%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUN065+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 : n014.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 08:19:20 AM UTC 2026
% Result : Theorem 2.46s 0.79s
% Output : CNFRefutation 2.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 8
% Syntax : Number of formulae : 118 ( 43 unt; 0 def)
% Number of atoms : 266 ( 141 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 217 ( 69 ~; 96 |; 52 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 1 con; 0-2 aty)
% Number of variables : 244 ( 47 sgn 60 !; 23 ?)
% 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_3a,axiom,
! [X3,X10] :
( X3 = X10
| ! [Y12] :
( ~ r2(X10,Y12)
| ! [Y13] :
( Y13 != Y12
| ~ r2(X3,Y13) ) ) ),
file('theBenchmark.p',axiom_3a) ).
fof(axiom_4a,axiom,
! [X4] :
? [Y9] :
( Y9 = X4
& ? [Y16] :
( r3(X4,Y16,Y9)
& r1(Y16) ) ),
file('theBenchmark.p',axiom_4a) ).
fof(axiom_7a,axiom,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( Y20 != Y10
| ~ r1(Y20) ) ),
file('theBenchmark.p',axiom_7a) ).
fof(nononesexist,conjecture,
? [Y1] :
( ! [Y4] :
( Y1 != Y4
| ~ r1(Y4) )
& ! [Y2] :
( Y1 != Y2
| ! [Y3] :
( ~ r2(Y3,Y2)
| ~ r1(Y3) ) ) ),
file('theBenchmark.p',nononesexist) ).
fof(nononesexist_neg,negated_conjecture,
~ ? [Y1] :
( ! [Y4] :
( Y1 != Y4
| ~ r1(Y4) )
& ! [Y2] :
( Y1 != Y2
| ! [Y3] :
( ~ r2(Y3,Y2)
| ~ r1(Y3) ) ) ),
inference(assume_negation,[status(cth)],[nononesexist]) ).
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,sK3(X1,X8))
& r2(sK3(X1,X8),sK8(X1,X8))
& sK8(X1,X8) = sK2(X1,X8)
& r3(X1,sK1(X1,X8),sK2(X1,X8))
& r2(X8,sK1(X1,X8)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK8,sK3]),skolemize(Y4,sK8(X1,X8)),skolemize(Y5,sK2(X1,X8)),skolemize(Y15,sK1(X1,X8)),skolemize(Y7,sK3(X1,X8))],[nnf_5]) ).
cnf(c_15,plain,
r3(A,sK1(A,B),sK2(A,B)),
inference(split_conjunct,[status(thm)],[sk_axiom_1a]) ).
cnf(c_16,plain,
r3(A,B,sK3(A,B)),
inference(split_conjunct,[status(thm)],[sk_axiom_1a]) ).
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_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] :
( ( sK6 = X19
& r1(X19) )
| ( sK6 != X19
& ~ r1(X19) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(Y24,sK6)],[nnf_1]) ).
fof(sk_axiom_1,plain,
( ! [VAR_0] :
( r1(VAR_0)
| sK6 != VAR_0 )
& ! [VAR_0] :
( sK6 = VAR_0
| ~ r1(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_1_sk]) ).
cnf(c_29,plain,
( sK6 = A
| ~ r1(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_1]) ).
cnf(c_30,plain,
( r1(A)
| sK6 != A ),
inference(split_conjunct,[status(thm)],[sk_axiom_1]) ).
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_31,plain,
( sK7(A) = B
| ~ r2(A,B) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_32,plain,
( r2(A,B)
| sK7(A) != B ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_33,plain,
r2(A,sK1(B,A)),
inference(split_conjunct,[status(thm)],[sk_axiom_1a]) ).
cnf(c_34,plain,
sK8(A,B) = sK2(A,B),
inference(split_conjunct,[status(thm)],[sk_axiom_1a]) ).
cnf(c_35,plain,
r2(sK3(A,B),sK8(A,B)),
inference(split_conjunct,[status(thm)],[sk_axiom_1a]) ).
cnf(c_36,plain,
r2(sK3(A,B),sK2(A,B)),
inference(paramod,[status(thm)],[c_34,c_35]) ).
cnf(c_40,plain,
( D = A
| ~ r2(D,C)
| C != B
| ~ r2(A,B) ),
inference(clausify,[status(thm)],[axiom_3a]) ).
cnf(c_41,plain,
r1(sK4(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
cnf(c_42,plain,
sK5(A) = A,
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
cnf(c_53,plain,
( ~ r2(C,B)
| B != A
| ~ r1(A) ),
inference(clausify,[status(thm)],[axiom_7a]) ).
fof(nnf_12,plain,
! [Y1] :
( ? [Y4] :
( Y1 = Y4
& r1(Y4) )
| ? [Y2] :
( Y1 = Y2
& ? [Y3] :
( r2(Y3,Y2)
& r1(Y3) ) ) ),
inference(fof_nnf,[status(thm)],[nononesexist_neg]) ).
fof(sk_nononesexist_neg_sk,plain,
! [Y1] :
( ( Y1 = sK10(Y1)
& r1(sK10(Y1)) )
| ( Y1 = sK11(Y1)
& r2(sK9(Y1),sK11(Y1))
& r1(sK9(Y1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK11,sK10]),skolemize(Y2,sK11(Y1)),skolemize(Y3,sK9(Y1)),skolemize(Y4,sK10(Y1))],[nnf_12]) ).
fof(sk_nononesexist_neg,plain,
( ! [VAR_0] :
( VAR_0 = sK10(VAR_0)
| VAR_0 = sK11(VAR_0) )
& ! [VAR_0] :
( r1(sK10(VAR_0))
| VAR_0 = sK11(VAR_0) )
& ! [VAR_0] :
( VAR_0 = sK10(VAR_0)
| r2(sK9(VAR_0),sK11(VAR_0)) )
& ! [VAR_0] :
( r1(sK10(VAR_0))
| r2(sK9(VAR_0),sK11(VAR_0)) )
& ! [VAR_0] :
( VAR_0 = sK10(VAR_0)
| r1(sK9(VAR_0)) )
& ! [VAR_0] :
( r1(sK10(VAR_0))
| r1(sK9(VAR_0)) ) ),
inference(cnf_transformation,[status(thm)],[sk_nononesexist_neg_sk]) ).
cnf(c_54,negated_conjecture,
( r1(sK10(A))
| r1(sK9(A)) ),
inference(split_conjunct,[status(thm)],[sk_nononesexist_neg]) ).
cnf(c_55,negated_conjecture,
( A = sK10(A)
| r1(sK9(A)) ),
inference(split_conjunct,[status(thm)],[sk_nononesexist_neg]) ).
cnf(c_56,negated_conjecture,
( sK10(A) = A
| r1(sK9(A)) ),
inference(copy,[status(thm)],[c_55]) ).
cnf(c_57,negated_conjecture,
( r1(sK10(A))
| r2(sK9(A),sK11(A)) ),
inference(split_conjunct,[status(thm)],[sk_nononesexist_neg]) ).
cnf(c_58,negated_conjecture,
( A = sK10(A)
| r2(sK9(A),sK11(A)) ),
inference(split_conjunct,[status(thm)],[sk_nononesexist_neg]) ).
cnf(c_59,negated_conjecture,
( sK10(A) = A
| r2(sK9(A),sK11(A)) ),
inference(copy,[status(thm)],[c_58]) ).
cnf(c_60,negated_conjecture,
( r1(sK10(A))
| A = sK11(A) ),
inference(split_conjunct,[status(thm)],[sk_nononesexist_neg]) ).
cnf(c_61,negated_conjecture,
( r1(sK10(A))
| sK11(A) = A ),
inference(copy,[status(thm)],[c_60]) ).
cnf(c_62,negated_conjecture,
( A = sK10(A)
| A = sK11(A) ),
inference(split_conjunct,[status(thm)],[sk_nononesexist_neg]) ).
cnf(c_959,negated_conjecture,
( A = sK10(A)
| sK11(A) = A ),
inference(copy,[status(thm)],[c_62]) ).
cnf(c_63,negated_conjecture,
( sK10(A) = A
| sK11(A) = A ),
inference(copy,[status(thm)],[c_959]) ).
cnf(c_64,plain,
sK0(A,sK1(A,B)) = sK2(A,B),
inference(resolve,[status(thm)],[c_15,c_14]) ).
cnf(c_65,plain,
sK2(A,B) = sK0(A,sK1(A,B)),
inference(copy,[status(thm)],[c_64]) ).
cnf(c_66,plain,
sK0(A,B) = sK3(A,B),
inference(resolve,[status(thm)],[c_16,c_14]) ).
cnf(c_69,plain,
sK0(A,sK4(A)) = sK5(A),
inference(resolve,[status(thm)],[c_18,c_14]) ).
cnf(c_960,plain,
sK3(A,sK4(A)) = sK5(A),
inference(paramod,[status(thm)],[c_66,c_69]) ).
cnf(c_70,plain,
sK3(A,sK4(A)) = A,
inference(paramod,[status(thm)],[c_42,c_960]) ).
cnf(c_961,plain,
r2(sK3(A,B),sK0(A,sK1(A,B))),
inference(paramod,[status(thm)],[c_65,c_36]) ).
cnf(c_73,plain,
r2(sK3(A,B),sK3(A,sK1(A,B))),
inference(paramod,[status(thm)],[c_66,c_961]) ).
cnf(c_78,plain,
r1(sK6),
inference(xxres,[status(thm)],[c_30]) ).
cnf(c_79,plain,
r2(A,sK7(A)),
inference(xxres,[status(thm)],[c_32]) ).
cnf(c_962,plain,
sK7(A) = sK1(B,A),
inference(resolve,[status(thm)],[c_33,c_31]) ).
cnf(c_80,plain,
sK1(A,B) = sK7(B),
inference(copy,[status(thm)],[c_962]) ).
cnf(c_963,plain,
sK6 = sK4(A),
inference(resolve,[status(thm)],[c_41,c_29]) ).
cnf(c_86,plain,
sK4(A) = sK6,
inference(copy,[status(thm)],[c_963]) ).
cnf(c_87,plain,
sK3(A,sK6) = A,
inference(paramod,[status(thm)],[c_86,c_70]) ).
cnf(c_964,plain,
A = sK5(A),
inference(copy,[status(thm)],[c_42]) ).
cnf(c_965,plain,
( ~ r2(B,A)
| ~ r1(sK5(A)) ),
inference(resolve,[status(thm)],[c_53,c_964]) ).
cnf(c_966,plain,
~ r1(sK5(sK1(A,B))),
inference(resolve,[status(thm)],[c_965,c_33]) ).
cnf(c_106,plain,
~ r1(sK1(A,B)),
inference(paramod,[status(thm)],[c_42,c_966]) ).
cnf(c_967,negated_conjecture,
( sK6 = sK10(A)
| r1(sK9(A)) ),
inference(resolve,[status(thm)],[c_54,c_29]) ).
cnf(c_107,negated_conjecture,
( sK10(A) = sK6
| r1(sK9(A)) ),
inference(copy,[status(thm)],[c_967]) ).
cnf(c_968,negated_conjecture,
( sK6 = sK9(A)
| sK10(A) = A ),
inference(resolve,[status(thm)],[c_56,c_29]) ).
cnf(c_108,negated_conjecture,
( sK9(A) = sK6
| sK10(A) = A ),
inference(copy,[status(thm)],[c_968]) ).
cnf(c_114,plain,
( sK7(sK9(A)) = sK11(A)
| sK10(A) = A ),
inference(resolve,[status(thm)],[c_59,c_31]) ).
cnf(c_969,plain,
( r1(A)
| sK11(A) = A
| sK11(A) = A ),
inference(paramod,[status(thm)],[c_63,c_61]) ).
cnf(c_118,plain,
( r1(A)
| sK11(A) = A ),
inference(copy,[status(thm)],[c_969]) ).
cnf(c_970,plain,
( ~ r2(B,A)
| A != sK6 ),
inference(resolve,[status(thm)],[c_53,c_78]) ).
cnf(c_125,plain,
sK1(A,B) != sK6,
inference(resolve,[status(thm)],[c_970,c_33]) ).
cnf(c_153,plain,
sK1(A,B) = sK1(C,B),
inference(paramod,[status(thm)],[c_80,c_80]) ).
cnf(c_971,plain,
sK7(B) = sK1(A,B),
inference(copy,[status(thm)],[c_80]) ).
cnf(c_972,plain,
( D = A
| ~ r2(D,sK7(C))
| ~ r2(A,sK1(B,C)) ),
inference(resolve,[status(thm)],[c_40,c_971]) ).
cnf(c_973,plain,
( C = A
| ~ r2(A,sK1(B,C)) ),
inference(resolve,[status(thm)],[c_972,c_79]) ).
cnf(c_170,plain,
~ r2(sK6,sK1(A,sK1(B,C))),
inference(resolve,[status(thm)],[c_973,c_125]) ).
cnf(c_184,plain,
r2(A,sK3(A,sK1(A,sK6))),
inference(paramod,[status(thm)],[c_87,c_73]) ).
cnf(c_195,plain,
sK11(sK1(A,B)) = sK1(A,B),
inference(resolve,[status(thm)],[c_118,c_106]) ).
cnf(c_197,plain,
( sK6 = A
| sK11(A) = A ),
inference(resolve,[status(thm)],[c_118,c_29]) ).
cnf(c_974,plain,
( sK6 = sK9(A)
| sK10(A) = sK6 ),
inference(resolve,[status(thm)],[c_107,c_29]) ).
cnf(c_200,plain,
( sK9(A) = sK6
| sK10(A) = sK6 ),
inference(copy,[status(thm)],[c_974]) ).
cnf(c_221,plain,
sK7(A) = sK3(A,sK1(A,sK6)),
inference(resolve,[status(thm)],[c_184,c_31]) ).
cnf(c_244,plain,
r2(A,sK3(A,sK1(B,sK6))),
inference(paramod,[status(thm)],[c_153,c_184]) ).
cnf(c_270,plain,
( sK3(sK9(A),sK1(sK9(A),sK6)) = sK11(A)
| sK10(A) = A ),
inference(paramod,[status(thm)],[c_221,c_114]) ).
cnf(c_289,plain,
( r1(sK10(A))
| r2(sK9(A),A)
| sK6 = A ),
inference(paramod,[status(thm)],[c_197,c_57]) ).
cnf(c_975,plain,
( D = C
| ~ r2(D,A)
| A != sK1(B,C) ),
inference(resolve,[status(thm)],[c_40,c_33]) ).
cnf(c_976,plain,
( A = D
| sK3(A,sK1(B,sK6)) != sK1(C,D) ),
inference(resolve,[status(thm)],[c_975,c_244]) ).
cnf(c_977,plain,
sK6 != sK1(A,B),
inference(copy,[status(thm)],[c_125]) ).
cnf(c_299,plain,
sK3(sK6,sK1(A,sK6)) != sK1(B,sK1(C,D)),
inference(resolve,[status(thm)],[c_976,c_977]) ).
cnf(c_978,plain,
( r1(A)
| A != sK6 ),
inference(copy,[status(thm)],[c_30]) ).
cnf(c_371,plain,
( r1(sK10(A))
| sK9(A) = sK6 ),
inference(resolve,[status(thm)],[c_200,c_978]) ).
cnf(c_979,plain,
( sK9(A) = sK6
| sK6 = A
| sK9(A) = sK6 ),
inference(paramod,[status(thm)],[c_200,c_108]) ).
cnf(c_372,plain,
( sK6 = A
| sK9(A) = sK6 ),
inference(copy,[status(thm)],[c_979]) ).
cnf(c_980,plain,
( r1(A)
| sK9(A) = sK6
| sK9(A) = sK6 ),
inference(paramod,[status(thm)],[c_108,c_371]) ).
cnf(c_376,plain,
( r1(A)
| sK9(A) = sK6 ),
inference(copy,[status(thm)],[c_980]) ).
cnf(c_381,plain,
sK9(sK1(A,B)) = sK6,
inference(resolve,[status(thm)],[c_376,c_106]) ).
cnf(c_981,plain,
( r1(sK10(A))
| r2(sK6,A)
| sK6 = A
| sK6 = A ),
inference(paramod,[status(thm)],[c_372,c_289]) ).
cnf(c_781,plain,
( r1(sK10(A))
| r2(sK6,A)
| sK6 = A ),
inference(copy,[status(thm)],[c_981]) ).
cnf(c_982,plain,
( r1(sK10(sK1(A,sK1(B,C))))
| sK6 = sK1(A,sK1(B,C)) ),
inference(resolve,[status(thm)],[c_781,c_170]) ).
cnf(c_983,plain,
( r1(sK10(sK1(A,sK1(B,C))))
| sK1(A,sK1(B,C)) = sK6 ),
inference(copy,[status(thm)],[c_982]) ).
cnf(c_791,plain,
r1(sK10(sK1(A,sK1(B,C)))),
inference(resolve,[status(thm)],[c_125,c_983]) ).
cnf(c_984,plain,
sK6 = sK10(sK1(A,sK1(B,C))),
inference(resolve,[status(thm)],[c_791,c_29]) ).
cnf(c_893,plain,
sK10(sK1(A,sK1(B,C))) = sK6,
inference(copy,[status(thm)],[c_984]) ).
cnf(c_985,plain,
( sK1(A,sK1(B,C)) = sK6
| sK3(sK9(sK1(A,sK1(B,C))),sK1(sK9(sK1(A,sK1(B,C))),sK6)) = sK11(sK1(A,sK1(B,C))) ),
inference(paramod,[status(thm)],[c_270,c_893]) ).
cnf(c_986,plain,
( sK1(A,sK1(B,C)) = sK6
| sK3(sK6,sK1(sK9(sK1(A,sK1(B,C))),sK6)) = sK11(sK1(A,sK1(B,C))) ),
inference(paramod,[status(thm)],[c_381,c_985]) ).
cnf(c_987,plain,
( sK1(A,sK1(B,C)) = sK6
| sK3(sK6,sK1(sK6,sK6)) = sK11(sK1(A,sK1(B,C))) ),
inference(paramod,[status(thm)],[c_381,c_986]) ).
cnf(c_988,plain,
( sK1(A,sK1(B,C)) = sK6
| sK3(sK6,sK1(sK6,sK6)) = sK1(A,sK1(B,C)) ),
inference(paramod,[status(thm)],[c_195,c_987]) ).
cnf(c_989,plain,
sK1(A,sK1(B,C)) = sK6,
inference(resolve,[status(thm)],[c_299,c_988]) ).
cnf(c_958,plain,
$false,
inference(resolve,[status(thm)],[c_125,c_989]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN065+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.36 % Computer : n014.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Sat Sep 26 04:30:03 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.37 % Process 2142953 was started by sandbox on n014,
% 0.12/0.37 % Sat Sep 26 04:30:03 2026
% 0.12/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.38
% 0.12/0.38 % From the command line: assign(max_seconds, 300).
% 2.46/0.79
% 2.46/0.79 % SZS status Theorem for theBenchmark
% 2.46/0.79
% 2.46/0.79 % Proof 1 at 0.27 (+ 0.12) seconds.
% 2.46/0.79 % Length of proof is 70.
% 2.46/0.79 % Level of proof is 9.
% 2.46/0.79 % Maximum clause weight is 14.000.
% 2.46/0.79 % Given clauses 174.
% 2.46/0.79
% 2.46/0.79 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------