sK2(A,sK6(A)),
inference(paramod,[status(thm)],[c_27,c_181]) ).
cnf(c_63,plain,
sK0(A,B) = sK1(A,B),
inference(resolve,[status(thm)],[c_16,c_14]) ).
cnf(c_64,plain,
sK0(sK2(A,B),A) = sK3(A,B),
inference(resolve,[status(thm)],[c_17,c_14]) ).
cnf(c_182,plain,
sK1(sK2(A,B),A) = sK3(A,B),
inference(paramod,[status(thm)],[c_63,c_64]) ).
cnf(c_183,plain,
sK1(sK2(A,B),A) = sK2(A,sK8(A,B)),
inference(paramod,[status(thm)],[c_46,c_182]) ).
cnf(c_65,plain,
sK2(A,sK8(A,B)) = sK1(sK2(A,B),A),
inference(copy,[status(thm)],[c_183]) ).
cnf(c_66,plain,
sK0(A,sK4(A)) = sK5(A),
inference(resolve,[status(thm)],[c_18,c_14]) ).
cnf(c_184,plain,
sK1(A,sK4(A)) = sK5(A),
inference(paramod,[status(thm)],[c_63,c_66]) ).
cnf(c_67,plain,
sK1(A,sK4(A)) = A,
inference(paramod,[status(thm)],[c_49,c_184]) ).
cnf(c_185,plain,
( sK2(B,sK8(B,C)) != A
| ~ r2(A,sK8(B,C))
| ~ r1(A) ),
inference(factor,[status(thm)],[c_33]) ).
cnf(c_71,plain,
( sK1(sK2(B,C),B) != A
| ~ r2(A,sK8(B,C))
| ~ r1(A) ),
inference(paramod,[status(thm)],[c_65,c_185]) ).
cnf(c_73,plain,
r1(sK2(A,sK6(A))),
inference(paramod,[status(thm)],[c_53,c_51]) ).
cnf(c_186,plain,
sK11 = sK4(A),
inference(resolve,[status(thm)],[c_48,c_36]) ).
cnf(c_98,plain,
sK4(A) = sK11,
inference(copy,[status(thm)],[c_186]) ).
cnf(c_103,plain,
sK1(A,sK11) = A,
inference(paramod,[status(thm)],[c_98,c_67]) ).
cnf(c_187,plain,
sK11 = sK6(A),
inference(resolve,[status(thm)],[c_50,c_36]) ).
cnf(c_104,plain,
sK6(A) = sK11,
inference(copy,[status(thm)],[c_187]) ).
cnf(c_105,plain,
r1(sK2(A,sK11)),
inference(paramod,[status(thm)],[c_104,c_73]) ).
cnf(c_188,plain,
sK11 = sK2(A,sK11),
inference(resolve,[status(thm)],[c_105,c_36]) ).
cnf(c_177,plain,
sK2(A,sK11) = sK11,
inference(copy,[status(thm)],[c_188]) ).
cnf(c_189,plain,
( sK1(sK2(B,C),B) != sK2(A,sK11)
| ~ r2(sK2(A,sK11),sK8(B,C)) ),
inference(resolve,[status(thm)],[c_71,c_105]) ).
cnf(c_190,plain,
sK1(sK2(A,sK2(B,sK11)),A) != sK2(B,sK11),
inference(resolve,[status(thm)],[c_189,c_44]) ).
cnf(c_191,plain,
sK1(sK2(A,sK11),A) != sK2(B,sK11),
inference(paramod,[status(thm)],[c_177,c_190]) ).
cnf(c_192,plain,
sK1(sK11,A) != sK2(B,sK11),
inference(paramod,[status(thm)],[c_177,c_191]) ).
cnf(c_178,plain,
sK1(sK11,A) != sK11,
inference(paramod,[status(thm)],[c_177,c_192]) ).
cnf(c_179,plain,
$false,
inference(resolve,[status(thm)],[c_178,c_103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN082+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n007.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 04:29:38 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 2787640 was started by sandbox on n007,
% 0.11/0.38 % Sat Sep 26 04:29:38 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 0.11/0.42
% 0.11/0.42 % SZS status Theorem for theBenchmark
% 0.11/0.42
% 0.11/0.42 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.11/0.42 % Length of proof is 48.
% 0.11/0.42 % Level of proof is 9.
% 0.11/0.42 % Maximum clause weight is 16.000.
% 0.11/0.42 % Given clauses 39.
% 0.11/0.42
% 0.11/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------