%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUN088+3 : 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 : 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 08:19:25 AM UTC 2026
% Result : Theorem 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 11 unt; 0 def)
% Number of atoms : 54 ( 24 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 58 ( 29 ~; 18 |; 11 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 27 ( 5 sgn 12 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_1,axiom,
? [Y24] :
! [X19] :
( ( X19 = Y24
& r1(X19) )
| ( X19 != Y24
& ~ r1(X19) ) ),
file('theBenchmark.p',axiom_1) ).
fof(axiom_7a,axiom,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( Y20 != Y10
| ~ r1(Y20) ) ),
file('theBenchmark.p',axiom_7a) ).
fof(zerouneqone2,conjecture,
! [Y0] :
( ~ r1(Y0)
| ! [Y1] :
( ~ r2(Y0,Y1)
| Y0 != Y1 ) ),
file('theBenchmark.p',zerouneqone2) ).
fof(zerouneqone2_neg,negated_conjecture,
~ ! [Y0] :
( ~ r1(Y0)
| ! [Y1] :
( ~ r2(Y0,Y1)
| Y0 != Y1 ) ),
inference(assume_negation,[status(cth)],[zerouneqone2]) ).
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_13,plain,
( r1(A)
| sK0 != A ),
inference(split_conjunct,[status(thm)],[sk_axiom_1]) ).
cnf(c_14,plain,
( sK0 = A
| ~ r1(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_1]) ).
cnf(c_20,plain,
( ~ r2(C,B)
| B != A
| ~ r1(A) ),
inference(clausify,[status(thm)],[axiom_7a]) ).
fof(nnf_12,plain,
? [Y0] :
( r1(Y0)
& ? [Y1] :
( r2(Y0,Y1)
& Y0 = Y1 ) ),
inference(fof_nnf,[status(thm)],[zerouneqone2_neg]) ).
fof(sk_zerouneqone2_neg,plain,
( r1(sK1)
& r2(sK1,sK2)
& sK1 = sK2 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(Y0,sK1),skolemize(Y1,sK2)],[nnf_12]) ).
cnf(c_21,negated_conjecture,
r1(sK1),
inference(split_conjunct,[status(thm)],[sk_zerouneqone2_neg]) ).
cnf(c_38,negated_conjecture,
sK0 = sK1,
inference(resolve,[status(thm)],[c_21,c_14]) ).
cnf(c_39,negated_conjecture,
sK1 = sK0,
inference(copy,[status(thm)],[c_38]) ).
cnf(c_42,plain,
( sK0 != B
| ~ r2(C,A)
| A != B ),
inference(resolve,[status(thm)],[c_20,c_13]) ).
cnf(c_63,negated_conjecture,
r2(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_zerouneqone2_neg]) ).
cnf(c_64,negated_conjecture,
r2(sK0,sK2),
inference(paramod,[status(thm)],[c_39,c_63]) ).
cnf(c_65,negated_conjecture,
sK1 = sK2,
inference(split_conjunct,[status(thm)],[sk_zerouneqone2_neg]) ).
cnf(c_93,negated_conjecture,
sK0 = sK2,
inference(paramod,[status(thm)],[c_39,c_65]) ).
cnf(c_66,negated_conjecture,
sK2 = sK0,
inference(copy,[status(thm)],[c_93]) ).
cnf(c_94,plain,
( ~ r2(B,sK0)
| sK0 != A ),
inference(factor,[status(thm)],[c_42]) ).
cnf(c_91,plain,
~ r2(A,sK0),
inference(copy,[status(thm)],[c_94]) ).
cnf(c_95,negated_conjecture,
r2(sK0,sK0),
inference(paramod,[status(thm)],[c_66,c_64]) ).
cnf(c_92,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_91,c_95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN088+3 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n012.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 04:32:35 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 3915827 was started by sandbox2 on n012,
% 0.09/0.35 % Sat Sep 26 04:32:35 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 0.12/0.37
% 0.12/0.37 % SZS status Theorem for theBenchmark
% 0.12/0.37
% 0.12/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.12/0.37 % Length of proof is 16.
% 0.12/0.37 % Level of proof is 5.
% 0.12/0.37 % Maximum clause weight is 9.000.
% 0.12/0.37 % Given clauses 0.
% 0.12/0.37
% 0.12/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------