%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL518+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 : 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 07:59:05 AM UTC 2026
% Result : Theorem 0.30s 0.42s
% Output : CNFRefutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 23
% Syntax : Number of formulae : 112 ( 71 unt; 0 def)
% Number of atoms : 172 ( 41 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 105 ( 45 ~; 39 |; 7 &)
% ( 7 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 15 ( 13 usr; 13 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 151 ( 3 sgn 28 !; 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(substitution_of_equivalents,axiom,
( substitution_of_equivalents
<=> ! [X,Y] :
( is_a_theorem(equiv(X,Y))
=> X = Y ) ),
file('theBenchmark.p',substitution_of_equivalents) ).
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_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(op_equiv,axiom,
( op_equiv
=> ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
file('theBenchmark.p',op_equiv) ).
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_37,plain,
( B = A
| ~ is_a_theorem(equiv(A,B))
| ~ substitution_of_equivalents ),
inference(clausify,[status(thm)],[substitution_of_equivalents]) ).
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_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_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]) ).
cnf(c_94,plain,
( and(implies(A,B),implies(B,A)) = equiv(A,B)
| ~ op_equiv ),
inference(clausify,[status(thm)],[op_equiv]) ).
fof(rosser_op_or,axiom,
op_or,
file('theBenchmark.p',rosser_op_or) ).
cnf(c_95,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_96,plain,
op_implies_and,
inference(clausify,[status(thm)],[rosser_op_implies_and]) ).
fof(rosser_op_equiv,axiom,
op_equiv,
file('theBenchmark.p',rosser_op_equiv) ).
cnf(c_97,plain,
op_equiv,
inference(clausify,[status(thm)],[rosser_op_equiv]) ).
fof(rosser_modus_ponens,axiom,
modus_ponens,
file('theBenchmark.p',rosser_modus_ponens) ).
cnf(c_98,plain,
modus_ponens,
inference(clausify,[status(thm)],[rosser_modus_ponens]) ).
fof(rosser_kn1,axiom,
kn1,
file('theBenchmark.p',rosser_kn1) ).
cnf(c_99,plain,
kn1,
inference(clausify,[status(thm)],[rosser_kn1]) ).
fof(rosser_kn2,axiom,
kn2,
file('theBenchmark.p',rosser_kn2) ).
cnf(c_100,plain,
kn2,
inference(clausify,[status(thm)],[rosser_kn2]) ).
fof(rosser_kn3,axiom,
kn3,
file('theBenchmark.p',rosser_kn3) ).
cnf(c_101,plain,
kn3,
inference(clausify,[status(thm)],[rosser_kn3]) ).
fof(use_substitution_of_equivalents,axiom,
substitution_of_equivalents,
file('theBenchmark.p',use_substitution_of_equivalents) ).
cnf(c_102,plain,
substitution_of_equivalents,
inference(clausify,[status(thm)],[use_substitution_of_equivalents]) ).
fof(principia_op_implies_or,axiom,
op_implies_or,
file('theBenchmark.p',principia_op_implies_or) ).
cnf(c_103,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_104,plain,
op_and,
inference(clausify,[status(thm)],[principia_op_and]) ).
cnf(c_105,negated_conjecture,
~ r1,
inference(clausify,[status(thm)],[principia_r1_neg]) ).
cnf(c_106,plain,
not(and(not(A),not(B))) = or(A,B),
inference(resolve,[status(thm)],[c_95,c_89]) ).
cnf(c_107,plain,
not(and(A,not(B))) = implies(A,B),
inference(resolve,[status(thm)],[c_96,c_92]) ).
cnf(c_108,plain,
and(implies(A,B),implies(B,A)) = equiv(A,B),
inference(resolve,[status(thm)],[c_97,c_94]) ).
cnf(c_109,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_110,plain,
is_a_theorem(implies(A,and(A,A))),
inference(resolve,[status(thm)],[c_99,c_66]) ).
cnf(c_111,plain,
is_a_theorem(implies(and(A,B),A)),
inference(resolve,[status(thm)],[c_100,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_101,c_70]) ).
cnf(c_113,plain,
( B = A
| ~ is_a_theorem(equiv(A,B)) ),
inference(resolve,[status(thm)],[c_102,c_37]) ).
cnf(c_114,plain,
or(not(A),B) = implies(A,B),
inference(resolve,[status(thm)],[c_103,c_93]) ).
cnf(c_1206,plain,
( not(implies(A,not(B))) = and(A,B)
| ~ op_and ),
inference(paramod,[status(thm)],[c_114,c_91]) ).
cnf(c_115,plain,
not(implies(A,not(B))) = and(A,B),
inference(resolve,[status(thm)],[c_104,c_1206]) ).
cnf(c_116,negated_conjecture,
~ is_a_theorem(implies(or(sK1,sK1),sK1)),
inference(resolve,[status(thm)],[c_105,c_79]) ).
cnf(c_1207,plain,
implies(not(A),B) = or(A,B),
inference(paramod,[status(thm)],[c_107,c_106]) ).
cnf(c_117,plain,
or(A,B) = implies(not(A),B),
inference(copy,[status(thm)],[c_1207]) ).
cnf(c_119,negated_conjecture,
~ is_a_theorem(implies(implies(not(sK1),sK1),sK1)),
inference(paramod,[status(thm)],[c_117,c_116]) ).
cnf(c_120,plain,
implies(not(not(A)),B) = implies(A,B),
inference(paramod,[status(thm)],[c_117,c_114]) ).
cnf(c_138,plain,
is_a_theorem(implies(implies(A,A),equiv(A,A))),
inference(paramod,[status(thm)],[c_108,c_110]) ).
cnf(c_140,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(and(A,B),A),C)) ),
inference(resolve,[status(thm)],[c_111,c_109]) ).
cnf(c_143,plain,
( is_a_theorem(implies(not(and(B,C)),not(and(C,A))))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_112,c_109]) ).
cnf(c_156,plain,
~ cn3,
inference(resolve,[status(thm)],[c_76,c_119]) ).
cnf(c_157,plain,
~ is_a_theorem(implies(implies(not(sK0),sK0),sK0)),
inference(resolve,[status(thm)],[c_156,c_77]) ).
cnf(c_158,plain,
implies(not(implies(A,B)),C) = implies(and(A,not(B)),C),
inference(paramod,[status(thm)],[c_107,c_120]) ).
cnf(c_160,plain,
and(implies(A,not(not(B))),implies(B,A)) = equiv(A,not(not(B))),
inference(paramod,[status(thm)],[c_120,c_108]) ).
cnf(c_161,plain,
is_a_theorem(implies(A,and(not(not(A)),not(not(A))))),
inference(paramod,[status(thm)],[c_120,c_110]) ).
cnf(c_1208,plain,
not(implies(A,not(B))) = and(not(not(A)),B),
inference(paramod,[status(thm)],[c_120,c_115]) ).
cnf(c_1209,plain,
and(A,B) = and(not(not(A)),B),
inference(paramod,[status(thm)],[c_115,c_1208]) ).
cnf(c_163,plain,
and(not(not(A)),B) = and(A,B),
inference(copy,[status(thm)],[c_1209]) ).
cnf(c_164,plain,
implies(not(and(A,B)),C) = implies(implies(A,not(B)),C),
inference(paramod,[status(thm)],[c_115,c_120]) ).
cnf(c_165,plain,
is_a_theorem(implies(A,and(A,not(not(A))))),
inference(paramod,[status(thm)],[c_163,c_161]) ).
cnf(c_170,plain,
( is_a_theorem(implies(implies(B,not(C)),not(and(C,A))))
| ~ is_a_theorem(implies(A,B)) ),
inference(paramod,[status(thm)],[c_164,c_143]) ).
cnf(c_187,plain,
( is_a_theorem(equiv(A,A))
| ~ is_a_theorem(implies(A,A)) ),
inference(resolve,[status(thm)],[c_138,c_109]) ).
cnf(c_225,plain,
and(not(and(A,B)),C) = and(implies(A,not(B)),C),
inference(paramod,[status(thm)],[c_115,c_163]) ).
cnf(c_1210,plain,
implies(and(A,B),C) = implies(and(A,not(not(B))),C),
inference(paramod,[status(thm)],[c_115,c_158]) ).
cnf(c_336,plain,
implies(and(A,not(not(B))),C) = implies(and(A,B),C),
inference(copy,[status(thm)],[c_1210]) ).
cnf(c_1211,plain,
and(implies(A,B),C) = and(implies(A,not(not(B))),C),
inference(paramod,[status(thm)],[c_107,c_225]) ).
cnf(c_348,plain,
and(implies(A,not(not(B))),C) = and(implies(A,B),C),
inference(copy,[status(thm)],[c_1211]) ).
cnf(c_1212,plain,
and(implies(A,B),implies(B,A)) = equiv(A,not(not(B))),
inference(paramod,[status(thm)],[c_348,c_160]) ).
cnf(c_1213,plain,
equiv(A,B) = equiv(A,not(not(B))),
inference(paramod,[status(thm)],[c_108,c_1212]) ).
cnf(c_364,plain,
equiv(A,not(not(B))) = equiv(A,B),
inference(copy,[status(thm)],[c_1213]) ).
cnf(c_1214,plain,
is_a_theorem(implies(implies(and(A,not(not(A))),not(B)),not(and(B,A)))),
inference(resolve,[status(thm)],[c_170,c_165]) ).
cnf(c_628,plain,
is_a_theorem(implies(implies(and(A,A),not(B)),not(and(B,A)))),
inference(paramod,[status(thm)],[c_336,c_1214]) ).
cnf(c_1215,plain,
is_a_theorem(not(and(A,not(A)))),
inference(resolve,[status(thm)],[c_628,c_140]) ).
cnf(c_636,plain,
is_a_theorem(implies(A,A)),
inference(paramod,[status(thm)],[c_107,c_1215]) ).
cnf(c_638,plain,
( is_a_theorem(not(and(B,A)))
| ~ is_a_theorem(implies(and(A,A),not(B))) ),
inference(resolve,[status(thm)],[c_628,c_109]) ).
cnf(c_669,plain,
is_a_theorem(equiv(A,A)),
inference(resolve,[status(thm)],[c_636,c_187]) ).
cnf(c_693,plain,
is_a_theorem(implies(A,not(not(A)))),
inference(paramod,[status(thm)],[c_120,c_636]) ).
cnf(c_875,plain,
is_a_theorem(equiv(not(not(A)),A)),
inference(paramod,[status(thm)],[c_364,c_669]) ).
cnf(c_1216,plain,
is_a_theorem(not(and(not(and(A,A)),A))),
inference(resolve,[status(thm)],[c_693,c_638]) ).
cnf(c_1006,plain,
is_a_theorem(not(and(implies(A,not(A)),A))),
inference(paramod,[status(thm)],[c_225,c_1216]) ).
cnf(c_1217,plain,
A = not(not(A)),
inference(resolve,[status(thm)],[c_875,c_113]) ).
cnf(c_1027,plain,
not(not(A)) = A,
inference(copy,[status(thm)],[c_1217]) ).
cnf(c_1038,plain,
not(and(A,B)) = implies(A,not(B)),
inference(paramod,[status(thm)],[c_1027,c_107]) ).
cnf(c_1043,plain,
is_a_theorem(implies(implies(A,not(A)),not(A))),
inference(paramod,[status(thm)],[c_1038,c_1006]) ).
cnf(c_1218,plain,
is_a_theorem(implies(implies(not(A),A),not(not(A)))),
inference(paramod,[status(thm)],[c_1027,c_1043]) ).
cnf(c_1204,plain,
is_a_theorem(implies(implies(not(A),A),A)),
inference(paramod,[status(thm)],[c_1027,c_1218]) ).
cnf(c_1205,plain,
$false,
inference(resolve,[status(thm)],[c_1204,c_157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL518+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Fri Sep 25 22:41:20 UTC 2026
% 0.02/0.30 % CPUTime :
% 0.02/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/0.30 % Process 3241347 was started by sandbox2 on n012,
% 0.02/0.30 % Fri Sep 25 22:41:20 2026
% 0.02/0.30 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.02/0.30
% 0.02/0.30 % From the command line: assign(max_seconds, 300).
% 0.30/0.42
% 0.30/0.42 % Assigning unary symbol not kb_weight 0 and highest precedence (93).
% 0.30/0.42
% 0.30/0.42 % SZS status Theorem for theBenchmark
% 0.30/0.42
% 0.30/0.42 % Proof 1 at 0.08 (+ 0.03) seconds.
% 0.30/0.42 % Length of proof is 82.
% 0.30/0.42 % Level of proof is 16.
% 0.30/0.42 % Maximum clause weight is 44.000.
% 0.30/0.42 % Given clauses 147.
% 0.30/0.42
% 0.30/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------