%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUN080+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 : n005.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 08:19:23 AM UTC 2026
% Result : Theorem 0.15s 0.45s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 51 ( 18 unt; 0 def)
% Number of atoms : 141 ( 54 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 142 ( 52 ~; 34 |; 56 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 142 ( 20 sgn 42 !; 36 ?)
% 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_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(xplustwoeqy,conjecture,
? [Y1,Y2,Y3] :
( ? [Y4] :
( ? [Y5] :
( ? [Y6] :
( r2(Y6,Y5)
& r1(Y6) )
& r2(Y5,Y4) )
& r3(Y1,Y4,Y3) )
& Y3 = Y2 ),
file('theBenchmark.p',xplustwoeqy) ).
fof(xplustwoeqy_neg,negated_conjecture,
~ ? [Y1,Y2,Y3] :
( ? [Y4] :
( ? [Y5] :
( ? [Y6] :
( r2(Y6,Y5)
& r1(Y6) )
& r2(Y5,Y4) )
& r3(Y1,Y4,Y3) )
& Y3 = Y2 ),
inference(assume_negation,[status(cth)],[xplustwoeqy]) ).
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_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] :
( sK1(X5) = sK10(X5)
& r1(sK1(X5))
& r4(X5,sK9(X5),sK10(X5))
& r1(sK9(X5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK1]),skolemize(Y8,sK10(X5)),skolemize(Y17,sK9(X5)),skolemize(Y18,sK1(X5))],[nnf_9]) ).
cnf(c_17,plain,
r1(sK1(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_21,negated_conjecture,
( ~ r2(F,E)
| ~ r1(F)
| ~ r2(E,D)
| ~ r3(C,D,B)
| A != B ),
inference(clausify,[status(thm)],[xplustwoeqy_neg]) ).
cnf(c_25,negated_conjecture,
( ~ r2(sK1(F),E)
| ~ r2(E,D)
| ~ r3(C,D,B)
| A != B ),
inference(resolve,[status(thm)],[c_21,c_17]) ).
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) = sK6(X2,X9)
& r4(X2,sK5(X2,X9),sK6(X2,X9))
& r2(X9,sK5(X2,X9)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK3,sK2]),skolemize(Y2,sK3(X2,X9)),skolemize(Y3,sK6(X2,X9)),skolemize(Y14,sK5(X2,X9)),skolemize(Y6,sK2(X2,X9))],[nnf_6]) ).
cnf(c_29,plain,
r3(sK2(A,B),A,sK3(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] :
( ( sK4(X16,X17) = X18
& r4(X16,X17,X18) )
| ( sK4(X16,X17) != X18
& ~ r4(X16,X17,X18) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(Y23,sK4(X16,X17))],[nnf_4]) ).
fof(sk_axiom_4,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( r4(VAR_0,VAR_1,VAR_2)
| sK4(VAR_0,VAR_1) != VAR_2 )
& ! [VAR_0,VAR_1,VAR_2] :
( sK4(VAR_0,VAR_1) = VAR_2
| ~ r4(VAR_0,VAR_1,VAR_2) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_4_sk]) ).
cnf(c_35,plain,
( sK4(A,B) = C
| ~ r4(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_axiom_4]) ).
cnf(c_36,plain,
r4(A,sK5(A,B),sK6(A,B)),
inference(split_conjunct,[status(thm)],[sk_axiom_2a]) ).
cnf(c_37,plain,
r4(A,B,sK2(A,B)),
inference(split_conjunct,[status(thm)],[sk_axiom_2a]) ).
cnf(c_41,plain,
sK4(A,B) = sK2(A,B),
inference(resolve,[status(thm)],[c_37,c_35]) ).
cnf(c_42,plain,
sK4(A,sK5(A,B)) = sK6(A,B),
inference(resolve,[status(thm)],[c_36,c_35]) ).
cnf(c_221,plain,
sK2(A,sK5(A,B)) = sK6(A,B),
inference(paramod,[status(thm)],[c_41,c_42]) ).
cnf(c_43,plain,
sK6(A,B) = sK2(A,sK5(A,B)),
inference(copy,[status(thm)],[c_221]) ).
cnf(c_59,plain,
sK0 = sK1(A),
inference(resolve,[status(thm)],[c_17,c_14]) ).
cnf(c_60,plain,
sK1(A) = sK0,
inference(copy,[status(thm)],[c_59]) ).
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,sK11(X4),sK7(X4))
& r1(sK11(X4)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK7]),skolemize(Y9,sK7(X4)),skolemize(Y16,sK11(X4))],[nnf_8]) ).
cnf(c_71,plain,
sK7(A) = A,
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
cnf(c_73,plain,
sK3(A,B) = sK6(A,B),
inference(split_conjunct,[status(thm)],[sk_axiom_2a]) ).
cnf(c_74,plain,
sK3(A,B) = sK2(A,sK5(A,B)),
inference(paramod,[status(thm)],[c_43,c_73]) ).
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] :
( ( sK8(X11) = X12
& r2(X11,X12) )
| ( sK8(X11) != X12
& ~ r2(X11,X12) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(Y21,sK8(X11))],[nnf_2]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1] :
( r2(VAR_0,VAR_1)
| sK8(VAR_0) != VAR_1 )
& ! [VAR_0,VAR_1] :
( sK8(VAR_0) = VAR_1
| ~ r2(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_79,plain,
( r2(A,B)
| sK8(A) != B ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_95,negated_conjecture,
( ~ r2(sK1(E),D)
| ~ r2(D,B)
| A != sK3(B,C) ),
inference(resolve,[status(thm)],[c_29,c_25]) ).
cnf(c_222,negated_conjecture,
( ~ r2(sK1(E),D)
| ~ r2(D,B)
| A != sK2(B,sK5(B,C)) ),
inference(paramod,[status(thm)],[c_74,c_95]) ).
cnf(c_223,negated_conjecture,
( ~ r2(sK0,D)
| ~ r2(D,B)
| A != sK2(B,sK5(B,C)) ),
inference(paramod,[status(thm)],[c_60,c_222]) ).
cnf(c_224,negated_conjecture,
( ~ r2(sK0,D)
| ~ r2(D,B)
| sK2(B,sK5(B,C)) != A ),
inference(copy,[status(thm)],[c_223]) ).
cnf(c_96,negated_conjecture,
( ~ r2(sK0,A)
| ~ r2(A,B) ),
inference(copy,[status(thm)],[c_224]) ).
cnf(c_225,plain,
A = sK7(A),
inference(copy,[status(thm)],[c_71]) ).
cnf(c_226,plain,
r2(A,sK7(sK8(A))),
inference(resolve,[status(thm)],[c_79,c_225]) ).
cnf(c_177,plain,
r2(A,sK8(A)),
inference(paramod,[status(thm)],[c_71,c_226]) ).
cnf(c_219,plain,
~ r2(sK8(sK0),A),
inference(resolve,[status(thm)],[c_177,c_96]) ).
cnf(c_220,plain,
$false,
inference(resolve,[status(thm)],[c_219,c_177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUN080+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n005.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat Sep 26 04:30:48 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.42 % Process 1201984 was started by sandbox2 on n005,
% 0.15/0.42 % Sat Sep 26 04:30:48 2026
% 0.15/0.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.43
% 0.15/0.43 % From the command line: assign(max_seconds, 300).
% 0.15/0.45
% 0.15/0.45 % SZS status Theorem for theBenchmark
% 0.15/0.45
% 0.15/0.45 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.15/0.45 % Length of proof is 29.
% 0.15/0.45 % Level of proof is 7.
% 0.15/0.45 % Maximum clause weight is 24.000.
% 0.15/0.45 % Given clauses 33.
% 0.15/0.45
% 0.15/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------