%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL040-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 07:57:49 AM UTC 2026
% Result : Unsatisfiable 24.12s 8.58s
% Output : CNFRefutation 24.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 17 unt; 0 def)
% Number of atoms : 43 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 16 ~; 14 |; 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 75 ( 12 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(cn_18,axiom,
! [VAR_0,VAR_1] : is_a_theorem(implies(VAR_0,implies(VAR_1,VAR_0))),
file('theBenchmark.p',cn_18) ).
cnf(c_2,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(clausify,[status(thm)],[cn_18]) ).
fof(cn_35,axiom,
! [VAR_0,VAR_1,VAR_2] : is_a_theorem(implies(implies(VAR_0,implies(VAR_1,VAR_2)),implies(implies(VAR_0,VAR_1),implies(VAR_0,VAR_2)))),
file('theBenchmark.p',cn_35) ).
cnf(c_3,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(A,B),implies(A,C)))),
inference(clausify,[status(thm)],[cn_35]) ).
fof(prove_cn_21,axiom,
~ is_a_theorem(implies(implies(a,implies(b,c)),implies(b,implies(a,c)))),
file('theBenchmark.p',prove_cn_21) ).
cnf(c_7,plain,
~ is_a_theorem(implies(implies(a,implies(b,c)),implies(b,implies(a,c)))),
inference(clausify,[status(thm)],[prove_cn_21]) ).
cnf(c_10911,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_8,plain,
is_a_theorem(implies(A,implies(B,implies(C,B)))),
inference(resolve,[status(thm)],[c_10911,c_2]) ).
cnf(c_10912,plain,
( is_a_theorem(implies(implies(A,B),implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_9,plain,
is_a_theorem(implies(implies(implies(A,implies(B,C)),implies(A,B)),implies(implies(A,implies(B,C)),implies(A,C)))),
inference(resolve,[status(thm)],[c_10912,c_3]) ).
cnf(c_10913,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_10,plain,
is_a_theorem(implies(A,implies(implies(B,implies(C,D)),implies(implies(B,C),implies(B,D))))),
inference(resolve,[status(thm)],[c_10913,c_3]) ).
cnf(c_10914,plain,
( is_a_theorem(implies(implies(A,implies(B,C)),implies(A,C)))
| ~ is_a_theorem(implies(implies(A,implies(B,C)),implies(A,B))) ),
inference(resolve,[status(thm)],[c_1,c_9]) ).
cnf(c_33,plain,
is_a_theorem(implies(implies(A,implies(implies(B,A),C)),implies(A,C))),
inference(resolve,[status(thm)],[c_10914,c_8]) ).
cnf(c_10915,plain,
( is_a_theorem(implies(implies(A,implies(B,C)),implies(A,C)))
| ~ is_a_theorem(implies(implies(A,implies(B,C)),implies(A,B))) ),
inference(resolve,[status(thm)],[c_1,c_9]) ).
cnf(c_53,plain,
is_a_theorem(implies(implies(implies(A,implies(B,C)),implies(implies(implies(A,B),implies(A,C)),D)),implies(implies(A,implies(B,C)),D))),
inference(resolve,[status(thm)],[c_10915,c_10]) ).
cnf(c_10916,plain,
( is_a_theorem(implies(A,C))
| ~ is_a_theorem(implies(A,implies(implies(B,A),C))) ),
inference(resolve,[status(thm)],[c_1,c_33]) ).
cnf(c_679,plain,
is_a_theorem(implies(implies(A,B),implies(implies(C,A),implies(C,B)))),
inference(resolve,[status(thm)],[c_10916,c_10]) ).
cnf(c_10917,plain,
( is_a_theorem(implies(implies(A,B),implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_774,plain,
is_a_theorem(implies(implies(implies(A,B),implies(C,A)),implies(implies(A,B),implies(C,B)))),
inference(resolve,[status(thm)],[c_10917,c_679]) ).
cnf(c_10918,plain,
( is_a_theorem(implies(implies(A,B),implies(C,B)))
| ~ is_a_theorem(implies(implies(A,B),implies(C,A))) ),
inference(resolve,[status(thm)],[c_1,c_774]) ).
cnf(c_1089,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))),
inference(resolve,[status(thm)],[c_10918,c_8]) ).
cnf(c_10919,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_1103,plain,
is_a_theorem(implies(A,implies(implies(implies(B,C),D),implies(C,D)))),
inference(resolve,[status(thm)],[c_10919,c_1089]) ).
cnf(c_10920,plain,
( is_a_theorem(implies(implies(A,implies(B,C)),D))
| ~ is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(implies(A,B),implies(A,C)),D))) ),
inference(resolve,[status(thm)],[c_1,c_53]) ).
cnf(c_10909,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(B,implies(A,C)))),
inference(resolve,[status(thm)],[c_10920,c_1103]) ).
cnf(c_10910,plain,
$false,
inference(resolve,[status(thm)],[c_10909,c_7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL040-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/5.47 % Computer : n015.cluster.edu
% 0.19/5.47 % Model : x86_64 x86_64
% 0.19/5.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.47 % Memory : 8046.5625MB
% 0.19/5.47 % OS : Linux 6.8.0-71-generic
% 0.19/5.47 % CPULimit : 300
% 0.19/5.47 % WCLimit : 300
% 0.19/5.47 % DateTime : Fri Sep 25 21:48:47 UTC 2026
% 0.19/5.47 % CPUTime :
% 0.19/5.47 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/5.47 % Process 2337365 was started by sandbox on n015,
% 0.19/5.47 % Fri Sep 25 21:48:47 2026
% 0.19/5.47 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.19/5.48
% 0.19/5.48 % From the command line: assign(max_seconds, 300).
% 24.12/8.58
% 24.12/8.58 % SZS status Unsatisfiable for theBenchmark
% 24.12/8.58
% 24.12/8.58 % Proof 1 at 2.10 (+ 0.97) seconds.
% 24.12/8.58 % Length of proof is 15.
% 24.12/8.58 % Level of proof is 8.
% 24.12/8.58 % Maximum clause weight is 54.000.
% 24.12/8.58 % Given clauses 335.
% 24.12/8.58
% 24.12/8.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------