%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUN072+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 : n006.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 08:19:22 AM UTC 2026
% Result : Theorem 61.26s 8.28s
% Output : CNFRefutation 61.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 9
% Syntax : Number of formulae : 117 ( 68 unt; 0 def)
% Number of atoms : 300 ( 108 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 310 ( 127 ~; 98 |; 85 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 1 con; 0-2 aty)
% Number of variables : 297 ( 17 sgn 63 !; 52 ?)
% 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_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(onetimestwoeqtwo,conjecture,
? [Y1] :
( ? [Y3] :
( ? [Y6] :
( ? [Y9] :
( r2(Y9,Y6)
& r1(Y9) )
& r2(Y6,Y3) )
& Y1 = Y3 )
& ? [Y2] :
( ? [Y5] :
( ? [Y8] :
( r2(Y8,Y5)
& r1(Y8) )
& r4(Y5,Y2,Y1) )
& ? [Y4] :
( ? [Y7] :
( r2(Y7,Y4)
& r1(Y7) )
& r2(Y4,Y2) ) ) ),
file('theBenchmark.p',onetimestwoeqtwo) ).
fof(onetimestwoeqtwo_neg,negated_conjecture,
~ ? [Y1] :
( ? [Y3] :
( ? [Y6] :
( ? [Y9] :
( r2(Y9,Y6)
& r1(Y9) )
& r2(Y6,Y3) )
& Y1 = Y3 )
& ? [Y2] :
( ? [Y5] :
( ? [Y8] :
( r2(Y8,Y5)
& r1(Y8) )
& r4(Y5,Y2,Y1) )
& ? [Y4] :
( ? [Y7] :
( r2(Y7,Y4)
& r1(Y7) )
& r2(Y4,Y2) ) ) ),
inference(assume_negation,[status(cth)],[onetimestwoeqtwo]) ).
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),sK15(X1,X8))
& sK15(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,sK15,sK3]),skolemize(Y4,sK15(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_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,sK4(X2,X9))
& r3(sK4(X2,X9),X2,sK5(X2,X9))
& sK5(X2,X9) = sK11(X2,X9)
& r4(X2,sK10(X2,X9),sK11(X2,X9))
& r2(X9,sK10(X2,X9)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK5,sK4]),skolemize(Y2,sK5(X2,X9)),skolemize(Y3,sK11(X2,X9)),skolemize(Y14,sK10(X2,X9)),skolemize(Y6,sK4(X2,X9))],[nnf_6]) ).
cnf(c_17,plain,
r3(sK4(A,B),A,sK5(A,B)),
inference(split_conjunct,[status(thm)],[sk_axiom_2a]) ).
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,sK6(X4),sK7(X4))
& r1(sK6(X4)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(Y9,sK7(X4)),skolemize(Y16,sK6(X4))],[nnf_8]) ).
cnf(c_18,plain,
r3(A,sK6(A),sK7(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] :
( sK16(X5) = sK9(X5)
& r1(sK16(X5))
& r4(X5,sK8(X5),sK9(X5))
& r1(sK8(X5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK16]),skolemize(Y8,sK9(X5)),skolemize(Y17,sK8(X5)),skolemize(Y18,sK16(X5))],[nnf_9]) ).
cnf(c_19,plain,
r4(A,sK8(A),sK9(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_20,negated_conjecture,
( ~ r2(V8,V7)
| ~ r1(V8)
| ~ r2(V7,V6)
| E != V6
| ~ r2(F,D)
| ~ r1(F)
| ~ r4(D,B,E)
| ~ r2(C,A)
| ~ r1(C)
| ~ r2(A,B) ),
inference(clausify,[status(thm)],[onetimestwoeqtwo_neg]) ).
cnf(c_21,plain,
r4(A,B,sK4(A,B)),
inference(split_conjunct,[status(thm)],[sk_axiom_2a]) ).
cnf(c_22,plain,
r4(A,sK10(A,B),sK11(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] :
( ( sK12(X16,X17) = X18
& r4(X16,X17,X18) )
| ( sK12(X16,X17) != X18
& ~ r4(X16,X17,X18) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(Y23,sK12(X16,X17))],[nnf_4]) ).
fof(sk_axiom_4,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( r4(VAR_0,VAR_1,VAR_2)
| sK12(VAR_0,VAR_1) != VAR_2 )
& ! [VAR_0,VAR_1,VAR_2] :
( sK12(VAR_0,VAR_1) = VAR_2
| ~ r4(VAR_0,VAR_1,VAR_2) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_4_sk]) ).
cnf(c_23,plain,
( r4(A,B,C)
| sK12(A,B) != C ),
inference(split_conjunct,[status(thm)],[sk_axiom_4]) ).
cnf(c_24,plain,
( sK12(A,B) = C
| ~ r4(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_axiom_4]) ).
cnf(c_25,plain,
sK12(A,sK8(A)) = sK9(A),
inference(resolve,[status(thm)],[c_24,c_19]) ).
cnf(c_26,plain,
sK9(A) = sK12(A,sK8(A)),
inference(copy,[status(thm)],[c_25]) ).
cnf(c_27,plain,
sK12(A,B) = sK4(A,B),
inference(resolve,[status(thm)],[c_24,c_21]) ).
cnf(c_28,plain,
sK12(A,sK10(A,B)) = sK11(A,B),
inference(resolve,[status(thm)],[c_24,c_22]) ).
cnf(c_5766,plain,
sK4(A,sK10(A,B)) = sK11(A,B),
inference(paramod,[status(thm)],[c_27,c_28]) ).
cnf(c_29,plain,
sK11(A,B) = sK4(A,sK10(A,B)),
inference(copy,[status(thm)],[c_5766]) ).
cnf(c_30,negated_conjecture,
( ~ r2(V8,V7)
| ~ r1(V8)
| ~ r2(V7,V6)
| C != V6
| ~ r2(F,A)
| ~ r1(F)
| ~ r2(E,D)
| ~ r1(E)
| ~ r2(D,B)
| sK12(A,B) != C ),
inference(resolve,[status(thm)],[c_23,c_20]) ).
cnf(c_31,negated_conjecture,
( ~ r2(V8,V7)
| ~ r1(V8)
| ~ r2(V7,V6)
| C != V6
| ~ r2(F,A)
| ~ r1(F)
| ~ r2(E,D)
| ~ r1(E)
| ~ r2(D,B)
| sK4(A,B) != C ),
inference(paramod,[status(thm)],[c_27,c_30]) ).
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] :
( ( sK13 = X19
& r1(X19) )
| ( sK13 != X19
& ~ r1(X19) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(Y24,sK13)],[nnf_1]) ).
fof(sk_axiom_1,plain,
( ! [VAR_0] :
( r1(VAR_0)
| sK13 != VAR_0 )
& ! [VAR_0] :
( sK13 = VAR_0
| ~ r1(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_1_sk]) ).
cnf(c_36,plain,
( sK13 = A
| ~ r1(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_1]) ).
cnf(c_37,plain,
( r1(A)
| sK13 != 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] :
( ( sK14(X11) = X12
& r2(X11,X12) )
| ( sK14(X11) != X12
& ~ r2(X11,X12) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(Y21,sK14(X11))],[nnf_2]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1] :
( r2(VAR_0,VAR_1)
| sK14(VAR_0) != VAR_1 )
& ! [VAR_0,VAR_1] :
( sK14(VAR_0) = VAR_1
| ~ r2(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_38,plain,
( sK14(A) = B
| ~ r2(A,B) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_39,plain,
( r2(A,B)
| sK14(A) != B ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_40,plain,
r2(A,sK1(B,A)),
inference(split_conjunct,[status(thm)],[sk_axiom_1a]) ).
cnf(c_41,plain,
sK15(A,B) = sK2(A,B),
inference(split_conjunct,[status(thm)],[sk_axiom_1a]) ).
cnf(c_42,plain,
r2(sK3(A,B),sK15(A,B)),
inference(split_conjunct,[status(thm)],[sk_axiom_1a]) ).
cnf(c_43,plain,
r2(sK3(A,B),sK2(A,B)),
inference(paramod,[status(thm)],[c_41,c_42]) ).
cnf(c_44,plain,
r2(A,sK10(B,A)),
inference(split_conjunct,[status(thm)],[sk_axiom_2a]) ).
cnf(c_45,plain,
sK5(A,B) = sK11(A,B),
inference(split_conjunct,[status(thm)],[sk_axiom_2a]) ).
cnf(c_46,plain,
sK5(A,B) = sK4(A,sK10(A,B)),
inference(paramod,[status(thm)],[c_29,c_45]) ).
cnf(c_48,plain,
r1(sK6(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
cnf(c_49,plain,
sK7(A) = A,
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
cnf(c_50,plain,
r1(sK8(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_51,plain,
r1(sK16(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_52,plain,
sK16(A) = sK9(A),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_5767,plain,
sK16(A) = sK12(A,sK8(A)),
inference(paramod,[status(thm)],[c_26,c_52]) ).
cnf(c_53,plain,
sK16(A) = sK4(A,sK8(A)),
inference(paramod,[status(thm)],[c_27,c_5767]) ).
cnf(c_61,plain,
sK0(A,sK1(A,B)) = sK2(A,B),
inference(resolve,[status(thm)],[c_15,c_14]) ).
cnf(c_62,plain,
sK2(A,B) = sK0(A,sK1(A,B)),
inference(copy,[status(thm)],[c_61]) ).
cnf(c_63,plain,
sK0(A,B) = sK3(A,B),
inference(resolve,[status(thm)],[c_16,c_14]) ).
cnf(c_64,plain,
sK0(sK4(A,B),A) = sK5(A,B),
inference(resolve,[status(thm)],[c_17,c_14]) ).
cnf(c_5768,plain,
sK3(sK4(A,B),A) = sK5(A,B),
inference(paramod,[status(thm)],[c_63,c_64]) ).
cnf(c_5769,plain,
sK3(sK4(A,B),A) = sK4(A,sK10(A,B)),
inference(paramod,[status(thm)],[c_46,c_5768]) ).
cnf(c_65,plain,
sK4(A,sK10(A,B)) = sK3(sK4(A,B),A),
inference(copy,[status(thm)],[c_5769]) ).
cnf(c_66,plain,
sK0(A,sK6(A)) = sK7(A),
inference(resolve,[status(thm)],[c_18,c_14]) ).
cnf(c_5770,plain,
sK3(A,sK6(A)) = sK7(A),
inference(paramod,[status(thm)],[c_63,c_66]) ).
cnf(c_67,plain,
sK3(A,sK6(A)) = A,
inference(paramod,[status(thm)],[c_49,c_5770]) ).
cnf(c_108,plain,
r1(sK4(A,sK8(A))),
inference(paramod,[status(thm)],[c_53,c_51]) ).
cnf(c_5771,plain,
r2(sK3(A,B),sK0(A,sK1(A,B))),
inference(paramod,[status(thm)],[c_62,c_43]) ).
cnf(c_109,plain,
r2(sK3(A,B),sK3(A,sK1(A,B))),
inference(paramod,[status(thm)],[c_63,c_5771]) ).
cnf(c_429,plain,
r1(sK13),
inference(xxres,[status(thm)],[c_37]) ).
cnf(c_430,plain,
r2(A,sK14(A)),
inference(xxres,[status(thm)],[c_39]) ).
cnf(c_5772,plain,
sK14(A) = sK1(B,A),
inference(resolve,[status(thm)],[c_40,c_38]) ).
cnf(c_431,plain,
sK1(A,B) = sK14(B),
inference(copy,[status(thm)],[c_5772]) ).
cnf(c_5773,negated_conjecture,
( ~ r2(V8,V7)
| ~ r1(V8)
| ~ r2(V7,V6)
| C != V6
| ~ r2(F,A)
| ~ r1(F)
| ~ r1(E)
| ~ r2(sK1(D,E),B)
| sK4(A,B) != C ),
inference(resolve,[status(thm)],[c_40,c_31]) ).
cnf(c_440,negated_conjecture,
( ~ r2(V7,V6)
| ~ r1(V7)
| ~ r2(V6,F)
| C != F
| ~ r2(E,A)
| ~ r1(E)
| ~ r1(D)
| ~ r2(sK14(D),B)
| sK4(A,B) != C ),
inference(paramod,[status(thm)],[c_431,c_5773]) ).
cnf(c_444,plain,
r2(sK3(A,B),sK3(A,sK14(B))),
inference(paramod,[status(thm)],[c_431,c_109]) ).
cnf(c_5774,plain,
sK14(A) = sK10(B,A),
inference(resolve,[status(thm)],[c_44,c_38]) ).
cnf(c_910,plain,
sK10(A,B) = sK14(B),
inference(copy,[status(thm)],[c_5774]) ).
cnf(c_5775,plain,
sK4(A,sK14(B)) = sK3(sK4(A,B),A),
inference(paramod,[status(thm)],[c_910,c_65]) ).
cnf(c_986,plain,
sK3(sK4(A,B),A) = sK4(A,sK14(B)),
inference(copy,[status(thm)],[c_5775]) ).
cnf(c_5776,plain,
sK13 = sK6(A),
inference(resolve,[status(thm)],[c_48,c_36]) ).
cnf(c_991,plain,
sK6(A) = sK13,
inference(copy,[status(thm)],[c_5776]) ).
cnf(c_998,plain,
sK3(A,sK13) = A,
inference(paramod,[status(thm)],[c_991,c_67]) ).
cnf(c_5777,plain,
sK13 = sK8(A),
inference(resolve,[status(thm)],[c_50,c_36]) ).
cnf(c_1364,plain,
sK8(A) = sK13,
inference(copy,[status(thm)],[c_5777]) ).
cnf(c_1365,plain,
r1(sK4(A,sK13)),
inference(paramod,[status(thm)],[c_1364,c_108]) ).
cnf(c_5778,plain,
sK13 = sK4(A,sK13),
inference(resolve,[status(thm)],[c_1365,c_36]) ).
cnf(c_3345,plain,
sK4(A,sK13) = sK13,
inference(copy,[status(thm)],[c_5778]) ).
cnf(c_4501,plain,
r2(A,sK3(A,sK14(sK13))),
inference(paramod,[status(thm)],[c_998,c_444]) ).
cnf(c_5779,plain,
sK14(A) = sK3(A,sK14(sK13)),
inference(resolve,[status(thm)],[c_4501,c_38]) ).
cnf(c_5066,plain,
sK3(A,sK14(sK13)) = sK14(A),
inference(copy,[status(thm)],[c_5779]) ).
cnf(c_5780,plain,
( ~ r2(V6,F)
| ~ r1(V6)
| ~ r2(F,E)
| sK4(D,B) != E
| ~ r2(C,D)
| ~ r1(C)
| ~ r1(A)
| ~ r2(sK14(A),B) ),
inference(xxres,[status(thm)],[c_440]) ).
cnf(c_5781,plain,
( ~ r2(F,E)
| ~ r1(F)
| ~ r2(E,D)
| sK4(C,sK14(sK14(A))) != D
| ~ r2(B,C)
| ~ r1(B)
| ~ r1(A) ),
inference(resolve,[status(thm)],[c_5780,c_430]) ).
cnf(c_5782,plain,
( ~ r2(E,D)
| ~ r1(E)
| ~ r2(D,C)
| sK4(B,sK14(sK14(sK13))) != C
| ~ r2(A,B)
| ~ r1(A) ),
inference(resolve,[status(thm)],[c_5781,c_429]) ).
cnf(c_5783,plain,
( ~ r2(D,C)
| ~ r1(D)
| ~ r2(C,B)
| sK4(A,sK14(sK14(sK13))) != B
| ~ r2(sK13,A) ),
inference(resolve,[status(thm)],[c_5782,c_429]) ).
cnf(c_5784,plain,
( ~ r2(C,B)
| ~ r1(C)
| ~ r2(B,A)
| sK4(sK14(sK13),sK14(sK14(sK13))) != A ),
inference(resolve,[status(thm)],[c_5783,c_430]) ).
cnf(c_5785,plain,
sK4(A,sK14(B)) = sK3(sK4(A,B),A),
inference(copy,[status(thm)],[c_986]) ).
cnf(c_5786,plain,
( ~ r2(B,A)
| ~ r1(B)
| ~ r2(A,sK3(sK4(sK14(sK13),sK14(sK13)),sK14(sK13))) ),
inference(resolve,[status(thm)],[c_5784,c_5785]) ).
cnf(c_5787,plain,
( ~ r2(A,sK3(sK4(sK14(sK13),sK14(sK13)),sK13))
| ~ r1(A) ),
inference(resolve,[status(thm)],[c_5786,c_444]) ).
cnf(c_5788,plain,
~ r2(sK13,sK3(sK4(sK14(sK13),sK14(sK13)),sK13)),
inference(resolve,[status(thm)],[c_5787,c_429]) ).
cnf(c_5756,plain,
~ r2(sK13,sK4(sK14(sK13),sK14(sK13))),
inference(paramod,[status(thm)],[c_998,c_5788]) ).
cnf(c_5789,plain,
sK3(sK13,A) = sK4(A,sK14(sK13)),
inference(paramod,[status(thm)],[c_3345,c_986]) ).
cnf(c_5758,plain,
sK4(A,sK14(sK13)) = sK3(sK13,A),
inference(copy,[status(thm)],[c_5789]) ).
cnf(c_5790,plain,
~ r2(sK13,sK3(sK13,sK14(sK13))),
inference(paramod,[status(thm)],[c_5758,c_5756]) ).
cnf(c_5791,plain,
~ r2(sK13,sK14(sK13)),
inference(paramod,[status(thm)],[c_5066,c_5790]) ).
cnf(c_5765,plain,
$false,
inference(resolve,[status(thm)],[c_430,c_5791]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUN072+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n006.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Sat Sep 26 04:28:56 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 372328 was started by sandbox2 on n006,
% 0.18/0.45 % Sat Sep 26 04:28:56 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.46
% 0.18/0.46 % From the command line: assign(max_seconds, 300).
% 61.26/8.28
% 61.26/8.28 % SZS status Theorem for theBenchmark
% 61.26/8.28
% 61.26/8.28 % Proof 1 at 7.02 (+ 0.75) seconds.
% 61.26/8.28 % Length of proof is 70.
% 61.26/8.28 % Level of proof is 9.
% 61.26/8.28 % Maximum clause weight is 39.000.
% 61.26/8.28 % Given clauses 179.
% 61.26/8.28
% 61.26/8.28 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------