%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUN060+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 : n020.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 0.53s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 57 ( 19 unt; 0 def)
% Number of atoms : 180 ( 57 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 194 ( 71 ~; 51 |; 72 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 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 : 187 ( 29 sgn 48 !; 48 ?)
% 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_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(greq4,conjecture,
? [Y1,Y2,Y3] :
( ? [Y4] :
( ? [Y5] :
( ? [Y6] :
( ? [Y7] :
( ? [Y8] :
( r2(Y8,Y7)
& r1(Y8) )
& r2(Y7,Y6) )
& r2(Y6,Y5) )
& r2(Y5,Y4) )
& r3(Y2,Y4,Y3) )
& Y3 = Y1 ),
file('theBenchmark.p',greq4) ).
fof(greq4_neg,negated_conjecture,
~ ? [Y1,Y2,Y3] :
( ? [Y4] :
( ? [Y5] :
( ? [Y6] :
( ? [Y7] :
( ? [Y8] :
( r2(Y8,Y7)
& r1(Y8) )
& r2(Y7,Y6) )
& r2(Y6,Y5) )
& r2(Y5,Y4) )
& r3(Y2,Y4,Y3) )
& Y3 = Y1 ),
inference(assume_negation,[status(cth)],[greq4]) ).
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) = sK11(X5)
& r1(sK1(X5))
& r4(X5,sK10(X5),sK11(X5))
& r1(sK10(X5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK1]),skolemize(Y8,sK11(X5)),skolemize(Y17,sK10(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(V7,V6)
| ~ r1(V7)
| ~ r2(V6,F)
| ~ r2(F,E)
| ~ r2(E,D)
| ~ r3(C,D,B)
| A != B ),
inference(clausify,[status(thm)],[greq4_neg]) ).
cnf(c_25,negated_conjecture,
( ~ r2(sK1(V7),V6)
| ~ r2(V6,F)
| ~ r2(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_252,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_252]) ).
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,sK12(X4),sK7(X4))
& r1(sK12(X4)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK7]),skolemize(Y9,sK7(X4)),skolemize(Y16,sK12(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_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,sK15(X1,X8))
& r2(sK15(X1,X8),sK14(X1,X8))
& sK14(X1,X8) = sK13(X1,X8)
& r3(X1,sK8(X1,X8),sK13(X1,X8))
& r2(X8,sK8(X1,X8)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK13,sK14,sK15]),skolemize(Y4,sK14(X1,X8)),skolemize(Y5,sK13(X1,X8)),skolemize(Y15,sK8(X1,X8)),skolemize(Y7,sK15(X1,X8))],[nnf_5]) ).
cnf(c_78,plain,
r2(A,sK8(B,A)),
inference(split_conjunct,[status(thm)],[sk_axiom_1a]) ).
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] :
( ( sK9(X11) = X12
& r2(X11,X12) )
| ( sK9(X11) != X12
& ~ r2(X11,X12) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(Y21,sK9(X11))],[nnf_2]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1] :
( r2(VAR_0,VAR_1)
| sK9(VAR_0) != VAR_1 )
& ! [VAR_0,VAR_1] :
( sK9(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)
| sK9(A) != B ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_95,negated_conjecture,
( ~ r2(sK1(V6),F)
| ~ r2(F,E)
| ~ r2(E,D)
| ~ r2(D,B)
| A != sK3(B,C) ),
inference(resolve,[status(thm)],[c_29,c_25]) ).
cnf(c_253,negated_conjecture,
( ~ r2(sK1(V6),F)
| ~ r2(F,E)
| ~ r2(E,D)
| ~ r2(D,B)
| A != sK2(B,sK5(B,C)) ),
inference(paramod,[status(thm)],[c_74,c_95]) ).
cnf(c_254,negated_conjecture,
( ~ r2(sK0,F)
| ~ r2(F,E)
| ~ r2(E,D)
| ~ r2(D,B)
| A != sK2(B,sK5(B,C)) ),
inference(paramod,[status(thm)],[c_60,c_253]) ).
cnf(c_255,negated_conjecture,
( ~ r2(sK0,F)
| ~ r2(F,E)
| ~ r2(E,D)
| ~ r2(D,B)
| sK2(B,sK5(B,C)) != A ),
inference(copy,[status(thm)],[c_254]) ).
cnf(c_96,negated_conjecture,
( ~ r2(sK0,D)
| ~ r2(D,C)
| ~ r2(C,A)
| ~ r2(A,B) ),
inference(copy,[status(thm)],[c_255]) ).
cnf(c_256,plain,
A = sK7(A),
inference(copy,[status(thm)],[c_71]) ).
cnf(c_257,plain,
r2(A,sK7(sK9(A))),
inference(resolve,[status(thm)],[c_79,c_256]) ).
cnf(c_174,plain,
r2(A,sK9(A)),
inference(paramod,[status(thm)],[c_71,c_257]) ).
cnf(c_258,negated_conjecture,
( ~ r2(sK0,D)
| ~ r2(D,B)
| ~ r2(sK8(A,B),C) ),
inference(resolve,[status(thm)],[c_96,c_78]) ).
cnf(c_259,negated_conjecture,
( ~ r2(sK0,C)
| ~ r2(sK8(A,sK8(B,C)),D) ),
inference(resolve,[status(thm)],[c_258,c_78]) ).
cnf(c_250,negated_conjecture,
~ r2(sK8(A,sK8(B,sK8(C,sK0))),D),
inference(resolve,[status(thm)],[c_259,c_78]) ).
cnf(c_251,plain,
$false,
inference(resolve,[status(thm)],[c_250,c_174]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUN060+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.42 % Computer : n020.cluster.edu
% 0.10/0.42 % Model : x86_64 x86_64
% 0.10/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.42 % Memory : 8046.5625MB
% 0.10/0.42 % OS : Linux 6.8.0-71-generic
% 0.10/0.43 % CPULimit : 300
% 0.10/0.43 % WCLimit : 300
% 0.10/0.43 % DateTime : Sat Sep 26 04:29:03 UTC 2026
% 0.10/0.43 % CPUTime :
% 0.10/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.44 % Process 613973 was started by sandbox on n020,
% 0.10/0.44 % Sat Sep 26 04:29:03 2026
% 0.10/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.44
% 0.10/0.44 % From the command line: assign(max_seconds, 300).
% 0.13/0.53
% 0.13/0.53 % SZS status Theorem for theBenchmark
% 0.13/0.53
% 0.13/0.53 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.13/0.53 % Length of proof is 31.
% 0.13/0.53 % Level of proof is 7.
% 0.13/0.53 % Maximum clause weight is 12.000.
% 0.13/0.53 % Given clauses 21.
% 0.13/0.53
% 0.13/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------