%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUN057+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 : n011.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 23.21s 3.33s
% Output : CNFRefutation 23.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 69 ( 35 unt; 0 def)
% Number of atoms : 191 ( 54 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 209 ( 87 ~; 65 |; 57 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 176 ( 6 sgn 39 !; 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_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(twoplustwoeqfour,conjecture,
? [Y1] :
( ? [Y5] :
( ? [Y7] :
( ? [Y9] :
( r2(Y9,Y7)
& r1(Y9) )
& r2(Y7,Y5) )
& r3(Y5,Y5,Y1) )
& ? [Y2] :
( ? [Y3] :
( ? [Y4] :
( ? [Y6] :
( ? [Y8] :
( r2(Y8,Y6)
& r1(Y8) )
& r2(Y6,Y4) )
& r2(Y4,Y3) )
& r2(Y3,Y2) )
& Y1 = Y2 ) ),
file('theBenchmark.p',twoplustwoeqfour) ).
fof(twoplustwoeqfour_neg,negated_conjecture,
~ ? [Y1] :
( ? [Y5] :
( ? [Y7] :
( ? [Y9] :
( r2(Y9,Y7)
& r1(Y9) )
& r2(Y7,Y5) )
& r3(Y5,Y5,Y1) )
& ? [Y2] :
( ? [Y3] :
( ? [Y4] :
( ? [Y6] :
( ? [Y8] :
( r2(Y8,Y6)
& r1(Y8) )
& r2(Y6,Y4) )
& r2(Y4,Y3) )
& r2(Y3,Y2) )
& Y1 = Y2 ) ),
inference(assume_negation,[status(cth)],[twoplustwoeqfour]) ).
cnf(c_23,negated_conjecture,
( ~ r2(V8,V7)
| ~ r1(V8)
| ~ r2(V7,V6)
| ~ r3(V6,V6,A)
| ~ r2(F,E)
| ~ r1(F)
| ~ r2(E,D)
| ~ r2(D,C)
| ~ r2(C,B)
| A != B ),
inference(clausify,[status(thm)],[twoplustwoeqfour_neg]) ).
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] :
( sK0(X4) = X4
& r3(X4,sK1(X4),sK0(X4))
& r1(sK1(X4)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0]),skolemize(Y9,sK0(X4)),skolemize(Y16,sK1(X4))],[nnf_8]) ).
cnf(c_36,plain,
sK0(A) = A,
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
cnf(c_37,plain,
r3(A,sK1(A),sK0(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
cnf(c_38,plain,
r3(A,sK1(A),A),
inference(paramod,[status(thm)],[c_36,c_37]) ).
cnf(c_39,plain,
r1(sK1(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
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,sK2(X1,X8))
& r2(sK2(X1,X8),sK3(X1,X8))
& sK3(X1,X8) = sK4(X1,X8)
& r3(X1,sK5(X1,X8),sK4(X1,X8))
& r2(X8,sK5(X1,X8)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK4,sK3,sK2]),skolemize(Y4,sK3(X1,X8)),skolemize(Y5,sK4(X1,X8)),skolemize(Y15,sK5(X1,X8)),skolemize(Y7,sK2(X1,X8))],[nnf_5]) ).
cnf(c_45,plain,
r3(A,B,sK2(A,B)),
inference(split_conjunct,[status(thm)],[sk_axiom_1a]) ).
cnf(c_46,plain,
r2(sK2(A,B),sK3(A,B)),
inference(split_conjunct,[status(thm)],[sk_axiom_1a]) ).
cnf(c_47,plain,
sK3(A,B) = sK4(A,B),
inference(split_conjunct,[status(thm)],[sk_axiom_1a]) ).
cnf(c_48,plain,
r3(A,sK5(A,B),sK4(A,B)),
inference(split_conjunct,[status(thm)],[sk_axiom_1a]) ).
cnf(c_49,plain,
r2(A,sK5(B,A)),
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_51,plain,
( sK6(A,B) = C
| ~ r3(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_axiom_3]) ).
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] :
( ( sK7(X11) = X12
& r2(X11,X12) )
| ( sK7(X11) != X12
& ~ r2(X11,X12) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(Y21,sK7(X11))],[nnf_2]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1] :
( r2(VAR_0,VAR_1)
| sK7(VAR_0) != VAR_1 )
& ! [VAR_0,VAR_1] :
( sK7(VAR_0) = VAR_1
| ~ r2(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_52,plain,
( r2(A,B)
| sK7(A) != B ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_53,plain,
( sK7(A) = B
| ~ r2(A,B) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
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] :
( ( sK8 = X19
& r1(X19) )
| ( sK8 != X19
& ~ r1(X19) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(Y24,sK8)],[nnf_1]) ).
fof(sk_axiom_1,plain,
( ! [VAR_0] :
( r1(VAR_0)
| sK8 != VAR_0 )
& ! [VAR_0] :
( sK8 = VAR_0
| ~ r1(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_1_sk]) ).
cnf(c_54,plain,
( r1(A)
| sK8 != A ),
inference(split_conjunct,[status(thm)],[sk_axiom_1]) ).
cnf(c_55,plain,
( sK8 = A
| ~ r1(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_1]) ).
cnf(c_74,plain,
r2(sK2(A,B),sK4(A,B)),
inference(paramod,[status(thm)],[c_47,c_46]) ).
cnf(c_183,plain,
( ~ r2(V7,V6)
| ~ r1(V7)
| ~ r2(V6,F)
| ~ r3(F,F,B)
| ~ r2(E,D)
| ~ r1(E)
| ~ r2(D,C)
| ~ r2(C,A)
| ~ r2(A,B) ),
inference(xxres,[status(thm)],[c_23]) ).
cnf(c_2681,plain,
sK6(A,sK5(A,B)) = sK4(A,B),
inference(resolve,[status(thm)],[c_51,c_48]) ).
cnf(c_4810,plain,
sK6(A,B) = sK2(A,B),
inference(resolve,[status(thm)],[c_51,c_45]) ).
cnf(c_2682,plain,
sK2(A,B) = sK6(A,B),
inference(copy,[status(thm)],[c_4810]) ).
cnf(c_2683,plain,
sK6(A,sK1(A)) = A,
inference(resolve,[status(thm)],[c_51,c_38]) ).
cnf(c_3577,plain,
r2(sK6(A,B),sK4(A,B)),
inference(paramod,[status(thm)],[c_2682,c_74]) ).
cnf(c_4811,plain,
A = sK0(A),
inference(copy,[status(thm)],[c_36]) ).
cnf(c_4812,plain,
r2(A,sK0(sK7(A))),
inference(resolve,[status(thm)],[c_52,c_4811]) ).
cnf(c_3578,plain,
r2(A,sK7(A)),
inference(paramod,[status(thm)],[c_36,c_4812]) ).
cnf(c_4813,plain,
sK7(A) = sK5(B,A),
inference(resolve,[status(thm)],[c_53,c_49]) ).
cnf(c_3580,plain,
sK5(A,B) = sK7(B),
inference(copy,[status(thm)],[c_4813]) ).
cnf(c_3602,plain,
sK6(A,sK7(B)) = sK4(A,B),
inference(paramod,[status(thm)],[c_3580,c_2681]) ).
cnf(c_3707,plain,
r3(A,sK7(B),sK4(A,B)),
inference(paramod,[status(thm)],[c_3580,c_48]) ).
cnf(c_4814,plain,
A = sK0(A),
inference(copy,[status(thm)],[c_36]) ).
cnf(c_4815,plain,
r1(sK0(sK8)),
inference(resolve,[status(thm)],[c_54,c_4814]) ).
cnf(c_3729,plain,
r1(sK8),
inference(paramod,[status(thm)],[c_36,c_4815]) ).
cnf(c_4816,plain,
sK8 = sK1(A),
inference(resolve,[status(thm)],[c_55,c_39]) ).
cnf(c_3731,plain,
sK1(A) = sK8,
inference(copy,[status(thm)],[c_4816]) ).
cnf(c_3739,plain,
sK6(A,sK8) = A,
inference(paramod,[status(thm)],[c_3731,c_2683]) ).
cnf(c_4519,plain,
r2(A,sK4(A,sK8)),
inference(paramod,[status(thm)],[c_3739,c_3577]) ).
cnf(c_4817,plain,
sK7(A) = sK4(A,sK8),
inference(resolve,[status(thm)],[c_4519,c_53]) ).
cnf(c_4774,plain,
sK4(A,sK8) = sK7(A),
inference(copy,[status(thm)],[c_4817]) ).
cnf(c_4818,plain,
( ~ r2(V7,V6)
| ~ r1(V7)
| ~ r2(V6,F)
| ~ r3(F,F,sK4(B,C))
| ~ r2(E,D)
| ~ r1(E)
| ~ r2(D,A)
| ~ r2(A,sK6(B,C)) ),
inference(resolve,[status(thm)],[c_183,c_3577]) ).
cnf(c_4819,plain,
( ~ r2(V6,F)
| ~ r1(V6)
| ~ r2(F,E)
| ~ r3(E,E,sK4(B,C))
| ~ r2(D,A)
| ~ r1(D)
| ~ r2(sK7(A),sK6(B,C)) ),
inference(resolve,[status(thm)],[c_4818,c_3578]) ).
cnf(c_4820,plain,
( ~ r2(F,E)
| ~ r1(F)
| ~ r2(E,D)
| ~ r3(D,D,sK4(B,C))
| ~ r2(sK8,A)
| ~ r2(sK7(A),sK6(B,C)) ),
inference(resolve,[status(thm)],[c_4819,c_3729]) ).
cnf(c_4821,plain,
( ~ r2(E,D)
| ~ r1(E)
| ~ r2(D,C)
| ~ r3(C,C,sK4(A,B))
| ~ r2(sK7(sK7(sK8)),sK6(A,B)) ),
inference(resolve,[status(thm)],[c_4820,c_3578]) ).
cnf(c_4822,plain,
( ~ r2(C,B)
| ~ r1(C)
| ~ r2(B,sK7(A))
| ~ r2(sK7(sK7(sK8)),sK6(sK7(A),A)) ),
inference(resolve,[status(thm)],[c_4821,c_3707]) ).
cnf(c_4823,plain,
( ~ r2(B,A)
| ~ r1(B)
| ~ r2(sK7(sK7(sK8)),sK6(sK7(A),A)) ),
inference(resolve,[status(thm)],[c_4822,c_3578]) ).
cnf(c_4824,plain,
( ~ r2(sK8,A)
| ~ r2(sK7(sK7(sK8)),sK6(sK7(A),A)) ),
inference(resolve,[status(thm)],[c_4823,c_3729]) ).
cnf(c_4825,plain,
~ r2(sK7(sK7(sK8)),sK6(sK7(sK7(sK8)),sK7(sK8))),
inference(resolve,[status(thm)],[c_4824,c_3578]) ).
cnf(c_4826,plain,
~ r2(sK7(sK7(sK8)),sK4(sK7(sK7(sK8)),sK8)),
inference(paramod,[status(thm)],[c_3602,c_4825]) ).
cnf(c_4827,plain,
~ r2(sK7(sK7(sK8)),sK7(sK7(sK7(sK8)))),
inference(paramod,[status(thm)],[c_4774,c_4826]) ).
cnf(c_4809,plain,
$false,
inference(resolve,[status(thm)],[c_3578,c_4827]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN057+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n011.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 04:27:44 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 3770799 was started by sandbox2 on n011,
% 0.10/0.36 % Sat Sep 26 04:27:44 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 23.21/3.33
% 23.21/3.33 % SZS status Theorem for theBenchmark
% 23.21/3.33
% 23.21/3.33 % Proof 1 at 2.40 (+ 0.52) seconds.
% 23.21/3.33 % Length of proof is 37.
% 23.21/3.33 % Level of proof is 7.
% 23.21/3.33 % Maximum clause weight is 34.000.
% 23.21/3.33 % Given clauses 96.
% 23.21/3.33
% 23.21/3.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------