%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL454+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 07:58:58 AM UTC 2026
% Result : Theorem 0.12s 0.44s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of formulae : 58 ( 30 unt; 0 def)
% Number of atoms : 103 ( 9 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 81 ( 36 ~; 29 |; 7 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 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 : 64 ( 2 sgn 21 !; 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(implies_1,axiom,
( implies_1
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,X))) ),
file('theBenchmark.p',implies_1) ).
fof(implies_2,axiom,
( implies_2
<=> ! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
file('theBenchmark.p',implies_2) ).
fof(or_3,axiom,
( or_3
<=> ! [X,Y,Z] : is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z)))) ),
file('theBenchmark.p',or_3) ).
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(principia_r1,conjecture,
r1,
file('theBenchmark.p',principia_r1) ).
fof(principia_r1_neg,negated_conjecture,
~ r1,
inference(assume_negation,[status(cth)],[principia_r1]) ).
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_42,plain,
( is_a_theorem(implies(A,implies(B,A)))
| ~ implies_1 ),
inference(clausify,[status(thm)],[implies_1]) ).
cnf(c_44,plain,
( is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B)))
| ~ implies_2 ),
inference(clausify,[status(thm)],[implies_2]) ).
cnf(c_58,plain,
( is_a_theorem(implies(implies(A,B),implies(implies(C,B),implies(or(A,C),B))))
| ~ or_3 ),
inference(clausify,[status(thm)],[or_3]) ).
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_76,plain,
( is_a_theorem(implies(implies(not(A),A),A))
| ~ cn3 ),
inference(split_conjunct,[status(thm)],[sk_cn3]) ).
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_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(hilbert_op_or,axiom,
op_or,
file('theBenchmark.p',hilbert_op_or) ).
cnf(c_96,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_97,plain,
op_implies_and,
inference(clausify,[status(thm)],[hilbert_op_implies_and]) ).
fof(hilbert_modus_ponens,axiom,
modus_ponens,
file('theBenchmark.p',hilbert_modus_ponens) ).
cnf(c_99,plain,
modus_ponens,
inference(clausify,[status(thm)],[hilbert_modus_ponens]) ).
fof(hilbert_implies_1,axiom,
implies_1,
file('theBenchmark.p',hilbert_implies_1) ).
cnf(c_101,plain,
implies_1,
inference(clausify,[status(thm)],[hilbert_implies_1]) ).
fof(hilbert_implies_2,axiom,
implies_2,
file('theBenchmark.p',hilbert_implies_2) ).
cnf(c_102,plain,
implies_2,
inference(clausify,[status(thm)],[hilbert_implies_2]) ).
fof(hilbert_or_3,axiom,
or_3,
file('theBenchmark.p',hilbert_or_3) ).
cnf(c_109,plain,
or_3,
inference(clausify,[status(thm)],[hilbert_or_3]) ).
cnf(c_116,negated_conjecture,
~ r1,
inference(clausify,[status(thm)],[principia_r1_neg]) ).
cnf(c_117,plain,
not(and(not(A),not(B))) = or(A,B),
inference(resolve,[status(thm)],[c_96,c_89]) ).
cnf(c_118,plain,
not(and(A,not(B))) = implies(A,B),
inference(resolve,[status(thm)],[c_97,c_92]) ).
cnf(c_120,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_122,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(resolve,[status(thm)],[c_101,c_42]) ).
cnf(c_123,plain,
is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))),
inference(resolve,[status(thm)],[c_102,c_44]) ).
cnf(c_130,plain,
is_a_theorem(implies(implies(A,B),implies(implies(C,B),implies(or(A,C),B)))),
inference(resolve,[status(thm)],[c_109,c_58]) ).
cnf(c_134,negated_conjecture,
~ is_a_theorem(implies(or(sK1,sK1),sK1)),
inference(resolve,[status(thm)],[c_116,c_79]) ).
cnf(c_795,plain,
implies(not(A),B) = or(A,B),
inference(paramod,[status(thm)],[c_118,c_117]) ).
cnf(c_135,plain,
or(A,B) = implies(not(A),B),
inference(copy,[status(thm)],[c_795]) ).
cnf(c_144,plain,
( is_a_theorem(implies(A,B))
| ~ is_a_theorem(implies(A,implies(A,B))) ),
inference(resolve,[status(thm)],[c_123,c_120]) ).
cnf(c_178,plain,
( ~ is_a_theorem(implies(or(sK0,sK0),sK0))
| cn3 ),
inference(paramod,[status(thm)],[c_135,c_77]) ).
cnf(c_213,plain,
~ is_a_theorem(implies(implies(not(sK1),sK1),sK1)),
inference(paramod,[status(thm)],[c_135,c_134]) ).
cnf(c_334,plain,
~ cn3,
inference(resolve,[status(thm)],[c_76,c_213]) ).
cnf(c_335,plain,
~ is_a_theorem(implies(or(sK0,sK0),sK0)),
inference(resolve,[status(thm)],[c_334,c_178]) ).
cnf(c_687,plain,
is_a_theorem(implies(implies(A,B),implies(or(A,A),B))),
inference(resolve,[status(thm)],[c_144,c_130]) ).
cnf(c_690,plain,
is_a_theorem(implies(A,A)),
inference(resolve,[status(thm)],[c_144,c_122]) ).
cnf(c_796,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(implies(A,A),B)) ),
inference(resolve,[status(thm)],[c_120,c_690]) ).
cnf(c_793,plain,
~ is_a_theorem(implies(implies(A,A),implies(or(sK0,sK0),sK0))),
inference(resolve,[status(thm)],[c_796,c_335]) ).
cnf(c_794,plain,
$false,
inference(resolve,[status(thm)],[c_793,c_687]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL454+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n005.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Fri Sep 25 22:35:32 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.37 % Process 433588 was started by sandbox2 on n005,
% 0.12/0.37 % Fri Sep 25 22:35:32 2026
% 0.12/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.39
% 0.12/0.39 % From the command line: assign(max_seconds, 300).
% 0.12/0.44
% 0.12/0.44 % SZS status Theorem for theBenchmark
% 0.12/0.44
% 0.12/0.44 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.12/0.44 % Length of proof is 43.
% 0.12/0.44 % Level of proof is 9.
% 0.12/0.44 % Maximum clause weight is 15.000.
% 0.12/0.44 % Given clauses 99.
% 0.12/0.44
% 0.12/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------