%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUN085+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 : n012.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 08:19:24 AM UTC 2026
% Result : Theorem 0.07s 0.35s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 77 ( 47 unt; 0 def)
% Number of atoms : 161 ( 71 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 138 ( 54 ~; 35 |; 49 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 130 ( 13 sgn 52 !; 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_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(zeroplusoneidzero,conjecture,
! [Y1] :
( ! [Y5] :
( ~ r1(Y5)
| Y1 != Y5 )
| ! [Y2] :
( ! [Y4] :
( ~ r2(Y4,Y2)
| ~ r1(Y4) )
| ! [Y3] :
( ~ r3(Y3,Y2,Y1)
| ~ r1(Y3) ) ) ),
file('theBenchmark.p',zeroplusoneidzero) ).
fof(zeroplusoneidzero_neg,negated_conjecture,
~ ! [Y1] :
( ! [Y5] :
( ~ r1(Y5)
| Y1 != Y5 )
| ! [Y2] :
( ! [Y4] :
( ~ r2(Y4,Y2)
| ~ r1(Y4) )
| ! [Y3] :
( ~ r3(Y3,Y2,Y1)
| ~ r1(Y3) ) ) ),
inference(assume_negation,[status(cth)],[zeroplusoneidzero]) ).
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_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] :
( sK9(X4) = X4
& r3(X4,sK1(X4),sK9(X4))
& r1(sK1(X4)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK9]),skolemize(Y9,sK9(X4)),skolemize(Y16,sK1(X4))],[nnf_8]) ).
cnf(c_15,plain,
r1(sK1(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
cnf(c_20,plain,
( ~ r2(C,B)
| B != A
| ~ r1(A) ),
inference(clausify,[status(thm)],[axiom_7a]) ).
fof(nnf_12,plain,
? [Y1] :
( ? [Y5] :
( r1(Y5)
& Y1 = Y5 )
& ? [Y2] :
( ? [Y4] :
( r2(Y4,Y2)
& r1(Y4) )
& ? [Y3] :
( r3(Y3,Y2,Y1)
& r1(Y3) ) ) ),
inference(fof_nnf,[status(thm)],[zeroplusoneidzero_neg]) ).
fof(sk_zeroplusoneidzero_neg,plain,
( r1(sK4)
& sK11 = sK4
& r2(sK3,sK10)
& r1(sK3)
& r3(sK2,sK10,sK11)
& r1(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK10,sK11,sK3,sK4]),skolemize(Y1,sK11),skolemize(Y2,sK10),skolemize(Y3,sK2),skolemize(Y4,sK3),skolemize(Y5,sK4)],[nnf_12]) ).
cnf(c_21,negated_conjecture,
r1(sK2),
inference(split_conjunct,[status(thm)],[sk_zeroplusoneidzero_neg]) ).
cnf(c_22,negated_conjecture,
r1(sK3),
inference(split_conjunct,[status(thm)],[sk_zeroplusoneidzero_neg]) ).
cnf(c_23,negated_conjecture,
r1(sK4),
inference(split_conjunct,[status(thm)],[sk_zeroplusoneidzero_neg]) ).
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] :
( ( sK5(X13,X14) = X15
& r3(X13,X14,X15) )
| ( sK5(X13,X14) != X15
& ~ r3(X13,X14,X15) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(Y22,sK5(X13,X14))],[nnf_3]) ).
fof(sk_axiom_3,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( r3(VAR_0,VAR_1,VAR_2)
| sK5(VAR_0,VAR_1) != VAR_2 )
& ! [VAR_0,VAR_1,VAR_2] :
( sK5(VAR_0,VAR_1) = VAR_2
| ~ r3(VAR_0,VAR_1,VAR_2) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_3_sk]) ).
cnf(c_24,plain,
( sK5(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,sK8(X1,X8))
& r2(sK8(X1,X8),sK12(X1,X8))
& sK12(X1,X8) = sK7(X1,X8)
& r3(X1,sK6(X1,X8),sK7(X1,X8))
& r2(X8,sK6(X1,X8)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK12,sK8]),skolemize(Y4,sK12(X1,X8)),skolemize(Y5,sK7(X1,X8)),skolemize(Y15,sK6(X1,X8)),skolemize(Y7,sK8(X1,X8))],[nnf_5]) ).
cnf(c_26,plain,
r3(A,sK6(A,B),sK7(A,B)),
inference(split_conjunct,[status(thm)],[sk_axiom_1a]) ).
cnf(c_27,plain,
r3(A,B,sK8(A,B)),
inference(split_conjunct,[status(thm)],[sk_axiom_1a]) ).
cnf(c_29,plain,
r3(A,sK1(A),sK9(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
cnf(c_30,negated_conjecture,
r3(sK2,sK10,sK11),
inference(split_conjunct,[status(thm)],[sk_zeroplusoneidzero_neg]) ).
cnf(c_41,negated_conjecture,
sK0 = sK4,
inference(resolve,[status(thm)],[c_23,c_14]) ).
cnf(c_42,negated_conjecture,
sK4 = sK0,
inference(copy,[status(thm)],[c_41]) ).
cnf(c_43,negated_conjecture,
( ~ r2(B,A)
| A != sK4 ),
inference(resolve,[status(thm)],[c_23,c_20]) ).
cnf(c_247,negated_conjecture,
( ~ r2(B,A)
| A != sK0 ),
inference(paramod,[status(thm)],[c_42,c_43]) ).
cnf(c_44,negated_conjecture,
( ~ r2(B,A)
| sK0 != A ),
inference(copy,[status(thm)],[c_247]) ).
cnf(c_45,negated_conjecture,
sK0 = sK3,
inference(resolve,[status(thm)],[c_22,c_14]) ).
cnf(c_46,negated_conjecture,
sK3 = sK0,
inference(copy,[status(thm)],[c_45]) ).
cnf(c_48,negated_conjecture,
sK0 = sK2,
inference(resolve,[status(thm)],[c_21,c_14]) ).
cnf(c_49,negated_conjecture,
sK2 = sK0,
inference(copy,[status(thm)],[c_48]) ).
cnf(c_70,plain,
sK0 = sK1(A),
inference(resolve,[status(thm)],[c_15,c_14]) ).
cnf(c_71,plain,
sK1(A) = sK0,
inference(copy,[status(thm)],[c_70]) ).
cnf(c_72,negated_conjecture,
sK11 = sK4,
inference(split_conjunct,[status(thm)],[sk_zeroplusoneidzero_neg]) ).
cnf(c_73,negated_conjecture,
sK11 = sK0,
inference(paramod,[status(thm)],[c_42,c_72]) ).
cnf(c_74,negated_conjecture,
r2(sK3,sK10),
inference(split_conjunct,[status(thm)],[sk_zeroplusoneidzero_neg]) ).
cnf(c_75,negated_conjecture,
r2(sK0,sK10),
inference(paramod,[status(thm)],[c_46,c_74]) ).
cnf(c_82,plain,
sK9(A) = A,
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
cnf(c_87,plain,
r2(sK8(A,B),sK12(A,B)),
inference(split_conjunct,[status(thm)],[sk_axiom_1a]) ).
cnf(c_88,plain,
sK12(A,B) = sK7(A,B),
inference(split_conjunct,[status(thm)],[sk_axiom_1a]) ).
cnf(c_89,plain,
r2(A,sK6(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] :
( ( sK13(X11) = X12
& r2(X11,X12) )
| ( sK13(X11) != X12
& ~ r2(X11,X12) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(Y21,sK13(X11))],[nnf_2]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1] :
( r2(VAR_0,VAR_1)
| sK13(VAR_0) != VAR_1 )
& ! [VAR_0,VAR_1] :
( sK13(VAR_0) = VAR_1
| ~ r2(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_91,plain,
( sK13(A) = B
| ~ r2(A,B) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_92,plain,
sK5(A,sK6(A,B)) = sK7(A,B),
inference(resolve,[status(thm)],[c_24,c_26]) ).
cnf(c_93,plain,
sK7(A,B) = sK5(A,sK6(A,B)),
inference(copy,[status(thm)],[c_92]) ).
cnf(c_94,plain,
sK5(A,B) = sK8(A,B),
inference(resolve,[status(thm)],[c_24,c_27]) ).
cnf(c_97,plain,
sK5(A,sK1(A)) = sK9(A),
inference(resolve,[status(thm)],[c_24,c_29]) ).
cnf(c_248,plain,
sK5(A,sK0) = sK9(A),
inference(paramod,[status(thm)],[c_71,c_97]) ).
cnf(c_249,plain,
sK8(A,sK0) = sK9(A),
inference(paramod,[status(thm)],[c_94,c_248]) ).
cnf(c_98,plain,
sK8(A,sK0) = A,
inference(paramod,[status(thm)],[c_82,c_249]) ).
cnf(c_99,negated_conjecture,
sK5(sK2,sK10) = sK11,
inference(resolve,[status(thm)],[c_24,c_30]) ).
cnf(c_250,negated_conjecture,
sK5(sK0,sK10) = sK11,
inference(paramod,[status(thm)],[c_49,c_99]) ).
cnf(c_251,negated_conjecture,
sK8(sK0,sK10) = sK11,
inference(paramod,[status(thm)],[c_94,c_250]) ).
cnf(c_100,negated_conjecture,
sK8(sK0,sK10) = sK0,
inference(paramod,[status(thm)],[c_73,c_251]) ).
cnf(c_252,plain,
r2(sK8(A,B),sK7(A,B)),
inference(paramod,[status(thm)],[c_88,c_87]) ).
cnf(c_253,plain,
r2(sK8(A,B),sK5(A,sK6(A,B))),
inference(paramod,[status(thm)],[c_93,c_252]) ).
cnf(c_103,plain,
r2(sK8(A,B),sK8(A,sK6(A,B))),
inference(paramod,[status(thm)],[c_94,c_253]) ).
cnf(c_254,plain,
sK13(A) = sK6(B,A),
inference(resolve,[status(thm)],[c_91,c_89]) ).
cnf(c_140,plain,
sK6(A,B) = sK13(B),
inference(copy,[status(thm)],[c_254]) ).
cnf(c_143,plain,
sK13(sK0) = sK10,
inference(resolve,[status(thm)],[c_91,c_75]) ).
cnf(c_152,plain,
r2(A,sK8(A,sK6(A,sK0))),
inference(paramod,[status(thm)],[c_98,c_103]) ).
cnf(c_211,plain,
sK6(A,sK0) = sK10,
inference(paramod,[status(thm)],[c_140,c_143]) ).
cnf(c_213,plain,
r2(A,sK8(A,sK10)),
inference(paramod,[status(thm)],[c_211,c_152]) ).
cnf(c_255,negated_conjecture,
sK0 != sK8(A,sK10),
inference(resolve,[status(thm)],[c_213,c_44]) ).
cnf(c_245,negated_conjecture,
sK8(A,sK10) != sK0,
inference(copy,[status(thm)],[c_255]) ).
cnf(c_246,plain,
$false,
inference(resolve,[status(thm)],[c_245,c_100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUN085+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sat Sep 26 04:32:05 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.04/0.31 % Process 3915002 was started by sandbox on n012,
% 0.04/0.31 % Sat Sep 26 04:32:05 2026
% 0.04/0.31 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.04/0.31
% 0.04/0.31 % From the command line: assign(max_seconds, 300).
% 0.07/0.35
% 0.07/0.35 % SZS status Theorem for theBenchmark
% 0.07/0.35
% 0.07/0.35 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.07/0.35 % Length of proof is 52.
% 0.07/0.35 % Level of proof is 9.
% 0.07/0.35 % Maximum clause weight is 9.000.
% 0.07/0.35 % Given clauses 50.
% 0.07/0.35
% 0.07/0.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------