%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL517+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 : 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 07:59:05 AM UTC 2026
% Result : Theorem 19.04s 2.85s
% Output : CNFRefutation 19.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 15
% Syntax : Number of formulae : 91 ( 55 unt; 0 def)
% Number of atoms : 144 ( 13 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 99 ( 46 ~; 37 |; 7 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 9 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 141 ( 9 sgn 20 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(modus_ponens,axiom,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(implies(X,Y))
& is_a_theorem(X) )
=> is_a_theorem(Y) ) ),
file('theBenchmark.p',modus_ponens) ).
fof(kn1,axiom,
( kn1
<=> ! [P] : is_a_theorem(implies(P,and(P,P))) ),
file('theBenchmark.p',kn1) ).
fof(kn2,axiom,
( kn2
<=> ! [P,Q] : is_a_theorem(implies(and(P,Q),P)) ),
file('theBenchmark.p',kn2) ).
fof(kn3,axiom,
( kn3
<=> ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) ),
file('theBenchmark.p',kn3) ).
fof(cn3,axiom,
( cn3
<=> ! [P] : is_a_theorem(implies(implies(not(P),P),P)) ),
file('theBenchmark.p',cn3) ).
fof(r1,axiom,
( r1
<=> ! [P] : is_a_theorem(implies(or(P,P),P)) ),
file('theBenchmark.p',r1) ).
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(luka_cn3,conjecture,
cn3,
file('theBenchmark.p',luka_cn3) ).
fof(luka_cn3_neg,negated_conjecture,
~ cn3,
inference(assume_negation,[status(cth)],[luka_cn3]) ).
cnf(c_33,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(A,B))
| ~ is_a_theorem(A)
| ~ modus_ponens ),
inference(clausify,[status(thm)],[modus_ponens]) ).
cnf(c_66,plain,
( is_a_theorem(implies(A,and(A,A)))
| ~ kn1 ),
inference(clausify,[status(thm)],[kn1]) ).
cnf(c_68,plain,
( is_a_theorem(implies(and(A,B),A))
| ~ kn2 ),
inference(clausify,[status(thm)],[kn2]) ).
cnf(c_70,plain,
( is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),not(and(C,A)))))
| ~ kn3 ),
inference(clausify,[status(thm)],[kn3]) ).
fof(nnf_21,plain,
( ( ? [P] : ~ is_a_theorem(implies(implies(not(P),P),P))
| cn3 )
& ( ! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0))
| ~ cn3 ) ),
inference(fof_nnf,[status(thm)],[cn3]) ).
fof(sk_cn3_sk,plain,
( ( ~ is_a_theorem(implies(implies(not(sK0),sK0),sK0))
| cn3 )
& ( ! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0))
| ~ cn3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(P,sK0)],[nnf_21]) ).
fof(sk_cn3,plain,
( ( ~ is_a_theorem(implies(implies(not(sK0),sK0),sK0))
| cn3 )
& ! [VAR_0] :
( is_a_theorem(implies(implies(not(VAR_0),VAR_0),VAR_0))
| ~ cn3 ) ),
inference(cnf_transformation,[status(thm)],[sk_cn3_sk]) ).
cnf(c_77,plain,
( ~ is_a_theorem(implies(implies(not(sK0),sK0),sK0))
| cn3 ),
inference(split_conjunct,[status(thm)],[sk_cn3]) ).
fof(nnf_22,plain,
( ( ? [P] : ~ is_a_theorem(implies(or(P,P),P))
| r1 )
& ( ! [X0] : is_a_theorem(implies(or(X0,X0),X0))
| ~ r1 ) ),
inference(fof_nnf,[status(thm)],[r1]) ).
fof(sk_r1_sk,plain,
( ( ~ is_a_theorem(implies(or(sK1,sK1),sK1))
| r1 )
& ( ! [X0] : is_a_theorem(implies(or(X0,X0),X0))
| ~ r1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(P,sK1)],[nnf_22]) ).
fof(sk_r1,plain,
( ( ~ is_a_theorem(implies(or(sK1,sK1),sK1))
| r1 )
& ! [VAR_0] :
( is_a_theorem(implies(or(VAR_0,VAR_0),VAR_0))
| ~ r1 ) ),
inference(cnf_transformation,[status(thm)],[sk_r1_sk]) ).
cnf(c_78,plain,
( is_a_theorem(implies(or(A,A),A))
| ~ r1 ),
inference(split_conjunct,[status(thm)],[sk_r1]) ).
cnf(c_79,plain,
( ~ is_a_theorem(implies(or(sK1,sK1),sK1))
| r1 ),
inference(split_conjunct,[status(thm)],[sk_r1]) ).
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]) ).
fof(rosser_op_or,axiom,
op_or,
file('theBenchmark.p',rosser_op_or) ).
cnf(c_96,plain,
op_or,
inference(clausify,[status(thm)],[rosser_op_or]) ).
fof(rosser_op_implies_and,axiom,
op_implies_and,
file('theBenchmark.p',rosser_op_implies_and) ).
cnf(c_97,plain,
op_implies_and,
inference(clausify,[status(thm)],[rosser_op_implies_and]) ).
fof(rosser_modus_ponens,axiom,
modus_ponens,
file('theBenchmark.p',rosser_modus_ponens) ).
cnf(c_99,plain,
modus_ponens,
inference(clausify,[status(thm)],[rosser_modus_ponens]) ).
fof(rosser_kn1,axiom,
kn1,
file('theBenchmark.p',rosser_kn1) ).
cnf(c_100,plain,
kn1,
inference(clausify,[status(thm)],[rosser_kn1]) ).
fof(rosser_kn2,axiom,
kn2,
file('theBenchmark.p',rosser_kn2) ).
cnf(c_101,plain,
kn2,
inference(clausify,[status(thm)],[rosser_kn2]) ).
fof(rosser_kn3,axiom,
kn3,
file('theBenchmark.p',rosser_kn3) ).
cnf(c_102,plain,
kn3,
inference(clausify,[status(thm)],[rosser_kn3]) ).
cnf(c_105,negated_conjecture,
~ cn3,
inference(clausify,[status(thm)],[luka_cn3_neg]) ).
cnf(c_106,plain,
not(and(not(A),not(B))) = or(A,B),
inference(resolve,[status(thm)],[c_96,c_89]) ).
cnf(c_107,plain,
not(and(A,not(B))) = implies(A,B),
inference(resolve,[status(thm)],[c_97,c_92]) ).
cnf(c_109,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(A,B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_99,c_33]) ).
cnf(c_110,plain,
is_a_theorem(implies(A,and(A,A))),
inference(resolve,[status(thm)],[c_100,c_66]) ).
cnf(c_111,plain,
is_a_theorem(implies(and(A,B),A)),
inference(resolve,[status(thm)],[c_101,c_68]) ).
cnf(c_112,plain,
is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),not(and(C,A))))),
inference(resolve,[status(thm)],[c_102,c_70]) ).
cnf(c_114,negated_conjecture,
~ is_a_theorem(implies(implies(not(sK0),sK0),sK0)),
inference(resolve,[status(thm)],[c_105,c_77]) ).
cnf(c_116,plain,
not(and(or(A,B),not(C))) = or(and(not(A),not(B)),C),
inference(paramod,[status(thm)],[c_106,c_106]) ).
cnf(c_118,plain,
not(and(implies(A,B),not(C))) = or(and(A,not(B)),C),
inference(paramod,[status(thm)],[c_107,c_106]) ).
cnf(c_15303,plain,
implies(not(A),B) = or(A,B),
inference(paramod,[status(thm)],[c_107,c_106]) ).
cnf(c_120,plain,
or(A,B) = implies(not(A),B),
inference(copy,[status(thm)],[c_15303]) ).
cnf(c_127,plain,
is_a_theorem(implies(implies(not(A),B),implies(not(and(B,not(C))),or(C,A)))),
inference(paramod,[status(thm)],[c_106,c_112]) ).
cnf(c_129,plain,
is_a_theorem(implies(implies(not(A),B),implies(not(and(B,C)),implies(C,A)))),
inference(paramod,[status(thm)],[c_107,c_112]) ).
cnf(c_139,plain,
or(and(not(A),not(B)),C) = implies(or(A,B),C),
inference(paramod,[status(thm)],[c_116,c_107]) ).
cnf(c_166,plain,
or(and(A,not(B)),C) = implies(implies(A,B),C),
inference(paramod,[status(thm)],[c_118,c_107]) ).
cnf(c_207,plain,
~ is_a_theorem(implies(or(sK0,sK0),sK0)),
inference(paramod,[status(thm)],[c_120,c_114]) ).
cnf(c_235,plain,
~ r1,
inference(resolve,[status(thm)],[c_78,c_207]) ).
cnf(c_236,plain,
~ is_a_theorem(implies(or(sK1,sK1),sK1)),
inference(resolve,[status(thm)],[c_235,c_79]) ).
cnf(c_316,plain,
~ is_a_theorem(implies(implies(not(sK1),sK1),sK1)),
inference(paramod,[status(thm)],[c_120,c_236]) ).
cnf(c_15304,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(implies(A,and(A,A)),B)) ),
inference(resolve,[status(thm)],[c_109,c_110]) ).
cnf(c_321,plain,
~ is_a_theorem(implies(implies(A,and(A,A)),implies(implies(not(sK1),sK1),sK1))),
inference(resolve,[status(thm)],[c_15304,c_316]) ).
cnf(c_462,plain,
is_a_theorem(implies(implies(not(A),B),implies(implies(B,C),or(C,A)))),
inference(paramod,[status(thm)],[c_107,c_127]) ).
cnf(c_605,plain,
( is_a_theorem(implies(implies(B,C),or(C,A)))
| ~ is_a_theorem(implies(not(A),B)) ),
inference(resolve,[status(thm)],[c_462,c_109]) ).
cnf(c_628,plain,
is_a_theorem(implies(or(A,B),implies(implies(B,C),or(C,A)))),
inference(paramod,[status(thm)],[c_120,c_462]) ).
cnf(c_632,plain,
is_a_theorem(implies(implies(not(A),B),implies(implies(B,and(C,not(D))),implies(implies(C,D),A)))),
inference(paramod,[status(thm)],[c_166,c_462]) ).
cnf(c_636,plain,
is_a_theorem(implies(implies(and(not(A),not(A)),B),or(B,A))),
inference(resolve,[status(thm)],[c_605,c_110]) ).
cnf(c_639,plain,
( is_a_theorem(implies(implies(B,C),or(C,A)))
| ~ is_a_theorem(or(A,B)) ),
inference(resolve,[status(thm)],[c_628,c_109]) ).
cnf(c_657,plain,
is_a_theorem(implies(or(A,not(B)),implies(or(B,C),or(C,A)))),
inference(paramod,[status(thm)],[c_120,c_628]) ).
cnf(c_720,plain,
is_a_theorem(implies(implies(not(A),B),or(and(B,C),implies(C,A)))),
inference(paramod,[status(thm)],[c_120,c_129]) ).
cnf(c_864,plain,
( is_a_theorem(implies(or(B,C),or(C,A)))
| ~ is_a_theorem(or(A,not(B))) ),
inference(resolve,[status(thm)],[c_657,c_109]) ).
cnf(c_928,plain,
is_a_theorem(implies(or(A,B),or(and(B,C),implies(C,A)))),
inference(paramod,[status(thm)],[c_120,c_720]) ).
cnf(c_1267,plain,
( is_a_theorem(or(and(B,C),implies(C,A)))
| ~ is_a_theorem(or(A,B)) ),
inference(resolve,[status(thm)],[c_928,c_109]) ).
cnf(c_2573,plain,
( is_a_theorem(or(B,A))
| ~ is_a_theorem(implies(and(not(A),not(A)),B)) ),
inference(resolve,[status(thm)],[c_636,c_109]) ).
cnf(c_2644,plain,
is_a_theorem(or(not(A),A)),
inference(resolve,[status(thm)],[c_2573,c_111]) ).
cnf(c_2648,plain,
is_a_theorem(implies(implies(A,B),or(B,not(A)))),
inference(resolve,[status(thm)],[c_2644,c_639]) ).
cnf(c_2688,plain,
is_a_theorem(implies(not(not(A)),A)),
inference(paramod,[status(thm)],[c_120,c_2644]) ).
cnf(c_2704,plain,
( is_a_theorem(A)
| ~ is_a_theorem(not(not(A))) ),
inference(resolve,[status(thm)],[c_2688,c_109]) ).
cnf(c_3436,plain,
( is_a_theorem(or(B,not(A)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_2648,c_109]) ).
cnf(c_3516,plain,
is_a_theorem(or(A,not(and(A,B)))),
inference(resolve,[status(thm)],[c_3436,c_111]) ).
cnf(c_3517,plain,
is_a_theorem(or(and(A,A),not(A))),
inference(resolve,[status(thm)],[c_3436,c_110]) ).
cnf(c_3569,plain,
is_a_theorem(implies(or(A,A),not(not(A)))),
inference(paramod,[status(thm)],[c_139,c_3517]) ).
cnf(c_3582,plain,
is_a_theorem(implies(or(and(A,B),C),or(C,A))),
inference(resolve,[status(thm)],[c_3516,c_864]) ).
cnf(c_3623,plain,
is_a_theorem(or(A,implies(A,B))),
inference(paramod,[status(thm)],[c_107,c_3516]) ).
cnf(c_4409,plain,
is_a_theorem(or(and(implies(A,B),C),implies(C,A))),
inference(resolve,[status(thm)],[c_3623,c_1267]) ).
cnf(c_5495,plain,
( is_a_theorem(not(not(A)))
| ~ is_a_theorem(or(A,A)) ),
inference(resolve,[status(thm)],[c_3569,c_109]) ).
cnf(c_12683,plain,
( is_a_theorem(or(C,A))
| ~ is_a_theorem(or(and(A,B),C)) ),
inference(resolve,[status(thm)],[c_3582,c_109]) ).
cnf(c_13943,plain,
is_a_theorem(or(implies(A,B),implies(B,C))),
inference(resolve,[status(thm)],[c_4409,c_12683]) ).
cnf(c_14028,plain,
is_a_theorem(not(not(implies(A,A)))),
inference(resolve,[status(thm)],[c_13943,c_5495]) ).
cnf(c_15156,plain,
is_a_theorem(implies(A,A)),
inference(resolve,[status(thm)],[c_14028,c_2704]) ).
cnf(c_15305,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(implies(A,A),B)) ),
inference(resolve,[status(thm)],[c_109,c_15156]) ).
cnf(c_15301,plain,
~ is_a_theorem(implies(implies(A,A),implies(implies(B,and(B,B)),implies(implies(not(sK1),sK1),sK1)))),
inference(resolve,[status(thm)],[c_15305,c_321]) ).
cnf(c_15302,plain,
$false,
inference(resolve,[status(thm)],[c_15301,c_632]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL517+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n026.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 : Fri Sep 25 22:44:09 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 3651778 was started by sandbox on n026,
% 0.09/0.36 % Fri Sep 25 22:44:09 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 19.04/2.85
% 19.04/2.85 % SZS status Theorem for theBenchmark
% 19.04/2.85
% 19.04/2.85 % Proof 1 at 1.93 (+ 0.51) seconds.
% 19.04/2.85 % Length of proof is 75.
% 19.04/2.85 % Level of proof is 19.
% 19.04/2.85 % Maximum clause weight is 48.000.
% 19.04/2.85 % Given clauses 278.
% 19.04/2.85
% 19.04/2.85 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------