%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL503+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 07:59:04 AM UTC 2026
% Result : Theorem 21.58s 3.10s
% Output : CNFRefutation 21.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 14
% Syntax : Number of formulae : 101 ( 62 unt; 0 def)
% Number of atoms : 153 ( 16 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 99 ( 47 ~; 40 |; 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 : 185 ( 21 sgn 20 !; 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(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(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(hilbert_implies_1,conjecture,
implies_1,
file('theBenchmark.p',hilbert_implies_1) ).
fof(hilbert_implies_1_neg,negated_conjecture,
~ implies_1,
inference(assume_negation,[status(cth)],[hilbert_implies_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_4,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(X,implies(Y,X)))
| implies_1 )
& ( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ) ),
inference(fof_nnf,[status(thm)],[implies_1]) ).
fof(sk_implies_1_sk,plain,
( ( ~ is_a_theorem(implies(sK0,implies(sK1,sK0)))
| implies_1 )
& ( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK0),skolemize(Y,sK1)],[nnf_4]) ).
fof(sk_implies_1,plain,
( ( ~ is_a_theorem(implies(sK0,implies(sK1,sK0)))
| implies_1 )
& ! [VAR_0,VAR_1] :
( is_a_theorem(implies(VAR_0,implies(VAR_1,VAR_0)))
| ~ implies_1 ) ),
inference(cnf_transformation,[status(thm)],[sk_implies_1_sk]) ).
cnf(c_43,plain,
( ~ is_a_theorem(implies(sK0,implies(sK1,sK0)))
| implies_1 ),
inference(split_conjunct,[status(thm)],[sk_implies_1]) ).
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]) ).
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(rosser_op_or,axiom,
op_or,
file('theBenchmark.p',rosser_op_or) ).
cnf(c_96,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_97,plain,
op_implies_and,
inference(clausify,[status(thm)],[rosser_op_implies_and]) ).
fof(rosser_modus_ponens,axiom,
modus_ponens,
file('theBenchmark.p',rosser_modus_ponens) ).
cnf(c_99,plain,
modus_ponens,
inference(clausify,[status(thm)],[rosser_modus_ponens]) ).
fof(rosser_kn1,axiom,
kn1,
file('theBenchmark.p',rosser_kn1) ).
cnf(c_100,plain,
kn1,
inference(clausify,[status(thm)],[rosser_kn1]) ).
fof(rosser_kn2,axiom,
kn2,
file('theBenchmark.p',rosser_kn2) ).
cnf(c_101,plain,
kn2,
inference(clausify,[status(thm)],[rosser_kn2]) ).
fof(rosser_kn3,axiom,
kn3,
file('theBenchmark.p',rosser_kn3) ).
cnf(c_102,plain,
kn3,
inference(clausify,[status(thm)],[rosser_kn3]) ).
cnf(c_104,negated_conjecture,
~ implies_1,
inference(clausify,[status(thm)],[hilbert_implies_1_neg]) ).
cnf(c_105,plain,
not(and(not(A),not(B))) = or(A,B),
inference(resolve,[status(thm)],[c_96,c_89]) ).
cnf(c_106,plain,
not(and(A,not(B))) = implies(A,B),
inference(resolve,[status(thm)],[c_97,c_92]) ).
cnf(c_108,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_109,plain,
is_a_theorem(implies(A,and(A,A))),
inference(resolve,[status(thm)],[c_100,c_66]) ).
cnf(c_110,plain,
is_a_theorem(implies(and(A,B),A)),
inference(resolve,[status(thm)],[c_101,c_68]) ).
cnf(c_111,plain,
is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),not(and(C,A))))),
inference(resolve,[status(thm)],[c_102,c_70]) ).
cnf(c_113,negated_conjecture,
~ is_a_theorem(implies(sK0,implies(sK1,sK0))),
inference(resolve,[status(thm)],[c_104,c_43]) ).
cnf(c_15827,plain,
implies(not(A),B) = or(A,B),
inference(paramod,[status(thm)],[c_106,c_105]) ).
cnf(c_114,plain,
or(A,B) = implies(not(A),B),
inference(copy,[status(thm)],[c_15827]) ).
cnf(c_121,plain,
not(and(A,implies(B,C))) = implies(A,and(B,not(C))),
inference(paramod,[status(thm)],[c_106,c_106]) ).
cnf(c_123,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(implies(A,and(A,A)),B)) ),
inference(resolve,[status(thm)],[c_109,c_108]) ).
cnf(c_124,plain,
( is_a_theorem(A)
| ~ is_a_theorem(and(A,B)) ),
inference(resolve,[status(thm)],[c_110,c_108]) ).
cnf(c_126,plain,
( is_a_theorem(implies(not(and(B,C)),not(and(C,A))))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_111,c_108]) ).
cnf(c_127,plain,
is_a_theorem(implies(implies(not(A),B),implies(not(and(B,C)),implies(C,A)))),
inference(paramod,[status(thm)],[c_106,c_111]) ).
cnf(c_146,plain,
or(and(A,not(B)),C) = implies(implies(A,B),C),
inference(paramod,[status(thm)],[c_106,c_114]) ).
cnf(c_149,plain,
( is_a_theorem(B)
| ~ is_a_theorem(or(A,B))
| ~ is_a_theorem(not(A)) ),
inference(paramod,[status(thm)],[c_114,c_108]) ).
cnf(c_152,plain,
is_a_theorem(implies(implies(A,B),or(and(B,C),not(and(C,A))))),
inference(paramod,[status(thm)],[c_114,c_111]) ).
cnf(c_156,plain,
not(and(A,or(B,C))) = implies(A,and(not(B),not(C))),
inference(paramod,[status(thm)],[c_114,c_121]) ).
cnf(c_15828,plain,
( is_a_theorem(implies(not(and(B,C)),not(and(C,not(A)))))
| ~ is_a_theorem(or(A,B)) ),
inference(paramod,[status(thm)],[c_114,c_126]) ).
cnf(c_172,plain,
( is_a_theorem(implies(not(and(B,C)),implies(C,A)))
| ~ is_a_theorem(or(A,B)) ),
inference(paramod,[status(thm)],[c_106,c_15828]) ).
cnf(c_176,plain,
is_a_theorem(implies(implies(not(A),B),or(and(B,C),implies(C,A)))),
inference(paramod,[status(thm)],[c_114,c_127]) ).
cnf(c_15829,plain,
or(and(not(A),not(B)),C) = implies(or(A,B),C),
inference(paramod,[status(thm)],[c_114,c_146]) ).
cnf(c_15830,plain,
implies(implies(not(A),B),C) = implies(or(A,B),C),
inference(paramod,[status(thm)],[c_146,c_15829]) ).
cnf(c_190,plain,
implies(or(A,B),C) = implies(implies(not(A),B),C),
inference(copy,[status(thm)],[c_15830]) ).
cnf(c_192,plain,
or(and(A,or(B,C)),D) = implies(implies(A,and(not(B),not(C))),D),
inference(paramod,[status(thm)],[c_156,c_114]) ).
cnf(c_196,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(or(A,B),C))
| ~ is_a_theorem(implies(not(A),B)) ),
inference(paramod,[status(thm)],[c_190,c_108]) ).
cnf(c_204,plain,
( is_a_theorem(or(and(B,C),implies(C,A)))
| ~ is_a_theorem(implies(not(A),B)) ),
inference(resolve,[status(thm)],[c_176,c_108]) ).
cnf(c_207,plain,
( is_a_theorem(or(and(B,C),implies(C,A)))
| ~ is_a_theorem(or(A,B)) ),
inference(paramod,[status(thm)],[c_114,c_204]) ).
cnf(c_225,plain,
is_a_theorem(or(and(and(A,A),B),not(and(B,A)))),
inference(resolve,[status(thm)],[c_152,c_123]) ).
cnf(c_226,plain,
( is_a_theorem(or(and(B,C),not(and(C,A))))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_152,c_108]) ).
cnf(c_228,plain,
( is_a_theorem(not(and(B,A)))
| ~ is_a_theorem(not(and(and(A,A),B))) ),
inference(resolve,[status(thm)],[c_225,c_149]) ).
cnf(c_236,plain,
( is_a_theorem(not(and(not(B),A)))
| ~ is_a_theorem(implies(and(A,A),B)) ),
inference(paramod,[status(thm)],[c_106,c_228]) ).
cnf(c_239,plain,
is_a_theorem(not(and(not(A),A))),
inference(resolve,[status(thm)],[c_236,c_110]) ).
cnf(c_15831,plain,
( is_a_theorem(B)
| ~ is_a_theorem(or(and(not(A),A),B)) ),
inference(resolve,[status(thm)],[c_149,c_239]) ).
cnf(c_245,plain,
~ is_a_theorem(or(and(not(A),A),implies(sK0,implies(sK1,sK0)))),
inference(resolve,[status(thm)],[c_15831,c_113]) ).
cnf(c_249,plain,
is_a_theorem(implies(not(not(A)),A)),
inference(paramod,[status(thm)],[c_106,c_239]) ).
cnf(c_262,plain,
~ is_a_theorem(implies(not(implies(sK1,sK0)),not(sK0))),
inference(resolve,[status(thm)],[c_204,c_245]) ).
cnf(c_15832,plain,
is_a_theorem(or(and(A,B),not(and(B,not(not(A)))))),
inference(resolve,[status(thm)],[c_249,c_226]) ).
cnf(c_295,plain,
is_a_theorem(or(and(A,B),implies(B,not(A)))),
inference(paramod,[status(thm)],[c_106,c_15832]) ).
cnf(c_372,plain,
( is_a_theorem(implies(B,not(A)))
| ~ is_a_theorem(not(and(A,B))) ),
inference(resolve,[status(thm)],[c_295,c_149]) ).
cnf(c_421,plain,
( is_a_theorem(implies(not(B),not(A)))
| ~ is_a_theorem(implies(A,B)) ),
inference(paramod,[status(thm)],[c_106,c_372]) ).
cnf(c_429,plain,
is_a_theorem(implies(not(A),not(and(A,B)))),
inference(resolve,[status(thm)],[c_421,c_110]) ).
cnf(c_430,plain,
is_a_theorem(implies(not(and(A,A)),not(A))),
inference(resolve,[status(thm)],[c_421,c_109]) ).
cnf(c_15833,plain,
is_a_theorem(or(and(not(and(A,B)),C),not(and(C,not(A))))),
inference(resolve,[status(thm)],[c_429,c_226]) ).
cnf(c_462,plain,
is_a_theorem(or(and(not(and(A,B)),C),implies(C,A))),
inference(paramod,[status(thm)],[c_106,c_15833]) ).
cnf(c_484,plain,
is_a_theorem(implies(not(A),implies(A,B))),
inference(paramod,[status(thm)],[c_106,c_429]) ).
cnf(c_15834,plain,
is_a_theorem(or(and(implies(A,B),C),not(and(C,not(A))))),
inference(resolve,[status(thm)],[c_484,c_226]) ).
cnf(c_492,plain,
is_a_theorem(or(and(implies(A,B),C),implies(C,A))),
inference(paramod,[status(thm)],[c_106,c_15834]) ).
cnf(c_522,plain,
is_a_theorem(or(A,implies(A,B))),
inference(paramod,[status(thm)],[c_114,c_484]) ).
cnf(c_667,plain,
is_a_theorem(or(not(A),or(A,B))),
inference(paramod,[status(thm)],[c_114,c_522]) ).
cnf(c_705,plain,
is_a_theorem(or(and(or(A,B),C),implies(C,not(A)))),
inference(resolve,[status(thm)],[c_667,c_207]) ).
cnf(c_15835,plain,
is_a_theorem(or(and(not(A),B),not(and(B,not(and(A,A)))))),
inference(resolve,[status(thm)],[c_430,c_226]) ).
cnf(c_865,plain,
is_a_theorem(or(and(not(A),B),implies(B,and(A,A)))),
inference(paramod,[status(thm)],[c_106,c_15835]) ).
cnf(c_1525,plain,
( is_a_theorem(implies(C,A))
| ~ is_a_theorem(not(and(implies(A,B),C))) ),
inference(resolve,[status(thm)],[c_492,c_149]) ).
cnf(c_2046,plain,
( is_a_theorem(B)
| ~ is_a_theorem(or(and(not(A),or(A,A)),B)) ),
inference(paramod,[status(thm)],[c_192,c_123]) ).
cnf(c_15836,plain,
is_a_theorem(or(and(or(A,B),not(C)),or(C,not(A)))),
inference(paramod,[status(thm)],[c_114,c_705]) ).
cnf(c_3239,plain,
is_a_theorem(implies(implies(or(A,B),C),or(C,not(A)))),
inference(paramod,[status(thm)],[c_146,c_15836]) ).
cnf(c_3636,plain,
( is_a_theorem(implies(not(C),A))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(paramod,[status(thm)],[c_106,c_1525]) ).
cnf(c_3904,plain,
is_a_theorem(implies(or(A,A),and(A,A))),
inference(resolve,[status(thm)],[c_2046,c_865]) ).
cnf(c_3913,plain,
( is_a_theorem(and(A,A))
| ~ is_a_theorem(implies(not(A),A)) ),
inference(resolve,[status(thm)],[c_3904,c_196]) ).
cnf(c_15837,plain,
( is_a_theorem(implies(C,A))
| ~ is_a_theorem(not(and(not(and(A,B)),C))) ),
inference(resolve,[status(thm)],[c_149,c_462]) ).
cnf(c_15838,plain,
~ is_a_theorem(not(and(not(and(not(sK0),A)),not(implies(sK1,sK0))))),
inference(resolve,[status(thm)],[c_15837,c_262]) ).
cnf(c_14587,plain,
~ is_a_theorem(implies(not(and(not(sK0),A)),implies(sK1,sK0))),
inference(paramod,[status(thm)],[c_106,c_15838]) ).
cnf(c_15626,plain,
is_a_theorem(implies(not(or(A,not(B))),or(B,C))),
inference(resolve,[status(thm)],[c_3239,c_3636]) ).
cnf(c_15753,plain,
is_a_theorem(and(or(A,not(A)),or(A,not(A)))),
inference(resolve,[status(thm)],[c_15626,c_3913]) ).
cnf(c_15779,plain,
is_a_theorem(or(A,not(A))),
inference(resolve,[status(thm)],[c_15753,c_124]) ).
cnf(c_15825,plain,
is_a_theorem(implies(not(and(not(A),B)),implies(B,A))),
inference(resolve,[status(thm)],[c_15779,c_172]) ).
cnf(c_15826,plain,
$false,
inference(resolve,[status(thm)],[c_15825,c_14587]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL503+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Fri Sep 25 22:40:20 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.30 % Process 3239711 was started by sandbox on n012,
% 0.03/0.30 % Fri Sep 25 22:40:20 2026
% 0.03/0.30 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.03/0.30
% 0.03/0.30 % From the command line: assign(max_seconds, 300).
% 21.58/3.10
% 21.58/3.10 % given #500 (A,wt=29): 266 -is_a_theorem(or(and(implies(A,B),and(A,not(B))),implies(c7,implies(c8,c7)))). [para(106(a,1),245(a,1,1,1))].
% 21.58/3.10
% 21.58/3.10 % SZS status Theorem for theBenchmark
% 21.58/3.10
% 21.58/3.10 % Proof 1 at 1.87 (+ 0.86) seconds.
% 21.58/3.10 % Length of proof is 79.
% 21.58/3.10 % Level of proof is 24.
% 21.58/3.10 % Maximum clause weight is 30.000.
% 21.58/3.10 % Given clauses 609.
% 21.58/3.10
% 21.58/3.10 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------