%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL456+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 : n019.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 0.11s 0.38s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 14
% Syntax : Number of formulae : 51 ( 30 unt; 0 def)
% Number of atoms : 83 ( 9 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 58 ( 26 ~; 20 |; 4 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 8 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 71 ( 8 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(or_1,axiom,
( or_1
<=> ! [X,Y] : is_a_theorem(implies(X,or(X,Y))) ),
file('theBenchmark.p',or_1) ).
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(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(principia_r3,conjecture,
r3,
file('theBenchmark.p',principia_r3) ).
fof(principia_r3_neg,negated_conjecture,
~ r3,
inference(assume_negation,[status(cth)],[principia_r3]) ).
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_54,plain,
( is_a_theorem(implies(A,or(A,B)))
| ~ or_1 ),
inference(clausify,[status(thm)],[or_1]) ).
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_24,plain,
( ( ? [P,Q] : ~ is_a_theorem(implies(or(P,Q),or(Q,P)))
| r3 )
& ( ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ) ),
inference(fof_nnf,[status(thm)],[r3]) ).
fof(sk_r3_sk,plain,
( ( ~ is_a_theorem(implies(or(sK0,sK1),or(sK1,sK0)))
| r3 )
& ( ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(P,sK0),skolemize(Q,sK1)],[nnf_24]) ).
fof(sk_r3,plain,
( ( ~ is_a_theorem(implies(or(sK0,sK1),or(sK1,sK0)))
| r3 )
& ! [VAR_0,VAR_1] :
( is_a_theorem(implies(or(VAR_0,VAR_1),or(VAR_1,VAR_0)))
| ~ r3 ) ),
inference(cnf_transformation,[status(thm)],[sk_r3_sk]) ).
cnf(c_83,plain,
( ~ is_a_theorem(implies(or(sK0,sK1),or(sK1,sK0)))
| r3 ),
inference(split_conjunct,[status(thm)],[sk_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]) ).
fof(hilbert_op_or,axiom,
op_or,
file('theBenchmark.p',hilbert_op_or) ).
cnf(c_95,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_96,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_98,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_100,plain,
implies_1,
inference(clausify,[status(thm)],[hilbert_implies_1]) ).
fof(hilbert_or_1,axiom,
or_1,
file('theBenchmark.p',hilbert_or_1) ).
cnf(c_106,plain,
or_1,
inference(clausify,[status(thm)],[hilbert_or_1]) ).
fof(hilbert_or_3,axiom,
or_3,
file('theBenchmark.p',hilbert_or_3) ).
cnf(c_108,plain,
or_3,
inference(clausify,[status(thm)],[hilbert_or_3]) ).
cnf(c_115,negated_conjecture,
~ r3,
inference(clausify,[status(thm)],[principia_r3_neg]) ).
cnf(c_116,plain,
not(and(not(A),not(B))) = or(A,B),
inference(resolve,[status(thm)],[c_95,c_89]) ).
cnf(c_117,plain,
not(and(A,not(B))) = implies(A,B),
inference(resolve,[status(thm)],[c_96,c_92]) ).
cnf(c_119,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(A,B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_98,c_33]) ).
cnf(c_121,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(resolve,[status(thm)],[c_100,c_42]) ).
cnf(c_127,plain,
is_a_theorem(implies(A,or(A,B))),
inference(resolve,[status(thm)],[c_106,c_54]) ).
cnf(c_129,plain,
is_a_theorem(implies(implies(A,B),implies(implies(C,B),implies(or(A,C),B)))),
inference(resolve,[status(thm)],[c_108,c_58]) ).
cnf(c_136,negated_conjecture,
~ is_a_theorem(implies(or(sK0,sK1),or(sK1,sK0))),
inference(resolve,[status(thm)],[c_115,c_83]) ).
cnf(c_289,plain,
implies(not(A),B) = or(A,B),
inference(paramod,[status(thm)],[c_117,c_116]) ).
cnf(c_137,plain,
or(A,B) = implies(not(A),B),
inference(copy,[status(thm)],[c_289]) ).
cnf(c_290,negated_conjecture,
~ is_a_theorem(implies(implies(not(sK0),sK1),or(sK1,sK0))),
inference(paramod,[status(thm)],[c_137,c_136]) ).
cnf(c_141,negated_conjecture,
~ is_a_theorem(implies(implies(not(sK0),sK1),implies(not(sK1),sK0))),
inference(paramod,[status(thm)],[c_137,c_290]) ).
cnf(c_143,plain,
is_a_theorem(implies(implies(A,B),implies(implies(C,B),implies(implies(not(A),C),B)))),
inference(paramod,[status(thm)],[c_137,c_129]) ).
cnf(c_144,plain,
is_a_theorem(implies(A,implies(not(A),B))),
inference(paramod,[status(thm)],[c_137,c_127]) ).
cnf(c_291,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(A,implies(B,A)),C)) ),
inference(resolve,[status(thm)],[c_119,c_121]) ).
cnf(c_259,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(not(C),A),implies(B,C)))),
inference(resolve,[status(thm)],[c_291,c_143]) ).
cnf(c_292,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(A,implies(not(A),B)),C)) ),
inference(resolve,[status(thm)],[c_119,c_144]) ).
cnf(c_287,plain,
~ is_a_theorem(implies(implies(A,implies(not(A),B)),implies(implies(not(sK0),sK1),implies(not(sK1),sK0)))),
inference(resolve,[status(thm)],[c_292,c_141]) ).
cnf(c_288,plain,
$false,
inference(resolve,[status(thm)],[c_287,c_259]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL456+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.33 % Computer : n019.cluster.edu
% 0.08/0.33 % Model : x86_64 x86_64
% 0.08/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.33 % Memory : 8046.5625MB
% 0.08/0.33 % OS : Linux 6.8.0-71-generic
% 0.08/0.33 % CPULimit : 300
% 0.08/0.33 % WCLimit : 300
% 0.08/0.33 % DateTime : Fri Sep 25 22:36:03 UTC 2026
% 0.08/0.33 % CPUTime :
% 0.08/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.34 % Process 3931787 was started by sandbox on n019,
% 0.08/0.34 % Fri Sep 25 22:36:03 2026
% 0.08/0.34 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.34
% 0.08/0.34 % From the command line: assign(max_seconds, 300).
% 0.11/0.38
% 0.11/0.38 % Assigning unary symbol not kb_weight 0 and highest precedence (93).
% 0.11/0.38
% 0.11/0.38 % SZS status Theorem for theBenchmark
% 0.11/0.38
% 0.11/0.38 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.11/0.38 % Length of proof is 37.
% 0.11/0.38 % Level of proof is 7.
% 0.11/0.38 % Maximum clause weight is 70.000.
% 0.11/0.38 % Given clauses 50.
% 0.11/0.38
% 0.11/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------