%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL092-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 07:57:57 AM UTC 2026
% Result : Unsatisfiable 2.05s 0.73s
% Output : CNFRefutation 2.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 3
% Syntax : Number of formulae : 64 ( 38 unt; 0 def)
% Number of atoms : 92 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 58 ( 30 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 252 ( 140 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(condensed_detachment,axiom,
! [VAR_0,VAR_1] :
( is_a_theorem(VAR_1)
| ~ is_a_theorem(VAR_0)
| ~ is_a_theorem(implies(VAR_0,VAR_1)) ),
file('theBenchmark.p',condensed_detachment) ).
cnf(c_1,plain,
( is_a_theorem(B)
| ~ is_a_theorem(A)
| ~ is_a_theorem(implies(A,B)) ),
inference(clausify,[status(thm)],[condensed_detachment]) ).
fof(ic_JLukasiewicz_5,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] : is_a_theorem(implies(implies(implies(VAR_0,VAR_1),implies(VAR_2,VAR_3)),implies(implies(VAR_3,VAR_0),implies(VAR_4,implies(VAR_2,VAR_0))))),
file('theBenchmark.p',ic_JLukasiewicz_5) ).
cnf(c_2,plain,
is_a_theorem(implies(implies(implies(A,B),implies(C,D)),implies(implies(D,A),implies(E,implies(C,A))))),
inference(clausify,[status(thm)],[ic_JLukasiewicz_5]) ).
fof(prove_ic_3,axiom,
~ is_a_theorem(implies(implies(implies(a,b),a),a)),
file('theBenchmark.p',prove_ic_3) ).
cnf(c_3,plain,
~ is_a_theorem(implies(implies(implies(a,b),a),a)),
inference(clausify,[status(thm)],[prove_ic_3]) ).
cnf(c_4,plain,
( is_a_theorem(implies(implies(D,A),implies(E,implies(C,A))))
| ~ is_a_theorem(implies(implies(A,B),implies(C,D))) ),
inference(resolve,[status(thm)],[c_2,c_1]) ).
cnf(c_549,plain,
( is_a_theorem(implies(implies(D,A),implies(E,implies(C,A))))
| ~ is_a_theorem(implies(implies(A,B),implies(C,D))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_5,plain,
is_a_theorem(implies(implies(implies(A,implies(B,C)),implies(C,D)),implies(E,implies(implies(F,C),implies(C,D))))),
inference(resolve,[status(thm)],[c_549,c_2]) ).
cnf(c_6,plain,
( is_a_theorem(implies(E,implies(implies(F,C),implies(C,D))))
| ~ is_a_theorem(implies(implies(A,implies(B,C)),implies(C,D))) ),
inference(resolve,[status(thm)],[c_5,c_1]) ).
cnf(c_550,plain,
( is_a_theorem(implies(E,implies(implies(F,C),implies(C,D))))
| ~ is_a_theorem(implies(implies(A,implies(B,C)),implies(C,D))) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_7,plain,
is_a_theorem(implies(A,implies(implies(B,C),implies(C,implies(implies(D,E),implies(E,C)))))),
inference(resolve,[status(thm)],[c_550,c_5]) ).
cnf(c_551,plain,
( is_a_theorem(implies(implies(B,C),implies(C,implies(implies(D,E),implies(E,C)))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_7]) ).
cnf(c_10,plain,
is_a_theorem(implies(implies(A,B),implies(B,implies(implies(C,D),implies(D,B))))),
inference(resolve,[status(thm)],[c_551,c_7]) ).
cnf(c_11,plain,
is_a_theorem(implies(implies(implies(implies(A,B),implies(B,C)),D),implies(E,implies(C,D)))),
inference(resolve,[status(thm)],[c_10,c_4]) ).
cnf(c_14,plain,
is_a_theorem(implies(A,implies(implies(B,C),implies(C,implies(D,implies(E,C)))))),
inference(resolve,[status(thm)],[c_11,c_6]) ).
cnf(c_552,plain,
( is_a_theorem(implies(E,implies(C,D)))
| ~ is_a_theorem(implies(implies(implies(A,B),implies(B,C)),D)) ),
inference(resolve,[status(thm)],[c_1,c_11]) ).
cnf(c_19,plain,
is_a_theorem(implies(A,implies(B,implies(implies(B,C),implies(D,implies(E,C)))))),
inference(resolve,[status(thm)],[c_552,c_2]) ).
cnf(c_553,plain,
( is_a_theorem(implies(implies(B,C),implies(C,implies(D,implies(E,C)))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_14]) ).
cnf(c_25,plain,
is_a_theorem(implies(implies(A,B),implies(B,implies(C,implies(D,B))))),
inference(resolve,[status(thm)],[c_553,c_14]) ).
cnf(c_27,plain,
is_a_theorem(implies(implies(implies(A,implies(B,C)),D),implies(E,implies(C,D)))),
inference(resolve,[status(thm)],[c_25,c_4]) ).
cnf(c_31,plain,
is_a_theorem(implies(implies(implies(A,B),implies(C,implies(D,A))),implies(E,implies(F,implies(C,implies(D,A)))))),
inference(resolve,[status(thm)],[c_27,c_4]) ).
cnf(c_35,plain,
is_a_theorem(implies(implies(implies(implies(A,B),implies(C,implies(D,B))),E),implies(F,implies(A,E)))),
inference(resolve,[status(thm)],[c_19,c_4]) ).
cnf(c_554,plain,
( is_a_theorem(implies(E,implies(F,implies(C,implies(D,A)))))
| ~ is_a_theorem(implies(implies(A,B),implies(C,implies(D,A)))) ),
inference(resolve,[status(thm)],[c_1,c_31]) ).
cnf(c_99,plain,
is_a_theorem(implies(A,implies(B,implies(implies(C,D),implies(E,implies(D,D)))))),
inference(resolve,[status(thm)],[c_554,c_2]) ).
cnf(c_555,plain,
( is_a_theorem(implies(B,implies(implies(C,D),implies(E,implies(D,D)))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_99]) ).
cnf(c_122,plain,
is_a_theorem(implies(A,implies(implies(B,C),implies(D,implies(C,C))))),
inference(resolve,[status(thm)],[c_555,c_99]) ).
cnf(c_556,plain,
( is_a_theorem(implies(implies(B,C),implies(D,implies(C,C))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_122]) ).
cnf(c_126,plain,
is_a_theorem(implies(implies(A,B),implies(C,implies(B,B)))),
inference(resolve,[status(thm)],[c_556,c_122]) ).
cnf(c_557,plain,
( is_a_theorem(implies(E,implies(F,implies(C,implies(D,A)))))
| ~ is_a_theorem(implies(implies(A,B),implies(C,implies(D,A)))) ),
inference(resolve,[status(thm)],[c_1,c_31]) ).
cnf(c_131,plain,
is_a_theorem(implies(A,implies(B,implies(C,implies(D,D))))),
inference(resolve,[status(thm)],[c_557,c_126]) ).
cnf(c_558,plain,
( is_a_theorem(implies(B,implies(C,implies(D,D))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_131]) ).
cnf(c_141,plain,
is_a_theorem(implies(A,implies(B,implies(C,C)))),
inference(resolve,[status(thm)],[c_558,c_131]) ).
cnf(c_559,plain,
( is_a_theorem(implies(B,implies(C,C)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_141]) ).
cnf(c_144,plain,
is_a_theorem(implies(A,implies(B,B))),
inference(resolve,[status(thm)],[c_559,c_141]) ).
cnf(c_146,plain,
is_a_theorem(implies(implies(A,B),implies(C,implies(A,B)))),
inference(resolve,[status(thm)],[c_144,c_4]) ).
cnf(c_560,plain,
( is_a_theorem(implies(B,B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_144]) ).
cnf(c_148,plain,
is_a_theorem(implies(A,A)),
inference(resolve,[status(thm)],[c_560,c_144]) ).
cnf(c_561,plain,
( is_a_theorem(implies(E,implies(F,implies(C,implies(D,A)))))
| ~ is_a_theorem(implies(implies(A,B),implies(C,implies(D,A)))) ),
inference(resolve,[status(thm)],[c_1,c_31]) ).
cnf(c_151,plain,
is_a_theorem(implies(A,implies(B,implies(C,implies(D,C))))),
inference(resolve,[status(thm)],[c_561,c_148]) ).
cnf(c_156,plain,
is_a_theorem(implies(implies(implies(A,B),A),implies(C,implies(D,A)))),
inference(resolve,[status(thm)],[c_146,c_4]) ).
cnf(c_562,plain,
( is_a_theorem(implies(B,implies(C,implies(D,C))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_151]) ).
cnf(c_174,plain,
is_a_theorem(implies(A,implies(B,implies(C,B)))),
inference(resolve,[status(thm)],[c_562,c_151]) ).
cnf(c_176,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(D,implies(B,C)))),
inference(resolve,[status(thm)],[c_174,c_4]) ).
cnf(c_194,plain,
( is_a_theorem(implies(C,implies(D,A)))
| ~ is_a_theorem(implies(implies(A,B),A)) ),
inference(resolve,[status(thm)],[c_156,c_1]) ).
cnf(c_563,plain,
( is_a_theorem(implies(C,implies(D,A)))
| ~ is_a_theorem(implies(implies(A,B),A)) ),
inference(resolve,[status(thm)],[c_1,c_156]) ).
cnf(c_196,plain,
is_a_theorem(implies(A,implies(B,implies(implies(C,D),implies(C,implies(E,D)))))),
inference(resolve,[status(thm)],[c_563,c_35]) ).
cnf(c_203,plain,
is_a_theorem(implies(implies(implies(A,B),implies(C,A)),implies(D,implies(E,implies(C,A))))),
inference(resolve,[status(thm)],[c_176,c_4]) ).
cnf(c_564,plain,
( is_a_theorem(implies(B,implies(implies(C,D),implies(C,implies(E,D)))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_196]) ).
cnf(c_228,plain,
is_a_theorem(implies(A,implies(implies(B,C),implies(B,implies(D,C))))),
inference(resolve,[status(thm)],[c_564,c_196]) ).
cnf(c_230,plain,
is_a_theorem(implies(implies(implies(A,implies(B,C)),D),implies(E,implies(implies(A,C),D)))),
inference(resolve,[status(thm)],[c_228,c_4]) ).
cnf(c_323,plain,
( is_a_theorem(implies(D,implies(E,implies(C,A))))
| ~ is_a_theorem(implies(implies(A,B),implies(C,A))) ),
inference(resolve,[status(thm)],[c_203,c_1]) ).
cnf(c_329,plain,
is_a_theorem(implies(A,implies(B,implies(C,implies(implies(C,D),D))))),
inference(resolve,[status(thm)],[c_230,c_194]) ).
cnf(c_565,plain,
( is_a_theorem(implies(B,implies(C,implies(implies(C,D),D))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_329]) ).
cnf(c_352,plain,
is_a_theorem(implies(A,implies(B,implies(implies(B,C),C)))),
inference(resolve,[status(thm)],[c_565,c_329]) ).
cnf(c_566,plain,
( is_a_theorem(implies(B,implies(implies(B,C),C)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_352]) ).
cnf(c_357,plain,
is_a_theorem(implies(A,implies(implies(A,B),B))),
inference(resolve,[status(thm)],[c_566,c_352]) ).
cnf(c_359,plain,
is_a_theorem(implies(A,implies(B,implies(implies(implies(C,D),C),C)))),
inference(resolve,[status(thm)],[c_357,c_323]) ).
cnf(c_567,plain,
( is_a_theorem(implies(implies(A,B),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_357]) ).
cnf(c_405,plain,
is_a_theorem(implies(implies(implies(A,implies(B,B)),C),C)),
inference(resolve,[status(thm)],[c_567,c_144]) ).
cnf(c_521,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(A,implies(B,B)),C)) ),
inference(resolve,[status(thm)],[c_405,c_1]) ).
cnf(c_541,plain,
is_a_theorem(implies(A,implies(implies(implies(B,C),B),B))),
inference(resolve,[status(thm)],[c_359,c_521]) ).
cnf(c_547,plain,
is_a_theorem(implies(implies(implies(A,B),A),A)),
inference(resolve,[status(thm)],[c_541,c_521]) ).
cnf(c_548,plain,
$false,
inference(resolve,[status(thm)],[c_547,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL092-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n026.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Fri Sep 25 21:53:10 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 3543530 was started by sandbox2 on n026,
% 0.19/0.45 % Fri Sep 25 21:53:10 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.45
% 0.19/0.45 % From the command line: assign(max_seconds, 300).
% 2.05/0.73
% 2.05/0.73 % SZS status Unsatisfiable for theBenchmark
% 2.05/0.73
% 2.05/0.73 % Proof 1 at 0.15 (+ 0.12) seconds.
% 2.05/0.73 % Length of proof is 42.
% 2.05/0.73 % Level of proof is 27.
% 2.05/0.73 % Maximum clause weight is 90.000.
% 2.05/0.73 % Given clauses 140.
% 2.05/0.73
% 2.05/0.73 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------