%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL486+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 : n020.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 07:59:02 AM UTC 2026
% Result : Theorem 0.81s 0.53s
% Output : CNFRefutation 0.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 46 ( 25 unt; 0 def)
% Number of atoms : 84 ( 3 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 68 ( 30 ~; 24 |; 7 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 88 ( 0 sgn 34 !; 6 ?)
% 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_3,axiom,
( implies_3
<=> ! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ),
file('theBenchmark.p',implies_3) ).
fof(cn1,axiom,
( cn1
<=> ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R)))) ),
file('theBenchmark.p',cn1) ).
fof(r4,axiom,
( r4
<=> ! [P,Q,R] : is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) ),
file('theBenchmark.p',r4) ).
fof(r5,axiom,
( r5
<=> ! [P,Q,R] : is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ),
file('theBenchmark.p',r5) ).
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_implies_3,conjecture,
implies_3,
file('theBenchmark.p',hilbert_implies_3) ).
fof(hilbert_implies_3_neg,negated_conjecture,
~ implies_3,
inference(assume_negation,[status(cth)],[hilbert_implies_3]) ).
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]) ).
fof(nnf_6,plain,
( ( ? [X,Y,Z] : ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| implies_3 )
& ( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ implies_3 ) ),
inference(fof_nnf,[status(thm)],[implies_3]) ).
fof(sk_implies_3_sk,plain,
( ( ~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2))))
| implies_3 )
& ( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ implies_3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X,sK0),skolemize(Y,sK1),skolemize(Z,sK2)],[nnf_6]) ).
fof(sk_implies_3,plain,
( ( ~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2))))
| implies_3 )
& ! [VAR_0,VAR_1,VAR_2] :
( is_a_theorem(implies(implies(VAR_0,VAR_1),implies(implies(VAR_1,VAR_2),implies(VAR_0,VAR_2))))
| ~ implies_3 ) ),
inference(cnf_transformation,[status(thm)],[sk_implies_3_sk]) ).
cnf(c_47,plain,
( ~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2))))
| implies_3 ),
inference(split_conjunct,[status(thm)],[sk_implies_3]) ).
fof(nnf_19,plain,
( ( ? [P,Q,R] : ~ is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))
| cn1 )
& ( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ cn1 ) ),
inference(fof_nnf,[status(thm)],[cn1]) ).
fof(sk_cn1_sk,plain,
( ( ~ is_a_theorem(implies(implies(sK3,sK4),implies(implies(sK4,sK5),implies(sK3,sK5))))
| cn1 )
& ( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ cn1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(P,sK3),skolemize(Q,sK4),skolemize(R,sK5)],[nnf_19]) ).
fof(sk_cn1,plain,
( ( ~ is_a_theorem(implies(implies(sK3,sK4),implies(implies(sK4,sK5),implies(sK3,sK5))))
| cn1 )
& ! [VAR_0,VAR_1,VAR_2] :
( is_a_theorem(implies(implies(VAR_0,VAR_1),implies(implies(VAR_1,VAR_2),implies(VAR_0,VAR_2))))
| ~ cn1 ) ),
inference(cnf_transformation,[status(thm)],[sk_cn1_sk]) ).
cnf(c_72,plain,
( is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C))))
| ~ cn1 ),
inference(split_conjunct,[status(thm)],[sk_cn1]) ).
cnf(c_73,plain,
( ~ is_a_theorem(implies(implies(sK3,sK4),implies(implies(sK4,sK5),implies(sK3,sK5))))
| cn1 ),
inference(split_conjunct,[status(thm)],[sk_cn1]) ).
cnf(c_84,plain,
( is_a_theorem(implies(or(A,or(B,C)),or(B,or(A,C))))
| ~ r4 ),
inference(clausify,[status(thm)],[r4]) ).
cnf(c_86,plain,
( is_a_theorem(implies(implies(A,B),implies(or(C,A),or(C,B))))
| ~ r5 ),
inference(clausify,[status(thm)],[r5]) ).
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_modus_ponens,axiom,
modus_ponens,
file('theBenchmark.p',principia_modus_ponens) ).
cnf(c_99,plain,
modus_ponens,
inference(clausify,[status(thm)],[principia_modus_ponens]) ).
fof(principia_r4,axiom,
r4,
file('theBenchmark.p',principia_r4) ).
cnf(c_103,plain,
r4,
inference(clausify,[status(thm)],[principia_r4]) ).
fof(principia_r5,axiom,
r5,
file('theBenchmark.p',principia_r5) ).
cnf(c_104,plain,
r5,
inference(clausify,[status(thm)],[principia_r5]) ).
cnf(c_108,negated_conjecture,
~ implies_3,
inference(clausify,[status(thm)],[hilbert_implies_3_neg]) ).
cnf(c_109,plain,
or(not(A),B) = implies(A,B),
inference(resolve,[status(thm)],[c_96,c_93]) ).
cnf(c_112,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_116,plain,
is_a_theorem(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(resolve,[status(thm)],[c_103,c_84]) ).
cnf(c_117,plain,
is_a_theorem(implies(implies(A,B),implies(or(C,A),or(C,B)))),
inference(resolve,[status(thm)],[c_104,c_86]) ).
cnf(c_121,negated_conjecture,
~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2)))),
inference(resolve,[status(thm)],[c_108,c_47]) ).
cnf(c_995,plain,
is_a_theorem(implies(or(A,implies(B,C)),or(not(B),or(A,C)))),
inference(paramod,[status(thm)],[c_109,c_116]) ).
cnf(c_145,plain,
is_a_theorem(implies(or(A,implies(B,C)),implies(B,or(A,C)))),
inference(paramod,[status(thm)],[c_109,c_995]) ).
cnf(c_996,plain,
is_a_theorem(implies(implies(A,B),implies(implies(C,A),or(not(C),B)))),
inference(paramod,[status(thm)],[c_109,c_117]) ).
cnf(c_149,plain,
is_a_theorem(implies(implies(A,B),implies(implies(C,A),implies(C,B)))),
inference(paramod,[status(thm)],[c_109,c_996]) ).
cnf(c_160,plain,
~ cn1,
inference(resolve,[status(thm)],[c_72,c_121]) ).
cnf(c_161,plain,
~ is_a_theorem(implies(implies(sK3,sK4),implies(implies(sK4,sK5),implies(sK3,sK5)))),
inference(resolve,[status(thm)],[c_160,c_73]) ).
cnf(c_997,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(B,or(not(A),C)))),
inference(paramod,[status(thm)],[c_109,c_145]) ).
cnf(c_672,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(B,implies(A,C)))),
inference(paramod,[status(thm)],[c_109,c_997]) ).
cnf(c_998,plain,
( is_a_theorem(D)
| ~ is_a_theorem(implies(implies(implies(A,B),implies(implies(C,A),implies(C,B))),D)) ),
inference(resolve,[status(thm)],[c_112,c_149]) ).
cnf(c_993,plain,
~ is_a_theorem(implies(implies(implies(A,B),implies(implies(C,A),implies(C,B))),implies(implies(sK3,sK4),implies(implies(sK4,sK5),implies(sK3,sK5))))),
inference(resolve,[status(thm)],[c_998,c_161]) ).
cnf(c_994,plain,
$false,
inference(resolve,[status(thm)],[c_993,c_672]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL486+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.36 % Computer : n020.cluster.edu
% 0.02/0.36 % Model : x86_64 x86_64
% 0.02/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.36 % Memory : 8046.5625MB
% 0.02/0.36 % OS : Linux 6.8.0-71-generic
% 0.02/0.36 % CPULimit : 300
% 0.02/0.36 % WCLimit : 300
% 0.02/0.36 % DateTime : Fri Sep 25 22:40:04 UTC 2026
% 0.02/0.37 % CPUTime :
% 0.02/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/0.37 % Process 3991209 was started by sandbox2 on n020,
% 0.02/0.37 % Fri Sep 25 22:40:04 2026
% 0.02/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.02/0.38
% 0.02/0.38 % From the command line: assign(max_seconds, 300).
% 0.81/0.53
% 0.81/0.53 % SZS status Theorem for theBenchmark
% 0.81/0.53
% 0.81/0.53 % Proof 1 at 0.10 (+ 0.03) seconds.
% 0.81/0.53 % Length of proof is 31.
% 0.81/0.53 % Level of proof is 6.
% 0.81/0.53 % Maximum clause weight is 99.000.
% 0.81/0.53 % Given clauses 128.
% 0.81/0.53
% 0.81/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------