%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUN070+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 : n015.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 08:19:21 AM UTC 2026
% Result : Theorem 0.18s 0.47s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 48 ( 20 unt; 0 def)
% Number of atoms : 139 ( 43 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 144 ( 53 ~; 38 |; 53 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 116 ( 10 sgn 32 !; 34 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_1,axiom,
? [Y24] :
! [X19] :
( ( X19 = Y24
& r1(X19) )
| ( X19 != Y24
& ~ r1(X19) ) ),
file('theBenchmark.p',axiom_1) ).
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_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(onepluszeroeqone,conjecture,
? [Y1] :
( ? [Y3] :
( ? [Y6] :
( r2(Y6,Y3)
& r1(Y6) )
& Y1 = Y3 )
& ? [Y2] :
( ? [Y5] :
( r2(Y5,Y2)
& r1(Y5) )
& ? [Y4] :
( r3(Y2,Y4,Y1)
& r1(Y4) ) ) ),
file('theBenchmark.p',onepluszeroeqone) ).
fof(onepluszeroeqone_neg,negated_conjecture,
~ ? [Y1] :
( ? [Y3] :
( ? [Y6] :
( r2(Y6,Y3)
& r1(Y6) )
& Y1 = Y3 )
& ? [Y2] :
( ? [Y5] :
( r2(Y5,Y2)
& r1(Y5) )
& ? [Y4] :
( r3(Y2,Y4,Y1)
& r1(Y4) ) ) ),
inference(assume_negation,[status(cth)],[onepluszeroeqone]) ).
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] :
( sK1(X4) = X4
& r3(X4,sK0(X4),sK1(X4))
& r1(sK0(X4)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(Y9,sK1(X4)),skolemize(Y16,sK0(X4))],[nnf_8]) ).
cnf(c_18,plain,
r3(A,sK0(A),sK1(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
cnf(c_19,negated_conjecture,
( ~ r2(F,E)
| ~ r1(F)
| C != E
| ~ r2(D,B)
| ~ r1(D)
| ~ r3(B,A,C)
| ~ r1(A) ),
inference(clausify,[status(thm)],[onepluszeroeqone_neg]) ).
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] :
( ( sK2(X16,X17) = X18
& r4(X16,X17,X18) )
| ( sK2(X16,X17) != X18
& ~ r4(X16,X17,X18) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(Y23,sK2(X16,X17))],[nnf_4]) ).
fof(sk_axiom_4,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( r4(VAR_0,VAR_1,VAR_2)
| sK2(VAR_0,VAR_1) != VAR_2 )
& ! [VAR_0,VAR_1,VAR_2] :
( sK2(VAR_0,VAR_1) = VAR_2
| ~ r4(VAR_0,VAR_1,VAR_2) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_4_sk]) ).
cnf(c_20,plain,
( sK2(A,B) = C
| ~ r4(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_axiom_4]) ).
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,sK3(X2,X9))
& r3(sK3(X2,X9),X2,sK10(X2,X9))
& sK10(X2,X9) = sK9(X2,X9)
& r4(X2,sK7(X2,X9),sK9(X2,X9))
& r2(X9,sK7(X2,X9)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK9,sK10,sK3]),skolemize(Y2,sK10(X2,X9)),skolemize(Y3,sK9(X2,X9)),skolemize(Y14,sK7(X2,X9)),skolemize(Y6,sK3(X2,X9))],[nnf_6]) ).
cnf(c_23,plain,
r4(A,B,sK3(A,B)),
inference(split_conjunct,[status(thm)],[sk_axiom_2a]) ).
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] :
( sK8(X5) = sK5(X5)
& r1(sK8(X5))
& r4(X5,sK4(X5),sK5(X5))
& r1(sK4(X5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK8]),skolemize(Y8,sK5(X5)),skolemize(Y17,sK4(X5)),skolemize(Y18,sK8(X5))],[nnf_9]) ).
cnf(c_24,plain,
r4(A,sK4(A),sK5(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_25,plain,
sK2(A,sK4(A)) = sK5(A),
inference(resolve,[status(thm)],[c_20,c_24]) ).
cnf(c_26,plain,
sK5(A) = sK2(A,sK4(A)),
inference(copy,[status(thm)],[c_25]) ).
cnf(c_27,plain,
sK2(A,B) = sK3(A,B),
inference(resolve,[status(thm)],[c_20,c_23]) ).
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_30,plain,
( sK6 = A
| ~ r1(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_1]) ).
cnf(c_38,plain,
r2(A,sK7(B,A)),
inference(split_conjunct,[status(thm)],[sk_axiom_2a]) ).
cnf(c_42,plain,
r1(sK0(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
cnf(c_43,plain,
sK1(A) = A,
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
cnf(c_44,plain,
r1(sK4(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_45,plain,
r1(sK8(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_46,plain,
sK8(A) = sK5(A),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_128,plain,
sK8(A) = sK2(A,sK4(A)),
inference(paramod,[status(thm)],[c_26,c_46]) ).
cnf(c_47,plain,
sK8(A) = sK3(A,sK4(A)),
inference(paramod,[status(thm)],[c_27,c_128]) ).
cnf(c_62,negated_conjecture,
( ~ r2(D,C)
| ~ r1(D)
| sK1(A) != C
| ~ r2(B,A)
| ~ r1(B)
| ~ r1(sK0(A)) ),
inference(resolve,[status(thm)],[c_19,c_18]) ).
cnf(c_129,negated_conjecture,
( ~ r2(D,C)
| ~ r1(D)
| A != C
| ~ r2(B,A)
| ~ r1(B)
| ~ r1(sK0(A)) ),
inference(paramod,[status(thm)],[c_43,c_62]) ).
cnf(c_63,negated_conjecture,
( ~ r2(D,C)
| ~ r1(D)
| B != C
| ~ r2(A,B)
| ~ r1(A) ),
inference(resolve,[status(thm)],[c_42,c_129]) ).
cnf(c_71,plain,
r1(sK3(A,sK4(A))),
inference(paramod,[status(thm)],[c_47,c_45]) ).
cnf(c_130,plain,
( ~ r1(A)
| B != B
| ~ r2(A,B)
| ~ r1(A) ),
inference(factor,[status(thm)],[c_63]) ).
cnf(c_131,plain,
( ~ r1(A)
| ~ r2(A,B)
| ~ r1(A) ),
inference(copy,[status(thm)],[c_130]) ).
cnf(c_78,plain,
( ~ r2(A,B)
| ~ r1(A) ),
inference(copy,[status(thm)],[c_131]) ).
cnf(c_132,plain,
sK6 = sK4(A),
inference(resolve,[status(thm)],[c_44,c_30]) ).
cnf(c_91,plain,
sK4(A) = sK6,
inference(copy,[status(thm)],[c_132]) ).
cnf(c_92,plain,
r1(sK3(A,sK6)),
inference(paramod,[status(thm)],[c_91,c_71]) ).
cnf(c_126,plain,
~ r1(A),
inference(resolve,[status(thm)],[c_78,c_38]) ).
cnf(c_127,plain,
$false,
inference(resolve,[status(thm)],[c_126,c_92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUN070+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n015.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sat Sep 26 04:32:43 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 3132452 was started by sandbox2 on n015,
% 0.18/0.44 % Sat Sep 26 04:32:43 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 0.18/0.47
% 0.18/0.47 % SZS status Theorem for theBenchmark
% 0.18/0.47
% 0.18/0.47 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.18/0.47 % Length of proof is 30.
% 0.18/0.47 % Level of proof is 7.
% 0.18/0.47 % Maximum clause weight is 22.000.
% 0.18/0.47 % Given clauses 24.
% 0.18/0.47
% 0.18/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------