%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUN089+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 : n002.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 0.15s 0.44s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 9 unt; 0 def)
% Number of atoms : 60 ( 23 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 70 ( 33 ~; 22 |; 15 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 33 ( 5 sgn 16 !; 6 ?)
% 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(zerouneqtwo,conjecture,
! [Y1] :
( ! [Y4] :
( ~ r1(Y4)
| Y4 != Y1 )
| ! [Y2] :
( ~ r2(Y2,Y1)
| ! [Y3] :
( ~ r2(Y3,Y2)
| ~ r1(Y3) ) ) ),
file('theBenchmark.p',zerouneqtwo) ).
fof(zerouneqtwo_neg,negated_conjecture,
~ ! [Y1] :
( ! [Y4] :
( ~ r1(Y4)
| Y4 != Y1 )
| ! [Y2] :
( ~ r2(Y2,Y1)
| ! [Y3] :
( ~ r2(Y3,Y2)
| ~ r1(Y3) ) ) ),
inference(assume_negation,[status(cth)],[zerouneqtwo]) ).
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,
? [Y1] :
( ? [Y4] :
( r1(Y4)
& Y1 = Y4 )
& ? [Y2] :
( r2(Y2,Y1)
& ? [Y3] :
( r2(Y3,Y2)
& r1(Y3) ) ) ),
inference(fof_nnf,[status(thm)],[zerouneqtwo_neg]) ).
fof(sk_zerouneqtwo_neg,plain,
( r1(sK1)
& sK2 = sK1
& r2(sK3,sK2)
& r2(sK4,sK3)
& r1(sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK3,sK2,sK1]),skolemize(Y1,sK2),skolemize(Y2,sK3),skolemize(Y3,sK4),skolemize(Y4,sK1)],[nnf_12]) ).
cnf(c_22,negated_conjecture,
r1(sK1),
inference(split_conjunct,[status(thm)],[sk_zerouneqtwo_neg]) ).
cnf(c_39,negated_conjecture,
sK0 = sK1,
inference(resolve,[status(thm)],[c_22,c_14]) ).
cnf(c_40,negated_conjecture,
sK1 = sK0,
inference(copy,[status(thm)],[c_39]) ).
cnf(c_46,plain,
( sK0 != B
| ~ r2(C,A)
| A != B ),
inference(resolve,[status(thm)],[c_20,c_13]) ).
cnf(c_67,negated_conjecture,
sK2 = sK1,
inference(split_conjunct,[status(thm)],[sk_zerouneqtwo_neg]) ).
cnf(c_68,negated_conjecture,
sK2 = sK0,
inference(paramod,[status(thm)],[c_40,c_67]) ).
cnf(c_69,negated_conjecture,
r2(sK3,sK2),
inference(split_conjunct,[status(thm)],[sk_zerouneqtwo_neg]) ).
cnf(c_70,negated_conjecture,
r2(sK3,sK0),
inference(paramod,[status(thm)],[c_68,c_69]) ).
cnf(c_99,plain,
( ~ r2(B,sK0)
| sK0 != A ),
inference(factor,[status(thm)],[c_46]) ).
cnf(c_97,plain,
~ r2(A,sK0),
inference(copy,[status(thm)],[c_99]) ).
cnf(c_98,plain,
$false,
inference(resolve,[status(thm)],[c_97,c_70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUN089+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.40 % Computer : n002.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat Sep 26 04:35:50 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.41 % Process 835643 was started by sandbox2 on n002,
% 0.15/0.41 % Sat Sep 26 04:35:50 2026
% 0.15/0.41 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.42
% 0.15/0.42 % From the command line: assign(max_seconds, 300).
% 0.15/0.44
% 0.15/0.44 % SZS status Theorem for theBenchmark
% 0.15/0.44
% 0.15/0.44 % Proof 1 at 0.00 (+ 0.01) seconds.
% 0.15/0.44 % Length of proof is 16.
% 0.15/0.44 % Level of proof is 6.
% 0.15/0.44 % Maximum clause weight is 9.000.
% 0.15/0.44 % Given clauses 0.
% 0.15/0.44
% 0.15/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------