%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL487+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 07:59:02 AM UTC 2026
% Result : Theorem 1.68s 0.57s
% Output : CNFRefutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 19
% Syntax : Number of formulae : 78 ( 44 unt; 0 def)
% Number of atoms : 129 ( 18 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 90 ( 39 ~; 33 |; 7 &)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 13 ( 11 usr; 11 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 120 ( 10 sgn 33 !; 4 ?)
% 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(and_1,axiom,
( and_1
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),X)) ),
file('theBenchmark.p',and_1) ).
fof(kn2,axiom,
( kn2
<=> ! [P,Q] : is_a_theorem(implies(and(P,Q),P)) ),
file('theBenchmark.p',kn2) ).
fof(r2,axiom,
( r2
<=> ! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) ),
file('theBenchmark.p',r2) ).
fof(r3,axiom,
( r3
<=> ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) ),
file('theBenchmark.p',r3) ).
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_or,axiom,
( op_or
=> ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
file('theBenchmark.p',op_or) ).
fof(op_and,axiom,
( op_and
=> ! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) ),
file('theBenchmark.p',op_and) ).
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_and_1,conjecture,
and_1,
file('theBenchmark.p',hilbert_and_1) ).
fof(hilbert_and_1_neg,negated_conjecture,
~ and_1,
inference(assume_negation,[status(cth)],[hilbert_and_1]) ).
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_7,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(and(X,Y),X))
| and_1 )
& ( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ) ),
inference(fof_nnf,[status(thm)],[and_1]) ).
fof(sk_and_1_sk,plain,
( ( ~ is_a_theorem(implies(and(sK0,sK1),sK0))
| and_1 )
& ( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK0),skolemize(Y,sK1)],[nnf_7]) ).
fof(sk_and_1,plain,
( ( ~ is_a_theorem(implies(and(sK0,sK1),sK0))
| and_1 )
& ! [VAR_0,VAR_1] :
( is_a_theorem(implies(and(VAR_0,VAR_1),VAR_0))
| ~ and_1 ) ),
inference(cnf_transformation,[status(thm)],[sk_and_1_sk]) ).
cnf(c_49,plain,
( ~ is_a_theorem(implies(and(sK0,sK1),sK0))
| and_1 ),
inference(split_conjunct,[status(thm)],[sk_and_1]) ).
fof(nnf_17,plain,
( ( ? [P,Q] : ~ is_a_theorem(implies(and(P,Q),P))
| kn2 )
& ( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ kn2 ) ),
inference(fof_nnf,[status(thm)],[kn2]) ).
fof(sk_kn2_sk,plain,
( ( ~ is_a_theorem(implies(and(sK2,sK3),sK2))
| kn2 )
& ( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ kn2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(P,sK2),skolemize(Q,sK3)],[nnf_17]) ).
fof(sk_kn2,plain,
( ( ~ is_a_theorem(implies(and(sK2,sK3),sK2))
| kn2 )
& ! [VAR_0,VAR_1] :
( is_a_theorem(implies(and(VAR_0,VAR_1),VAR_0))
| ~ kn2 ) ),
inference(cnf_transformation,[status(thm)],[sk_kn2_sk]) ).
cnf(c_68,plain,
( is_a_theorem(implies(and(A,B),A))
| ~ kn2 ),
inference(split_conjunct,[status(thm)],[sk_kn2]) ).
cnf(c_69,plain,
( ~ is_a_theorem(implies(and(sK2,sK3),sK2))
| kn2 ),
inference(split_conjunct,[status(thm)],[sk_kn2]) ).
cnf(c_80,plain,
( is_a_theorem(implies(A,or(B,A)))
| ~ r2 ),
inference(clausify,[status(thm)],[r2]) ).
cnf(c_82,plain,
( is_a_theorem(implies(or(A,B),or(B,A)))
| ~ r3 ),
inference(clausify,[status(thm)],[r3]) ).
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_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_90,plain,
( and(A,B) = not(or(not(A),not(B)))
| ~ op_and ),
inference(clausify,[status(thm)],[op_and]) ).
cnf(c_91,plain,
( not(or(not(A),not(B))) = and(A,B)
| ~ op_and ),
inference(copy,[status(thm)],[c_90]) ).
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_95,plain,
op_implies_or,
inference(clausify,[status(thm)],[principia_op_implies_or]) ).
fof(principia_op_and,axiom,
op_and,
file('theBenchmark.p',principia_op_and) ).
cnf(c_96,plain,
op_and,
inference(clausify,[status(thm)],[principia_op_and]) ).
fof(principia_modus_ponens,axiom,
modus_ponens,
file('theBenchmark.p',principia_modus_ponens) ).
cnf(c_98,plain,
modus_ponens,
inference(clausify,[status(thm)],[principia_modus_ponens]) ).
fof(principia_r2,axiom,
r2,
file('theBenchmark.p',principia_r2) ).
cnf(c_100,plain,
r2,
inference(clausify,[status(thm)],[principia_r2]) ).
fof(principia_r3,axiom,
r3,
file('theBenchmark.p',principia_r3) ).
cnf(c_101,plain,
r3,
inference(clausify,[status(thm)],[principia_r3]) ).
fof(principia_r5,axiom,
r5,
file('theBenchmark.p',principia_r5) ).
cnf(c_103,plain,
r5,
inference(clausify,[status(thm)],[principia_r5]) ).
fof(hilbert_op_or,axiom,
op_or,
file('theBenchmark.p',hilbert_op_or) ).
cnf(c_105,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_106,plain,
op_implies_and,
inference(clausify,[status(thm)],[hilbert_op_implies_and]) ).
cnf(c_107,negated_conjecture,
~ and_1,
inference(clausify,[status(thm)],[hilbert_and_1_neg]) ).
cnf(c_108,plain,
or(not(A),B) = implies(A,B),
inference(resolve,[status(thm)],[c_95,c_93]) ).
cnf(c_2037,plain,
( not(implies(A,not(B))) = and(A,B)
| ~ op_and ),
inference(paramod,[status(thm)],[c_108,c_91]) ).
cnf(c_109,plain,
not(implies(A,not(B))) = and(A,B),
inference(resolve,[status(thm)],[c_96,c_2037]) ).
cnf(c_111,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_113,plain,
is_a_theorem(implies(A,or(B,A))),
inference(resolve,[status(thm)],[c_100,c_80]) ).
cnf(c_114,plain,
is_a_theorem(implies(or(A,B),or(B,A))),
inference(resolve,[status(thm)],[c_101,c_82]) ).
cnf(c_116,plain,
is_a_theorem(implies(implies(A,B),implies(or(C,A),or(C,B)))),
inference(resolve,[status(thm)],[c_103,c_86]) ).
cnf(c_118,plain,
not(and(not(A),not(B))) = or(A,B),
inference(resolve,[status(thm)],[c_105,c_89]) ).
cnf(c_119,plain,
not(and(A,not(B))) = implies(A,B),
inference(resolve,[status(thm)],[c_106,c_92]) ).
cnf(c_120,negated_conjecture,
~ is_a_theorem(implies(and(sK0,sK1),sK0)),
inference(resolve,[status(thm)],[c_107,c_49]) ).
cnf(c_2038,plain,
implies(not(A),B) = or(A,B),
inference(paramod,[status(thm)],[c_119,c_118]) ).
cnf(c_122,plain,
or(A,B) = implies(not(A),B),
inference(copy,[status(thm)],[c_2038]) ).
cnf(c_2039,plain,
is_a_theorem(implies(implies(A,B),implies(implies(not(C),A),or(C,B)))),
inference(paramod,[status(thm)],[c_122,c_116]) ).
cnf(c_123,plain,
is_a_theorem(implies(implies(A,B),implies(implies(not(C),A),implies(not(C),B)))),
inference(paramod,[status(thm)],[c_122,c_2039]) ).
cnf(c_2040,plain,
is_a_theorem(implies(implies(not(A),B),or(B,A))),
inference(paramod,[status(thm)],[c_122,c_114]) ).
cnf(c_125,plain,
is_a_theorem(implies(implies(not(A),B),implies(not(B),A))),
inference(paramod,[status(thm)],[c_122,c_2040]) ).
cnf(c_126,plain,
is_a_theorem(implies(A,implies(not(B),A))),
inference(paramod,[status(thm)],[c_122,c_113]) ).
cnf(c_128,plain,
implies(not(not(A)),B) = implies(A,B),
inference(paramod,[status(thm)],[c_122,c_108]) ).
cnf(c_138,plain,
~ kn2,
inference(resolve,[status(thm)],[c_68,c_120]) ).
cnf(c_139,plain,
~ is_a_theorem(implies(and(sK2,sK3),sK2)),
inference(resolve,[status(thm)],[c_138,c_69]) ).
cnf(c_2041,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(implies(not(A),B),implies(not(B),A)),C)) ),
inference(resolve,[status(thm)],[c_111,c_125]) ).
cnf(c_153,plain,
is_a_theorem(implies(implies(not(A),implies(not(B),C)),implies(not(A),implies(not(C),B)))),
inference(resolve,[status(thm)],[c_2041,c_123]) ).
cnf(c_156,plain,
is_a_theorem(implies(implies(not(A),implies(B,not(C))),implies(and(B,C),A))),
inference(paramod,[status(thm)],[c_109,c_125]) ).
cnf(c_189,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(paramod,[status(thm)],[c_128,c_126]) ).
cnf(c_2042,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(A,implies(B,A)),C)) ),
inference(resolve,[status(thm)],[c_111,c_189]) ).
cnf(c_2043,plain,
is_a_theorem(implies(not(A),implies(not(not(A)),B))),
inference(resolve,[status(thm)],[c_2042,c_153]) ).
cnf(c_1799,plain,
is_a_theorem(implies(not(A),implies(A,B))),
inference(paramod,[status(thm)],[c_128,c_2043]) ).
cnf(c_2044,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(not(A),implies(A,B)),C)) ),
inference(resolve,[status(thm)],[c_111,c_1799]) ).
cnf(c_2035,plain,
~ is_a_theorem(implies(implies(not(A),implies(A,B)),implies(and(sK2,sK3),sK2))),
inference(resolve,[status(thm)],[c_2044,c_139]) ).
cnf(c_2036,plain,
$false,
inference(resolve,[status(thm)],[c_2035,c_156]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL487+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Fri Sep 25 22:38:51 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.31 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.31 % Process 3237370 was started by sandbox on n012,
% 0.03/0.31 % Fri Sep 25 22:38:51 2026
% 0.03/0.31 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.03/0.31
% 0.03/0.31 % From the command line: assign(max_seconds, 300).
% 1.68/0.57
% 1.68/0.57 % Assigning unary symbol not kb_weight 0 and highest precedence (93).
% 1.68/0.57
% 1.68/0.57 % SZS status Theorem for theBenchmark
% 1.68/0.57
% 1.68/0.57 % Proof 1 at 0.15 (+ 0.05) seconds.
% 1.68/0.57 % Length of proof is 55.
% 1.68/0.57 % Level of proof is 9.
% 1.68/0.57 % Maximum clause weight is 61.000.
% 1.68/0.57 % Given clauses 176.
% 1.68/0.57
% 1.68/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------