%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUN059+2 : TPTP v9.3.1. Bugfixed v7.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 08:19:19 AM UTC 2026
% Result : Theorem 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 54 ( 25 unt; 0 def)
% Number of atoms : 136 ( 51 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 130 ( 48 ~; 33 |; 49 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 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 : 138 ( 11 sgn 32 !; 36 ?)
% 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(axiom_5a,axiom,
! [X5] :
? [Y8] :
( ? [Y18] :
( Y8 = Y18
& r1(Y18) )
& ? [Y17] :
( r4(X5,Y17,Y8)
& r1(Y17) ) ),
file('theBenchmark.p',axiom_5a) ).
fof(fermattothepoweroftwo,conjecture,
? [Y1,Y3,Y2,Y4] :
( ? [Y6] :
( ? [Y7] :
( r3(Y7,Y6,Y4)
& r4(Y1,Y1,Y7) )
& r4(Y3,Y3,Y6) )
& ? [Y5] :
( Y4 = Y5
& r4(Y2,Y2,Y5) ) ),
file('theBenchmark.p',fermattothepoweroftwo) ).
fof(fermattothepoweroftwo_neg,negated_conjecture,
~ ? [Y1,Y3,Y2,Y4] :
( ? [Y6] :
( ? [Y7] :
( r3(Y7,Y6,Y4)
& r4(Y1,Y1,Y7) )
& r4(Y3,Y3,Y6) )
& ? [Y5] :
( Y4 = Y5
& r4(Y2,Y2,Y5) ) ),
inference(assume_negation,[status(cth)],[fermattothepoweroftwo]) ).
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_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] :
( sK4(X4) = X4
& r3(X4,sK1(X4),sK4(X4))
& r1(sK1(X4)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK4]),skolemize(Y9,sK4(X4)),skolemize(Y16,sK1(X4))],[nnf_8]) ).
cnf(c_15,plain,
r1(sK1(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] :
( sK3(X5) = sK7(X5)
& r1(sK3(X5))
& r4(X5,sK2(X5),sK7(X5))
& r1(sK2(X5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK7,sK3]),skolemize(Y8,sK7(X5)),skolemize(Y17,sK2(X5)),skolemize(Y18,sK3(X5))],[nnf_9]) ).
cnf(c_16,plain,
r1(sK2(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_17,plain,
r1(sK3(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_21,plain,
r3(A,sK1(A),sK4(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
cnf(c_22,negated_conjecture,
( ~ r3(V6,E,C)
| ~ r4(F,F,V6)
| ~ r4(D,D,E)
| C != B
| ~ r4(A,A,B) ),
inference(clausify,[status(thm)],[fermattothepoweroftwo_neg]) ).
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,sK5(X1,X8))
& r2(sK5(X1,X8),sK10(X1,X8))
& sK10(X1,X8) = sK9(X1,X8)
& r3(X1,sK8(X1,X8),sK9(X1,X8))
& r2(X8,sK8(X1,X8)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK5]),skolemize(Y4,sK10(X1,X8)),skolemize(Y5,sK9(X1,X8)),skolemize(Y15,sK8(X1,X8)),skolemize(Y7,sK5(X1,X8))],[nnf_5]) ).
cnf(c_24,plain,
r3(A,B,sK5(A,B)),
inference(split_conjunct,[status(thm)],[sk_axiom_1a]) ).
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] :
( ( sK6(X13,X14) = X15
& r3(X13,X14,X15) )
| ( sK6(X13,X14) != X15
& ~ r3(X13,X14,X15) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(Y22,sK6(X13,X14))],[nnf_3]) ).
fof(sk_axiom_3,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( r3(VAR_0,VAR_1,VAR_2)
| sK6(VAR_0,VAR_1) != VAR_2 )
& ! [VAR_0,VAR_1,VAR_2] :
( sK6(VAR_0,VAR_1) = VAR_2
| ~ r3(VAR_0,VAR_1,VAR_2) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_3_sk]) ).
cnf(c_26,plain,
( r3(A,B,C)
| sK6(A,B) != C ),
inference(split_conjunct,[status(thm)],[sk_axiom_3]) ).
cnf(c_27,plain,
( sK6(A,B) = C
| ~ r3(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_axiom_3]) ).
cnf(c_28,plain,
sK6(A,sK1(A)) = sK4(A),
inference(resolve,[status(thm)],[c_27,c_21]) ).
cnf(c_29,plain,
sK4(A) = sK6(A,sK1(A)),
inference(copy,[status(thm)],[c_28]) ).
cnf(c_32,plain,
sK6(A,B) = sK5(A,B),
inference(resolve,[status(thm)],[c_27,c_24]) ).
cnf(c_35,negated_conjecture,
( ~ r4(V6,V6,A)
| ~ r4(F,F,B)
| C != E
| ~ r4(D,D,E)
| sK6(A,B) != C ),
inference(resolve,[status(thm)],[c_26,c_22]) ).
cnf(c_36,negated_conjecture,
( ~ r4(V6,V6,A)
| ~ r4(F,F,B)
| C != E
| ~ r4(D,D,E)
| sK5(A,B) != C ),
inference(paramod,[status(thm)],[c_32,c_35]) ).
cnf(c_57,plain,
sK4(A) = A,
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
cnf(c_175,plain,
sK6(A,sK1(A)) = A,
inference(paramod,[status(thm)],[c_29,c_57]) ).
cnf(c_58,plain,
sK5(A,sK1(A)) = A,
inference(paramod,[status(thm)],[c_32,c_175]) ).
cnf(c_59,plain,
r4(A,sK2(A),sK7(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_60,plain,
sK3(A) = sK7(A),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_65,plain,
sK0 = sK1(A),
inference(resolve,[status(thm)],[c_15,c_14]) ).
cnf(c_66,plain,
sK1(A) = sK0,
inference(copy,[status(thm)],[c_65]) ).
cnf(c_67,plain,
sK0 = sK2(A),
inference(resolve,[status(thm)],[c_16,c_14]) ).
cnf(c_68,plain,
sK2(A) = sK0,
inference(copy,[status(thm)],[c_67]) ).
cnf(c_69,plain,
sK0 = sK3(A),
inference(resolve,[status(thm)],[c_17,c_14]) ).
cnf(c_176,plain,
sK0 = sK7(A),
inference(paramod,[status(thm)],[c_60,c_69]) ).
cnf(c_70,plain,
sK7(A) = sK0,
inference(copy,[status(thm)],[c_176]) ).
cnf(c_177,plain,
( ~ r4(E,E,A)
| ~ r4(D,D,B)
| ~ r4(C,C,sK5(A,B))
| sK5(A,B) != sK5(A,B) ),
inference(factor,[status(thm)],[c_36]) ).
cnf(c_86,plain,
( ~ r4(E,E,B)
| ~ r4(D,D,C)
| ~ r4(A,A,sK5(B,C)) ),
inference(copy,[status(thm)],[c_177]) ).
cnf(c_95,plain,
sK5(A,sK0) = A,
inference(paramod,[status(thm)],[c_66,c_58]) ).
cnf(c_178,plain,
r4(A,sK0,sK7(A)),
inference(paramod,[status(thm)],[c_68,c_59]) ).
cnf(c_96,plain,
r4(A,sK0,sK0),
inference(paramod,[status(thm)],[c_70,c_178]) ).
cnf(c_170,plain,
( ~ r4(D,D,B)
| ~ r4(C,C,sK0)
| ~ r4(A,A,B) ),
inference(paramod,[status(thm)],[c_95,c_86]) ).
cnf(c_171,plain,
( ~ r4(B,B,sK0)
| ~ r4(A,A,sK0) ),
inference(factor,[status(thm)],[c_170]) ).
cnf(c_173,plain,
~ r4(A,A,sK0),
inference(factor,[status(thm)],[c_171]) ).
cnf(c_174,plain,
$false,
inference(resolve,[status(thm)],[c_173,c_96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN059+2 : TPTP v9.3.1. Bugfixed v7.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.36 % Computer : n003.cluster.edu
% 0.07/0.36 % Model : x86_64 x86_64
% 0.07/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.36 % Memory : 8046.5625MB
% 0.07/0.36 % OS : Linux 6.8.0-71-generic
% 0.07/0.36 % CPULimit : 300
% 0.07/0.36 % WCLimit : 300
% 0.07/0.36 % DateTime : Sat Sep 26 04:30:09 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.07/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.36 % Process 2030093 was started by sandbox2 on n003,
% 0.07/0.36 % Sat Sep 26 04:30:09 2026
% 0.07/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.07/0.37
% 0.07/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.41
% 0.13/0.41 % SZS status Theorem for theBenchmark
% 0.13/0.41
% 0.13/0.41 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.13/0.41 % Length of proof is 37.
% 0.13/0.41 % Level of proof is 9.
% 0.13/0.41 % Maximum clause weight is 20.000.
% 0.13/0.41 % Given clauses 35.
% 0.13/0.41
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------