%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL091-1 : 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 : n018.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 0.18s 0.50s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 3
% Syntax : Number of formulae : 43 ( 23 unt; 0 def)
% Number of atoms : 65 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 46 ( 24 ~; 22 |; 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 : 191 ( 109 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_2,axiom,
~ is_a_theorem(implies(a,implies(b,a))),
file('theBenchmark.p',prove_ic_2) ).
cnf(c_3,plain,
~ is_a_theorem(implies(a,implies(b,a))),
inference(clausify,[status(thm)],[prove_ic_2]) ).
cnf(c_172,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_4,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_172,c_2]) ).
cnf(c_173,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_4]) ).
cnf(c_5,plain,
is_a_theorem(implies(A,implies(implies(B,C),implies(C,implies(implies(D,E),implies(E,C)))))),
inference(resolve,[status(thm)],[c_173,c_4]) ).
cnf(c_174,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_6,plain,
is_a_theorem(implies(implies(implies(implies(A,B),implies(B,C)),implies(D,implies(E,B))),implies(F,implies(V6,implies(D,implies(E,B)))))),
inference(resolve,[status(thm)],[c_174,c_4]) ).
cnf(c_175,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_5]) ).
cnf(c_7,plain,
is_a_theorem(implies(implies(A,B),implies(B,implies(implies(C,D),implies(D,B))))),
inference(resolve,[status(thm)],[c_175,c_5]) ).
cnf(c_176,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_11,plain,
is_a_theorem(implies(implies(implies(A,implies(B,implies(C,D))),implies(implies(E,D),implies(D,F))),implies(V6,implies(V7,implies(implies(E,D),implies(D,F)))))),
inference(resolve,[status(thm)],[c_176,c_6]) ).
cnf(c_177,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_14,plain,
is_a_theorem(implies(implies(implies(implies(A,B),implies(B,C)),D),implies(E,implies(C,D)))),
inference(resolve,[status(thm)],[c_177,c_7]) ).
cnf(c_178,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_4]) ).
cnf(c_20,plain,
is_a_theorem(implies(A,implies(implies(B,C),implies(C,implies(D,implies(E,C)))))),
inference(resolve,[status(thm)],[c_178,c_14]) ).
cnf(c_179,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_20]) ).
cnf(c_25,plain,
is_a_theorem(implies(implies(A,B),implies(B,implies(C,implies(D,B))))),
inference(resolve,[status(thm)],[c_179,c_20]) ).
cnf(c_180,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_30,plain,
is_a_theorem(implies(implies(implies(A,implies(B,C)),D),implies(E,implies(C,D)))),
inference(resolve,[status(thm)],[c_180,c_25]) ).
cnf(c_181,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_34,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_181,c_30]) ).
cnf(c_182,plain,
( is_a_theorem(implies(V6,implies(V7,implies(implies(E,D),implies(D,F)))))
| ~ is_a_theorem(implies(implies(A,implies(B,implies(C,D))),implies(implies(E,D),implies(D,F)))) ),
inference(resolve,[status(thm)],[c_1,c_11]) ).
cnf(c_39,plain,
is_a_theorem(implies(A,implies(B,implies(implies(implies(C,D),D),implies(D,implies(E,D)))))),
inference(resolve,[status(thm)],[c_182,c_2]) ).
cnf(c_183,plain,
( is_a_theorem(implies(B,implies(implies(implies(C,D),D),implies(D,implies(E,D)))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_39]) ).
cnf(c_93,plain,
is_a_theorem(implies(A,implies(implies(implies(B,C),C),implies(C,implies(D,C))))),
inference(resolve,[status(thm)],[c_183,c_39]) ).
cnf(c_184,plain,
( is_a_theorem(implies(implies(implies(B,C),C),implies(C,implies(D,C))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_93]) ).
cnf(c_98,plain,
is_a_theorem(implies(implies(implies(A,B),B),implies(B,implies(C,B)))),
inference(resolve,[status(thm)],[c_184,c_93]) ).
cnf(c_185,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_126,plain,
is_a_theorem(implies(implies(implies(A,B),implies(C,B)),implies(D,implies(B,implies(C,B))))),
inference(resolve,[status(thm)],[c_185,c_98]) ).
cnf(c_186,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_34]) ).
cnf(c_129,plain,
is_a_theorem(implies(A,implies(B,implies(C,implies(D,implies(E,D)))))),
inference(resolve,[status(thm)],[c_186,c_126]) ).
cnf(c_187,plain,
( is_a_theorem(implies(B,implies(C,implies(D,implies(E,D)))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_129]) ).
cnf(c_163,plain,
is_a_theorem(implies(A,implies(B,implies(C,implies(D,C))))),
inference(resolve,[status(thm)],[c_187,c_129]) ).
cnf(c_188,plain,
( is_a_theorem(implies(B,implies(C,implies(D,C))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_163]) ).
cnf(c_167,plain,
is_a_theorem(implies(A,implies(B,implies(C,B)))),
inference(resolve,[status(thm)],[c_188,c_163]) ).
cnf(c_189,plain,
( is_a_theorem(implies(B,implies(C,B)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_167]) ).
cnf(c_170,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(resolve,[status(thm)],[c_189,c_167]) ).
cnf(c_171,plain,
$false,
inference(resolve,[status(thm)],[c_170,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL091-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n018.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Fri Sep 25 21:52:51 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 2930294 was started by sandbox2 on n018,
% 0.18/0.44 % Fri Sep 25 21:52:51 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 0.18/0.50
% 0.18/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.50
% 0.18/0.50 % Proof 1 at 0.03 (+ 0.02) seconds.
% 0.18/0.50 % Length of proof is 22.
% 0.18/0.50 % Level of proof is 13.
% 0.18/0.50 % Maximum clause weight is 58.000.
% 0.18/0.50 % Given clauses 36.
% 0.18/0.50
% 0.18/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------