%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL363-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 07:58:40 AM UTC 2026
% Result : Unsatisfiable 0.12s 10.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 20 unt; 0 def)
% Number of atoms : 48 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 32 ( 17 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 81 ( 12 sgn 8 !; 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_1,axiom,
! [VAR_0,VAR_1,VAR_2] : is_a_theorem(implies(implies(VAR_0,VAR_1),implies(implies(VAR_1,VAR_2),implies(VAR_0,VAR_2)))),
file('theBenchmark.p',cn_1) ).
cnf(c_2,plain,
is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))),
inference(clausify,[status(thm)],[cn_1]) ).
fof(cn_2,axiom,
! [VAR_0] : is_a_theorem(implies(implies(not(VAR_0),VAR_0),VAR_0)),
file('theBenchmark.p',cn_2) ).
cnf(c_3,plain,
is_a_theorem(implies(implies(not(A),A),A)),
inference(clausify,[status(thm)],[cn_2]) ).
fof(cn_3,axiom,
! [VAR_0,VAR_1] : is_a_theorem(implies(VAR_0,implies(not(VAR_0),VAR_1))),
file('theBenchmark.p',cn_3) ).
cnf(c_4,plain,
is_a_theorem(implies(A,implies(not(A),B))),
inference(clausify,[status(thm)],[cn_3]) ).
fof(prove_cn_12,axiom,
~ is_a_theorem(implies(x,implies(implies(not(y),y),y))),
file('theBenchmark.p',prove_cn_12) ).
cnf(c_5,plain,
~ is_a_theorem(implies(x,implies(implies(not(y),y),y))),
inference(clausify,[status(thm)],[prove_cn_12]) ).
cnf(c_207,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_6,plain,
is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),D),implies(implies(C,A),D))),
inference(resolve,[status(thm)],[c_207,c_2]) ).
cnf(c_208,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_7,plain,
is_a_theorem(implies(implies(A,B),implies(implies(not(A),A),B))),
inference(resolve,[status(thm)],[c_208,c_3]) ).
cnf(c_209,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_9,plain,
is_a_theorem(implies(implies(implies(not(A),B),C),implies(A,C))),
inference(resolve,[status(thm)],[c_209,c_4]) ).
cnf(c_210,plain,
( is_a_theorem(implies(implies(C,A),D))
| ~ is_a_theorem(implies(implies(implies(A,B),implies(C,B)),D)) ),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_12,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(D,B),implies(A,implies(D,C))))),
inference(resolve,[status(thm)],[c_210,c_6]) ).
cnf(c_211,plain,
( is_a_theorem(implies(implies(C,A),D))
| ~ is_a_theorem(implies(implies(implies(A,B),implies(C,B)),D)) ),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_29,plain,
is_a_theorem(implies(implies(A,not(B)),implies(B,implies(A,C)))),
inference(resolve,[status(thm)],[c_211,c_9]) ).
cnf(c_212,plain,
( is_a_theorem(implies(A,C))
| ~ is_a_theorem(implies(implies(not(A),B),C)) ),
inference(resolve,[status(thm)],[c_1,c_9]) ).
cnf(c_34,plain,
is_a_theorem(implies(A,A)),
inference(resolve,[status(thm)],[c_212,c_3]) ).
cnf(c_213,plain,
( is_a_theorem(implies(not(A),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_36,plain,
is_a_theorem(implies(not(implies(A,A)),B)),
inference(resolve,[status(thm)],[c_213,c_34]) ).
cnf(c_214,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,not(B))) ),
inference(resolve,[status(thm)],[c_1,c_29]) ).
cnf(c_44,plain,
is_a_theorem(implies(A,implies(not(implies(B,B)),C))),
inference(resolve,[status(thm)],[c_214,c_36]) ).
cnf(c_215,plain,
( is_a_theorem(implies(implies(D,B),implies(A,implies(D,C))))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_12]) ).
cnf(c_127,plain,
is_a_theorem(implies(implies(A,implies(not(B),B)),implies(implies(B,C),implies(A,C)))),
inference(resolve,[status(thm)],[c_215,c_7]) ).
cnf(c_216,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,implies(not(B),B))) ),
inference(resolve,[status(thm)],[c_1,c_127]) ).
cnf(c_184,plain,
is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))),
inference(resolve,[status(thm)],[c_216,c_44]) ).
cnf(c_217,plain,
( is_a_theorem(implies(C,B))
| ~ is_a_theorem(implies(implies(A,A),B)) ),
inference(resolve,[status(thm)],[c_1,c_184]) ).
cnf(c_205,plain,
is_a_theorem(implies(A,implies(implies(not(B),B),B))),
inference(resolve,[status(thm)],[c_217,c_7]) ).
cnf(c_206,plain,
$false,
inference(resolve,[status(thm)],[c_205,c_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL363-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/10.37 % Computer : n002.cluster.edu
% 0.08/10.37 % Model : x86_64 x86_64
% 0.08/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/10.37 % Memory : 8046.5625MB
% 0.08/10.37 % OS : Linux 6.8.0-71-generic
% 0.08/10.37 % CPULimit : 300
% 0.08/10.37 % WCLimit : 300
% 0.08/10.37 % DateTime : Fri Sep 25 22:22:31 UTC 2026
% 0.08/10.37 % CPUTime :
% 0.08/10.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/10.37 % Process 146525 was started by sandbox2 on n002,
% 0.08/10.37 % Fri Sep 25 22:22:31 2026
% 0.08/10.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/10.38
% 0.08/10.38 % From the command line: assign(max_seconds, 300).
% 0.12/10.40
% 0.12/10.40 % SZS status Unsatisfiable for theBenchmark
% 0.12/10.40
% 0.12/10.40 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.12/10.40 % Length of proof is 17.
% 0.12/10.40 % Level of proof is 7.
% 0.12/10.40 % Maximum clause weight is 41.000.
% 0.12/10.40 % Given clauses 28.
% 0.12/10.40
% 0.12/10.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------