%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL483+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 07:59:01 AM UTC 2026
% Result : Theorem 0.03s 0.33s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 35 ( 21 unt; 0 def)
% Number of atoms : 55 ( 12 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 36 ( 16 ~; 12 |; 3 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 16 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(modus_tollens,axiom,
( modus_tollens
<=> ! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),
file('theBenchmark.p',modus_tollens) ).
fof(r3,axiom,
( r3
<=> ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) ),
file('theBenchmark.p',r3) ).
fof(op_or,axiom,
( op_or
=> ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
file('theBenchmark.p',op_or) ).
fof(op_implies_and,axiom,
( op_implies_and
=> ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ),
file('theBenchmark.p',op_implies_and) ).
fof(op_implies_or,axiom,
( op_implies_or
=> ! [X,Y] : implies(X,Y) = or(not(X),Y) ),
file('theBenchmark.p',op_implies_or) ).
fof(hilbert_modus_tollens,conjecture,
modus_tollens,
file('theBenchmark.p',hilbert_modus_tollens) ).
fof(hilbert_modus_tollens_neg,negated_conjecture,
~ modus_tollens,
inference(assume_negation,[status(cth)],[hilbert_modus_tollens]) ).
fof(nnf_3,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))
| modus_tollens )
& ( ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| ~ modus_tollens ) ),
inference(fof_nnf,[status(thm)],[modus_tollens]) ).
fof(sk_modus_tollens_sk,plain,
( ( ~ is_a_theorem(implies(implies(not(sK0),not(sK1)),implies(sK1,sK0)))
| modus_tollens )
& ( ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| ~ modus_tollens ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK1),skolemize(Y,sK0)],[nnf_3]) ).
fof(sk_modus_tollens,plain,
( ( ~ is_a_theorem(implies(implies(not(sK0),not(sK1)),implies(sK1,sK0)))
| modus_tollens )
& ! [VAR_0,VAR_1] :
( is_a_theorem(implies(implies(not(VAR_0),not(VAR_1)),implies(VAR_1,VAR_0)))
| ~ modus_tollens ) ),
inference(cnf_transformation,[status(thm)],[sk_modus_tollens_sk]) ).
cnf(c_41,plain,
( ~ is_a_theorem(implies(implies(not(sK0),not(sK1)),implies(sK1,sK0)))
| modus_tollens ),
inference(split_conjunct,[status(thm)],[sk_modus_tollens]) ).
cnf(c_82,plain,
( is_a_theorem(implies(or(A,B),or(B,A)))
| ~ r3 ),
inference(clausify,[status(thm)],[r3]) ).
cnf(c_88,plain,
( or(A,B) = not(and(not(A),not(B)))
| ~ op_or ),
inference(clausify,[status(thm)],[op_or]) ).
cnf(c_89,plain,
( not(and(not(A),not(B))) = or(A,B)
| ~ op_or ),
inference(copy,[status(thm)],[c_88]) ).
cnf(c_92,plain,
( not(and(A,not(B))) = implies(A,B)
| ~ op_implies_and ),
inference(clausify,[status(thm)],[op_implies_and]) ).
cnf(c_93,plain,
( or(not(A),B) = implies(A,B)
| ~ op_implies_or ),
inference(clausify,[status(thm)],[op_implies_or]) ).
fof(principia_op_implies_or,axiom,
op_implies_or,
file('theBenchmark.p',principia_op_implies_or) ).
cnf(c_96,plain,
op_implies_or,
inference(clausify,[status(thm)],[principia_op_implies_or]) ).
fof(principia_r3,axiom,
r3,
file('theBenchmark.p',principia_r3) ).
cnf(c_102,plain,
r3,
inference(clausify,[status(thm)],[principia_r3]) ).
fof(hilbert_op_or,axiom,
op_or,
file('theBenchmark.p',hilbert_op_or) ).
cnf(c_106,plain,
op_or,
inference(clausify,[status(thm)],[hilbert_op_or]) ).
fof(hilbert_op_implies_and,axiom,
op_implies_and,
file('theBenchmark.p',hilbert_op_implies_and) ).
cnf(c_107,plain,
op_implies_and,
inference(clausify,[status(thm)],[hilbert_op_implies_and]) ).
cnf(c_108,negated_conjecture,
~ modus_tollens,
inference(clausify,[status(thm)],[hilbert_modus_tollens_neg]) ).
cnf(c_109,plain,
or(not(A),B) = implies(A,B),
inference(resolve,[status(thm)],[c_96,c_93]) ).
cnf(c_115,plain,
is_a_theorem(implies(or(A,B),or(B,A))),
inference(resolve,[status(thm)],[c_102,c_82]) ).
cnf(c_119,plain,
not(and(not(A),not(B))) = or(A,B),
inference(resolve,[status(thm)],[c_106,c_89]) ).
cnf(c_120,plain,
not(and(A,not(B))) = implies(A,B),
inference(resolve,[status(thm)],[c_107,c_92]) ).
cnf(c_121,negated_conjecture,
~ is_a_theorem(implies(implies(not(sK0),not(sK1)),implies(sK1,sK0))),
inference(resolve,[status(thm)],[c_108,c_41]) ).
cnf(c_181,plain,
implies(not(A),B) = or(A,B),
inference(paramod,[status(thm)],[c_120,c_119]) ).
cnf(c_129,plain,
or(A,B) = implies(not(A),B),
inference(copy,[status(thm)],[c_181]) ).
cnf(c_139,plain,
is_a_theorem(implies(or(A,not(B)),implies(B,A))),
inference(paramod,[status(thm)],[c_109,c_115]) ).
cnf(c_182,plain,
~ is_a_theorem(implies(or(sK0,not(sK1)),implies(sK1,sK0))),
inference(paramod,[status(thm)],[c_129,c_121]) ).
cnf(c_180,plain,
$false,
inference(resolve,[status(thm)],[c_139,c_182]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL483+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.31 % Computer : n012.cluster.edu
% 0.03/0.31 % Model : x86_64 x86_64
% 0.03/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.31 % Memory : 8046.5625MB
% 0.03/0.31 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Fri Sep 25 22:38:35 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.31 % Process 3236975 was started by sandbox on n012,
% 0.03/0.31 % Fri Sep 25 22:38:35 2026
% 0.03/0.31 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.03/0.32
% 0.03/0.32 % From the command line: assign(max_seconds, 300).
% 0.03/0.33
% 0.03/0.33 % SZS status Theorem for theBenchmark
% 0.03/0.33
% 0.03/0.33 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.03/0.33 % Length of proof is 25.
% 0.03/0.33 % Level of proof is 5.
% 0.03/0.33 % Maximum clause weight is 11.000.
% 0.03/0.33 % Given clauses 61.
% 0.03/0.33
% 0.03/0.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------