%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUN069+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 : n026.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 0.10s 0.38s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 4 unt; 0 def)
% Number of atoms : 42 ( 10 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 35 ( 7 ~; 3 |; 25 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 0 con; 1-2 aty)
% Number of variables : 36 ( 5 sgn 9 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2a,axiom,
! [X2,X9] :
? [Y2] :
( ? [Y6] :
( r4(X2,X9,Y6)
& r3(Y6,X2,Y2) )
& ? [Y3] :
( Y3 = Y2
& ? [Y14] :
( r4(X2,Y14,Y3)
& r2(X9,Y14) ) ) ),
file('theBenchmark.p',axiom_2a) ).
fof(axiom_5a,axiom,
! [X5] :
? [Y8] :
( ? [Y18] :
( Y8 = Y18
& r1(Y18) )
& ? [Y17] :
( r4(X5,Y17,Y8)
& r1(Y17) ) ),
file('theBenchmark.p',axiom_5a) ).
fof(oneeqone,conjecture,
? [Y1] :
( ? [Y2] :
( r2(Y2,Y1)
& r1(Y2) )
& Y1 = Y1 ),
file('theBenchmark.p',oneeqone) ).
fof(oneeqone_neg,negated_conjecture,
~ ? [Y1] :
( ? [Y2] :
( r2(Y2,Y1)
& r1(Y2) )
& Y1 = Y1 ),
inference(assume_negation,[status(cth)],[oneeqone]) ).
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] :
( sK0(X5) = sK3(X5)
& r1(sK0(X5))
& r4(X5,sK2(X5),sK3(X5))
& r1(sK2(X5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK0]),skolemize(Y8,sK3(X5)),skolemize(Y17,sK2(X5)),skolemize(Y18,sK0(X5))],[nnf_9]) ).
cnf(c_17,plain,
r1(sK0(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_21,negated_conjecture,
( ~ r2(B,A)
| ~ r1(B)
| A != A ),
inference(clausify,[status(thm)],[oneeqone_neg]) ).
cnf(c_44,negated_conjecture,
( ~ r2(sK0(B),A)
| A != A ),
inference(resolve,[status(thm)],[c_21,c_17]) ).
cnf(c_45,negated_conjecture,
~ r2(sK0(A),B),
inference(copy,[status(thm)],[c_44]) ).
fof(nnf_6,plain,
! [X2,X9] :
? [Y2] :
( ? [Y6] :
( r4(X2,X9,Y6)
& r3(Y6,X2,Y2) )
& ? [Y3] :
( Y2 = Y3
& ? [Y14] :
( r4(X2,Y14,Y3)
& r2(X9,Y14) ) ) ),
inference(fof_nnf,[status(thm)],[axiom_2a]) ).
fof(sk_axiom_2a,plain,
! [X2,X9] :
( r4(X2,X9,sK6(X2,X9))
& r3(sK6(X2,X9),X2,sK5(X2,X9))
& sK5(X2,X9) = sK4(X2,X9)
& r4(X2,sK1(X2,X9),sK4(X2,X9))
& r2(X9,sK1(X2,X9)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK4,sK5,sK6]),skolemize(Y2,sK5(X2,X9)),skolemize(Y3,sK4(X2,X9)),skolemize(Y14,sK1(X2,X9)),skolemize(Y6,sK6(X2,X9))],[nnf_6]) ).
cnf(c_81,plain,
r2(A,sK1(B,A)),
inference(split_conjunct,[status(thm)],[sk_axiom_2a]) ).
cnf(c_82,plain,
$false,
inference(resolve,[status(thm)],[c_81,c_45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN069+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 04:32:26 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 73502 was started by sandbox on n026,
% 0.10/0.36 % Sat Sep 26 04:32:26 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.38
% 0.10/0.38 % SZS status Theorem for theBenchmark
% 0.10/0.38
% 0.10/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.38 % Length of proof is 9.
% 0.10/0.38 % Level of proof is 4.
% 0.10/0.38 % Maximum clause weight is 5.000.
% 0.10/0.38 % Given clauses 0.
% 0.10/0.38
% 0.10/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------