%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL087-1 : 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 07:57:56 AM UTC 2026
% Result : Unsatisfiable 0.11s 5.43s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 13 unt; 0 def)
% Number of atoms : 35 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 14 ~; 12 |; 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 : 75 ( 32 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_4,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(VAR_4,implies(implies(VAR_3,VAR_0),implies(VAR_2,VAR_0))))),
file('theBenchmark.p',ic_JLukasiewicz_4) ).
cnf(c_2,plain,
is_a_theorem(implies(implies(implies(A,B),implies(C,D)),implies(E,implies(implies(D,A),implies(C,A))))),
inference(clausify,[status(thm)],[ic_JLukasiewicz_4]) ).
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_37,plain,
( is_a_theorem(implies(E,implies(implies(D,A),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(A,implies(implies(implies(implies(B,C),implies(D,C)),implies(C,E)),implies(F,implies(C,E))))),
inference(resolve,[status(thm)],[c_37,c_2]) ).
cnf(c_38,plain,
( is_a_theorem(implies(implies(implies(implies(B,C),implies(D,C)),implies(C,E)),implies(F,implies(C,E))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_5,plain,
is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),implies(B,D)),implies(E,implies(B,D)))),
inference(resolve,[status(thm)],[c_38,c_4]) ).
cnf(c_39,plain,
( is_a_theorem(implies(E,implies(B,D)))
| ~ is_a_theorem(implies(implies(implies(A,B),implies(C,B)),implies(B,D))) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_6,plain,
is_a_theorem(implies(A,implies(implies(B,C),implies(C,implies(B,C))))),
inference(resolve,[status(thm)],[c_39,c_5]) ).
cnf(c_40,plain,
( is_a_theorem(implies(implies(B,C),implies(C,implies(B,C))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_8,plain,
is_a_theorem(implies(implies(A,B),implies(B,implies(A,B)))),
inference(resolve,[status(thm)],[c_40,c_6]) ).
cnf(c_41,plain,
( is_a_theorem(implies(E,implies(implies(D,A),implies(C,A))))
| ~ is_a_theorem(implies(implies(A,B),implies(C,D))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_10,plain,
is_a_theorem(implies(A,implies(implies(implies(B,C),B),implies(C,B)))),
inference(resolve,[status(thm)],[c_41,c_8]) ).
cnf(c_42,plain,
( is_a_theorem(implies(implies(implies(B,C),B),implies(C,B)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_10]) ).
cnf(c_21,plain,
is_a_theorem(implies(implies(implies(A,B),A),implies(B,A))),
inference(resolve,[status(thm)],[c_42,c_10]) ).
cnf(c_43,plain,
( is_a_theorem(implies(E,implies(B,D)))
| ~ is_a_theorem(implies(implies(implies(A,B),implies(C,B)),implies(B,D))) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_26,plain,
is_a_theorem(implies(A,implies(B,implies(C,B)))),
inference(resolve,[status(thm)],[c_43,c_21]) ).
cnf(c_44,plain,
( is_a_theorem(implies(B,implies(C,B)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_26]) ).
cnf(c_35,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(resolve,[status(thm)],[c_44,c_26]) ).
cnf(c_36,plain,
$false,
inference(resolve,[status(thm)],[c_35,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL087-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.41 % Computer : n018.cluster.edu
% 0.11/5.41 % Model : x86_64 x86_64
% 0.11/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.41 % Memory : 8046.5625MB
% 0.11/5.41 % OS : Linux 6.8.0-71-generic
% 0.11/5.41 % CPULimit : 300
% 0.11/5.41 % WCLimit : 300
% 0.11/5.41 % DateTime : Fri Sep 25 21:52:42 UTC 2026
% 0.11/5.41 % CPUTime :
% 0.11/5.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.41 % Process 2929313 was started by sandbox2 on n018,
% 0.11/5.41 % Fri Sep 25 21:52:42 2026
% 0.11/5.41 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/5.42
% 0.11/5.42 % From the command line: assign(max_seconds, 300).
% 0.11/5.43
% 0.11/5.43 % SZS status Unsatisfiable for theBenchmark
% 0.11/5.43
% 0.11/5.43 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.11/5.43 % Length of proof is 12.
% 0.11/5.43 % Level of proof is 9.
% 0.11/5.43 % Maximum clause weight is 90.000.
% 0.11/5.43 % Given clauses 16.
% 0.11/5.43
% 0.11/5.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------