%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUN068+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 : n001.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 0.14s 5.51s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 6
% Syntax : Number of formulae : 79 ( 15 unt; 0 def)
% Number of atoms : 197 ( 112 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 189 ( 71 ~; 85 |; 33 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-1 aty)
% Number of variables : 137 ( 23 sgn 39 !; 13 ?)
% 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_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(nonzerosnononesexist,conjecture,
? [Y1] :
( ! [Y4] :
( Y1 != Y4
| ~ r1(Y4) )
& ! [Y2] :
( Y1 != Y2
| ! [Y3] :
( ~ r2(Y3,Y2)
| ~ r1(Y3) ) ) ),
file('theBenchmark.p',nonzerosnononesexist) ).
fof(nonzerosnononesexist_neg,negated_conjecture,
~ ? [Y1] :
( ! [Y4] :
( Y1 != Y4
| ~ r1(Y4) )
& ! [Y2] :
( Y1 != Y2
| ! [Y3] :
( ~ r2(Y3,Y2)
| ~ r1(Y3) ) ) ),
inference(assume_negation,[status(cth)],[nonzerosnononesexist]) ).
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_29,plain,
( sK0 = A
| ~ r1(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_1]) ).
cnf(c_30,plain,
( r1(A)
| sK0 != 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] :
( ( sK1(X11) = X12
& r2(X11,X12) )
| ( sK1(X11) != X12
& ~ r2(X11,X12) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(Y21,sK1(X11))],[nnf_2]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1] :
( r2(VAR_0,VAR_1)
| sK1(VAR_0) != VAR_1 )
& ! [VAR_0,VAR_1] :
( sK1(VAR_0) = VAR_1
| ~ r2(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_32,plain,
( r2(A,B)
| sK1(A) != B ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_40,plain,
( D = A
| ~ r2(D,C)
| C != B
| ~ r2(A,B) ),
inference(clausify,[status(thm)],[axiom_3a]) ).
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] :
( sK2(X4) = X4
& r3(X4,sK6(X4),sK2(X4))
& r1(sK6(X4)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK2]),skolemize(Y9,sK2(X4)),skolemize(Y16,sK6(X4))],[nnf_8]) ).
cnf(c_42,plain,
sK2(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)],[nonzerosnononesexist_neg]) ).
fof(sk_nonzerosnononesexist_neg_sk,plain,
! [Y1] :
( ( Y1 = sK4(Y1)
& r1(sK4(Y1)) )
| ( Y1 = sK5(Y1)
& r2(sK3(Y1),sK5(Y1))
& r1(sK3(Y1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK5,sK4]),skolemize(Y2,sK5(Y1)),skolemize(Y3,sK3(Y1)),skolemize(Y4,sK4(Y1))],[nnf_12]) ).
fof(sk_nonzerosnononesexist_neg,plain,
( ! [VAR_0] :
( VAR_0 = sK4(VAR_0)
| VAR_0 = sK5(VAR_0) )
& ! [VAR_0] :
( r1(sK4(VAR_0))
| VAR_0 = sK5(VAR_0) )
& ! [VAR_0] :
( VAR_0 = sK4(VAR_0)
| r2(sK3(VAR_0),sK5(VAR_0)) )
& ! [VAR_0] :
( r1(sK4(VAR_0))
| r2(sK3(VAR_0),sK5(VAR_0)) )
& ! [VAR_0] :
( VAR_0 = sK4(VAR_0)
| r1(sK3(VAR_0)) )
& ! [VAR_0] :
( r1(sK4(VAR_0))
| r1(sK3(VAR_0)) ) ),
inference(cnf_transformation,[status(thm)],[sk_nonzerosnononesexist_neg_sk]) ).
cnf(c_54,negated_conjecture,
( r1(sK4(A))
| r1(sK3(A)) ),
inference(split_conjunct,[status(thm)],[sk_nonzerosnononesexist_neg]) ).
cnf(c_55,negated_conjecture,
( A = sK4(A)
| r1(sK3(A)) ),
inference(split_conjunct,[status(thm)],[sk_nonzerosnononesexist_neg]) ).
cnf(c_56,negated_conjecture,
( sK4(A) = A
| r1(sK3(A)) ),
inference(copy,[status(thm)],[c_55]) ).
cnf(c_57,negated_conjecture,
( r1(sK4(A))
| r2(sK3(A),sK5(A)) ),
inference(split_conjunct,[status(thm)],[sk_nonzerosnononesexist_neg]) ).
cnf(c_58,negated_conjecture,
( A = sK4(A)
| r2(sK3(A),sK5(A)) ),
inference(split_conjunct,[status(thm)],[sk_nonzerosnononesexist_neg]) ).
cnf(c_59,negated_conjecture,
( sK4(A) = A
| r2(sK3(A),sK5(A)) ),
inference(copy,[status(thm)],[c_58]) ).
cnf(c_60,negated_conjecture,
( r1(sK4(A))
| A = sK5(A) ),
inference(split_conjunct,[status(thm)],[sk_nonzerosnononesexist_neg]) ).
cnf(c_61,negated_conjecture,
( r1(sK4(A))
| sK5(A) = A ),
inference(copy,[status(thm)],[c_60]) ).
cnf(c_62,negated_conjecture,
( A = sK4(A)
| A = sK5(A) ),
inference(split_conjunct,[status(thm)],[sk_nonzerosnononesexist_neg]) ).
cnf(c_765,negated_conjecture,
( A = sK4(A)
| sK5(A) = A ),
inference(copy,[status(thm)],[c_62]) ).
cnf(c_63,negated_conjecture,
( sK4(A) = A
| sK5(A) = A ),
inference(copy,[status(thm)],[c_765]) ).
cnf(c_78,plain,
r1(sK0),
inference(xxres,[status(thm)],[c_30]) ).
cnf(c_79,plain,
r2(A,sK1(A)),
inference(xxres,[status(thm)],[c_32]) ).
cnf(c_766,plain,
( ~ r2(B,sK2(A))
| ~ r1(A) ),
inference(resolve,[status(thm)],[c_53,c_42]) ).
cnf(c_109,plain,
( ~ r2(B,A)
| ~ r1(A) ),
inference(paramod,[status(thm)],[c_42,c_766]) ).
cnf(c_767,negated_conjecture,
( sK0 = sK4(A)
| r1(sK3(A)) ),
inference(resolve,[status(thm)],[c_54,c_29]) ).
cnf(c_114,negated_conjecture,
( sK4(A) = sK0
| r1(sK3(A)) ),
inference(copy,[status(thm)],[c_767]) ).
cnf(c_768,negated_conjecture,
( sK0 = sK3(A)
| sK4(A) = A ),
inference(resolve,[status(thm)],[c_56,c_29]) ).
cnf(c_116,negated_conjecture,
( sK3(A) = sK0
| sK4(A) = A ),
inference(copy,[status(thm)],[c_768]) ).
cnf(c_769,plain,
( ~ r2(B,A)
| A != sK0 ),
inference(resolve,[status(thm)],[c_53,c_78]) ).
cnf(c_770,plain,
~ r2(A,sK2(sK0)),
inference(resolve,[status(thm)],[c_769,c_42]) ).
cnf(c_133,plain,
~ r2(A,sK0),
inference(paramod,[status(thm)],[c_42,c_770]) ).
cnf(c_134,plain,
sK1(A) != sK0,
inference(resolve,[status(thm)],[c_32,c_133]) ).
cnf(c_149,plain,
( sK1(B) != A
| ~ r1(A) ),
inference(resolve,[status(thm)],[c_79,c_53]) ).
cnf(c_150,plain,
( C = A
| sK1(C) != B
| ~ r2(A,B) ),
inference(resolve,[status(thm)],[c_79,c_40]) ).
cnf(c_771,negated_conjecture,
( sK5(B) = B
| sK1(A) != sK4(B) ),
inference(resolve,[status(thm)],[c_149,c_61]) ).
cnf(c_166,negated_conjecture,
( sK5(A) = A
| sK4(A) != sK1(B) ),
inference(copy,[status(thm)],[c_771]) ).
cnf(c_772,plain,
( sK0 = sK3(A)
| sK4(A) = sK0 ),
inference(resolve,[status(thm)],[c_114,c_29]) ).
cnf(c_183,plain,
( sK3(A) = sK0
| sK4(A) = sK0 ),
inference(copy,[status(thm)],[c_772]) ).
cnf(c_773,plain,
( r1(A)
| A != sK0 ),
inference(copy,[status(thm)],[c_30]) ).
cnf(c_240,plain,
( r1(sK4(A))
| sK3(A) = sK0 ),
inference(resolve,[status(thm)],[c_183,c_773]) ).
cnf(c_774,plain,
( sK1(B) != sK4(A)
| sK3(A) = sK0 ),
inference(resolve,[status(thm)],[c_240,c_149]) ).
cnf(c_242,plain,
( sK4(A) != sK1(B)
| sK3(A) = sK0 ),
inference(copy,[status(thm)],[c_774]) ).
cnf(c_775,negated_conjecture,
( sK5(sK1(A)) = sK1(A)
| sK5(sK1(A)) = sK1(A) ),
inference(resolve,[status(thm)],[c_166,c_63]) ).
cnf(c_273,negated_conjecture,
sK5(sK1(A)) = sK1(A),
inference(copy,[status(thm)],[c_775]) ).
cnf(c_776,plain,
( sK3(sK1(A)) = sK0
| sK3(sK1(A)) = sK0 ),
inference(resolve,[status(thm)],[c_242,c_116]) ).
cnf(c_277,plain,
sK3(sK1(A)) = sK0,
inference(copy,[status(thm)],[c_776]) ).
cnf(c_777,negated_conjecture,
( sK4(B) = B
| A = sK3(B)
| sK1(A) != sK5(B) ),
inference(resolve,[status(thm)],[c_150,c_59]) ).
cnf(c_778,negated_conjecture,
( sK4(B) = B
| A = sK3(B)
| sK5(B) != sK1(A) ),
inference(copy,[status(thm)],[c_777]) ).
cnf(c_370,negated_conjecture,
( sK4(A) = A
| sK3(A) = B
| sK5(A) != sK1(B) ),
inference(copy,[status(thm)],[c_778]) ).
cnf(c_779,negated_conjecture,
( r1(sK4(B))
| A = sK3(B)
| sK1(A) != sK5(B) ),
inference(resolve,[status(thm)],[c_150,c_57]) ).
cnf(c_780,negated_conjecture,
( r1(sK4(B))
| A = sK3(B)
| sK5(B) != sK1(A) ),
inference(copy,[status(thm)],[c_779]) ).
cnf(c_371,negated_conjecture,
( r1(sK4(A))
| sK3(A) = B
| sK5(A) != sK1(B) ),
inference(copy,[status(thm)],[c_780]) ).
cnf(c_781,plain,
( r1(sK4(sK1(A)))
| sK3(sK1(A)) = A ),
inference(resolve,[status(thm)],[c_371,c_273]) ).
cnf(c_468,plain,
( r1(sK4(sK1(A)))
| sK0 = A ),
inference(paramod,[status(thm)],[c_277,c_781]) ).
cnf(c_501,plain,
( ~ r2(B,sK4(sK1(A)))
| sK0 = A ),
inference(resolve,[status(thm)],[c_468,c_109]) ).
cnf(c_782,plain,
( sK4(sK1(A)) = sK1(A)
| sK3(sK1(A)) = A ),
inference(resolve,[status(thm)],[c_370,c_273]) ).
cnf(c_520,plain,
( sK4(sK1(A)) = sK1(A)
| sK0 = A ),
inference(paramod,[status(thm)],[c_277,c_782]) ).
cnf(c_783,plain,
sK0 != sK1(A),
inference(copy,[status(thm)],[c_134]) ).
cnf(c_547,plain,
~ r2(A,sK4(sK1(sK1(B)))),
inference(resolve,[status(thm)],[c_501,c_783]) ).
cnf(c_784,plain,
sK1(A) != sK4(sK1(sK1(B))),
inference(resolve,[status(thm)],[c_32,c_547]) ).
cnf(c_550,plain,
sK4(sK1(sK1(A))) != sK1(B),
inference(copy,[status(thm)],[c_784]) ).
cnf(c_785,plain,
sK0 = sK1(A),
inference(resolve,[status(thm)],[c_520,c_550]) ).
cnf(c_786,plain,
sK1(A) = sK0,
inference(copy,[status(thm)],[c_785]) ).
cnf(c_764,plain,
$false,
inference(resolve,[status(thm)],[c_134,c_786]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN068+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n001.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Sat Sep 26 04:35:33 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.38 % Process 913452 was started by sandbox on n001,
% 0.10/5.38 % Sat Sep 26 04:35:33 2026
% 0.10/5.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/5.38
% 0.10/5.38 % From the command line: assign(max_seconds, 300).
% 0.14/5.51
% 0.14/5.51 % SZS status Theorem for theBenchmark
% 0.14/5.51
% 0.14/5.51 % Proof 1 at 0.08 (+ 0.04) seconds.
% 0.14/5.51 % Length of proof is 45.
% 0.14/5.51 % Level of proof is 11.
% 0.14/5.51 % Maximum clause weight is 29.000.
% 0.14/5.51 % Given clauses 260.
% 0.14/5.51
% 0.14/5.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------