%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUN067+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 : 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 0.16s 0.44s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 12 unt; 0 def)
% Number of atoms : 77 ( 31 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 72 ( 27 ~; 15 |; 30 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 65 ( 17 sgn 21 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_1,axiom,
? [Y24] :
! [X19] :
( ( X19 = Y24
& r1(X19) )
| ( X19 != Y24
& ~ r1(X19) ) ),
file('theBenchmark.p',axiom_1) ).
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_5a,axiom,
! [X5] :
? [Y8] :
( ? [Y18] :
( Y8 = Y18
& r1(Y18) )
& ? [Y17] :
( r4(X5,Y17,Y8)
& r1(Y17) ) ),
file('theBenchmark.p',axiom_5a) ).
fof(axiom_7a,axiom,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( Y20 != Y10
| ~ r1(Y20) ) ),
file('theBenchmark.p',axiom_7a) ).
fof(nonzerosexist,conjecture,
? [Y1] :
! [Y2] :
( Y1 != Y2
| ~ r1(Y2) ),
file('theBenchmark.p',nonzerosexist) ).
fof(nonzerosexist_neg,negated_conjecture,
~ ? [Y1] :
! [Y2] :
( Y1 != Y2
| ~ r1(Y2) ),
inference(assume_negation,[status(cth)],[nonzerosexist]) ).
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_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] :
( sK1(X5) = sK5(X5)
& r1(sK1(X5))
& r4(X5,sK4(X5),sK5(X5))
& r1(sK4(X5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK1]),skolemize(Y8,sK5(X5)),skolemize(Y17,sK4(X5)),skolemize(Y18,sK1(X5))],[nnf_9]) ).
cnf(c_17,plain,
r1(sK1(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_20,plain,
( ~ r2(C,B)
| B != A
| ~ r1(A) ),
inference(clausify,[status(thm)],[axiom_7a]) ).
fof(nnf_12,plain,
! [Y1] :
? [Y2] :
( Y1 = Y2
& r1(Y2) ),
inference(fof_nnf,[status(thm)],[nonzerosexist_neg]) ).
fof(sk_nonzerosexist_neg,plain,
! [Y1] :
( Y1 = sK2(Y1)
& r1(sK2(Y1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(Y2,sK2(Y1))],[nnf_12]) ).
cnf(c_21,negated_conjecture,
r1(sK2(A)),
inference(split_conjunct,[status(thm)],[sk_nonzerosexist_neg]) ).
cnf(c_38,negated_conjecture,
sK0 = sK2(A),
inference(resolve,[status(thm)],[c_21,c_14]) ).
cnf(c_39,negated_conjecture,
sK2(A) = sK0,
inference(copy,[status(thm)],[c_38]) ).
cnf(c_47,plain,
( ~ r2(C,A)
| A != sK1(B) ),
inference(resolve,[status(thm)],[c_20,c_17]) ).
cnf(c_48,plain,
( ~ r2(C,B)
| sK1(A) != B ),
inference(copy,[status(thm)],[c_47]) ).
cnf(c_57,plain,
sK0 = sK1(A),
inference(resolve,[status(thm)],[c_17,c_14]) ).
cnf(c_58,plain,
sK1(A) = sK0,
inference(copy,[status(thm)],[c_57]) ).
cnf(c_63,negated_conjecture,
A = sK2(A),
inference(split_conjunct,[status(thm)],[sk_nonzerosexist_neg]) ).
cnf(c_92,negated_conjecture,
A = sK0,
inference(paramod,[status(thm)],[c_39,c_63]) ).
cnf(c_64,negated_conjecture,
sK0 = A,
inference(copy,[status(thm)],[c_92]) ).
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),sK7(X1,X8))
& sK7(X1,X8) = sK6(X1,X8)
& r3(X1,sK3(X1,X8),sK6(X1,X8))
& r2(X8,sK3(X1,X8)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK6,sK7,sK8]),skolemize(Y4,sK7(X1,X8)),skolemize(Y5,sK6(X1,X8)),skolemize(Y15,sK3(X1,X8)),skolemize(Y7,sK8(X1,X8))],[nnf_5]) ).
cnf(c_78,plain,
r2(A,sK3(B,A)),
inference(split_conjunct,[status(thm)],[sk_axiom_1a]) ).
cnf(c_93,plain,
( ~ r2(C,B)
| sK0 != B ),
inference(paramod,[status(thm)],[c_58,c_48]) ).
cnf(c_90,negated_conjecture,
~ r2(A,B),
inference(resolve,[status(thm)],[c_64,c_93]) ).
cnf(c_91,plain,
$false,
inference(resolve,[status(thm)],[c_90,c_78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUN067+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n014.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sat Sep 26 04:29:47 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.42 % Process 2142177 was started by sandbox2 on n014,
% 0.16/0.42 % Sat Sep 26 04:29:47 2026
% 0.16/0.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.43
% 0.16/0.43 % From the command line: assign(max_seconds, 300).
% 0.16/0.44
% 0.16/0.44 % SZS status Theorem for theBenchmark
% 0.16/0.44
% 0.16/0.44 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.16/0.44 % Length of proof is 20.
% 0.16/0.44 % Level of proof is 6.
% 0.16/0.44 % Maximum clause weight is 7.000.
% 0.16/0.44 % Given clauses 0.
% 0.16/0.44
% 0.16/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------