%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL045-1 : 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 : n016.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 99.51s 14.03s
% Output : CNFRefutation 99.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 51 ( 31 unt; 0 def)
% Number of atoms : 73 ( 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 124 ( 19 sgn 14 !; 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_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_2,plain,
is_a_theorem(implies(A,implies(not(A),B))),
inference(clausify,[status(thm)],[cn_3]) ).
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_3,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(clausify,[status(thm)],[cn_18]) ).
fof(cn_21,axiom,
! [VAR_0,VAR_1,VAR_2] : is_a_theorem(implies(implies(VAR_0,implies(VAR_1,VAR_2)),implies(VAR_1,implies(VAR_0,VAR_2)))),
file('theBenchmark.p',cn_21) ).
cnf(c_4,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(B,implies(A,C)))),
inference(clausify,[status(thm)],[cn_21]) ).
fof(cn_22,axiom,
! [VAR_0,VAR_1,VAR_2] : is_a_theorem(implies(implies(VAR_0,VAR_1),implies(implies(VAR_2,VAR_0),implies(VAR_2,VAR_1)))),
file('theBenchmark.p',cn_22) ).
cnf(c_5,plain,
is_a_theorem(implies(implies(A,B),implies(implies(C,A),implies(C,B)))),
inference(clausify,[status(thm)],[cn_22]) ).
fof(cn_54,axiom,
! [VAR_0,VAR_1] : is_a_theorem(implies(implies(VAR_0,VAR_1),implies(implies(not(VAR_0),VAR_1),VAR_1))),
file('theBenchmark.p',cn_54) ).
cnf(c_6,plain,
is_a_theorem(implies(implies(A,B),implies(implies(not(A),B),B))),
inference(clausify,[status(thm)],[cn_54]) ).
fof(prove_cn_46,axiom,
~ is_a_theorem(implies(implies(a,b),implies(not(b),not(a)))),
file('theBenchmark.p',prove_cn_46) ).
cnf(c_7,plain,
~ is_a_theorem(implies(implies(a,b),implies(not(b),not(a)))),
inference(clausify,[status(thm)],[prove_cn_46]) ).
cnf(c_19954,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_18,plain,
is_a_theorem(implies(A,implies(B,B))),
inference(resolve,[status(thm)],[c_19954,c_3]) ).
cnf(c_19955,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_19,plain,
is_a_theorem(implies(not(A),implies(A,B))),
inference(resolve,[status(thm)],[c_19955,c_2]) ).
cnf(c_20,plain,
( is_a_theorem(implies(implies(C,A),implies(C,B)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_5,c_1]) ).
cnf(c_19956,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_22,plain,
is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))),
inference(resolve,[status(thm)],[c_19956,c_5]) ).
cnf(c_19957,plain,
( is_a_theorem(implies(implies(C,A),implies(C,B)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_26,plain,
is_a_theorem(implies(implies(A,B),implies(A,implies(C,B)))),
inference(resolve,[status(thm)],[c_19957,c_3]) ).
cnf(c_19958,plain,
( is_a_theorem(implies(implies(C,A),implies(C,B)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_27,plain,
is_a_theorem(implies(implies(A,B),implies(A,implies(not(B),C)))),
inference(resolve,[status(thm)],[c_19958,c_2]) ).
cnf(c_19959,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_31,plain,
is_a_theorem(implies(implies(not(A),B),implies(implies(A,B),B))),
inference(resolve,[status(thm)],[c_19959,c_6]) ).
cnf(c_19960,plain,
( is_a_theorem(implies(B,B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_18]) ).
cnf(c_46,plain,
is_a_theorem(implies(A,A)),
inference(resolve,[status(thm)],[c_19960,c_18]) ).
cnf(c_19961,plain,
( is_a_theorem(implies(implies(not(A),B),B))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_48,plain,
is_a_theorem(implies(implies(not(A),A),A)),
inference(resolve,[status(thm)],[c_19961,c_46]) ).
cnf(c_71,plain,
is_a_theorem(implies(implies(A,implies(not(B),B)),implies(A,B))),
inference(resolve,[status(thm)],[c_48,c_20]) ).
cnf(c_185,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_22,c_1]) ).
cnf(c_19962,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_22]) ).
cnf(c_195,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(not(A),C))),
inference(resolve,[status(thm)],[c_19962,c_19]) ).
cnf(c_19963,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_22]) ).
cnf(c_201,plain,
is_a_theorem(implies(implies(implies(implies(not(A),B),B),C),implies(implies(A,B),C))),
inference(resolve,[status(thm)],[c_19963,c_6]) ).
cnf(c_262,plain,
( is_a_theorem(implies(A,implies(C,B)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_26,c_1]) ).
cnf(c_297,plain,
is_a_theorem(implies(implies(implies(A,implies(not(B),C)),D),implies(implies(A,B),D))),
inference(resolve,[status(thm)],[c_27,c_185]) ).
cnf(c_458,plain,
( is_a_theorem(implies(implies(A,B),B))
| ~ is_a_theorem(implies(not(A),B)) ),
inference(resolve,[status(thm)],[c_31,c_1]) ).
cnf(c_19964,plain,
( is_a_theorem(implies(not(A),C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_195]) ).
cnf(c_891,plain,
is_a_theorem(implies(not(implies(A,B)),implies(not(A),C))),
inference(resolve,[status(thm)],[c_19964,c_195]) ).
cnf(c_19965,plain,
( is_a_theorem(implies(A,B))
| ~ is_a_theorem(implies(A,implies(not(B),B))) ),
inference(resolve,[status(thm)],[c_1,c_71]) ).
cnf(c_1295,plain,
is_a_theorem(implies(not(implies(A,B)),A)),
inference(resolve,[status(thm)],[c_19965,c_891]) ).
cnf(c_1427,plain,
is_a_theorem(implies(not(implies(A,B)),implies(C,A))),
inference(resolve,[status(thm)],[c_1295,c_262]) ).
cnf(c_1517,plain,
is_a_theorem(implies(implies(implies(A,B),implies(C,A)),implies(C,A))),
inference(resolve,[status(thm)],[c_1427,c_458]) ).
cnf(c_19966,plain,
( is_a_theorem(implies(implies(A,B),D))
| ~ is_a_theorem(implies(implies(A,implies(not(B),C)),D)) ),
inference(resolve,[status(thm)],[c_1,c_297]) ).
cnf(c_19851,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(not(C),A))),
inference(resolve,[status(thm)],[c_19966,c_1517]) ).
cnf(c_19967,plain,
( is_a_theorem(implies(implies(A,B),C))
| ~ is_a_theorem(implies(implies(implies(not(A),B),B),C)) ),
inference(resolve,[status(thm)],[c_1,c_201]) ).
cnf(c_19952,plain,
is_a_theorem(implies(implies(A,B),implies(not(B),not(A)))),
inference(resolve,[status(thm)],[c_19967,c_19851]) ).
cnf(c_19953,plain,
$false,
inference(resolve,[status(thm)],[c_19952,c_7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL045-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 21:51:00 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 3379482 was started by sandbox on n016,
% 0.09/0.36 % Fri Sep 25 21:51:00 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 99.51/14.03
% 99.51/14.03 % Assigning unary symbol not kb_weight 0 and highest precedence (5).
% 99.51/14.03
% 99.51/14.03 % given #500 (T,wt=25): 14586 -is_a_theorem(implies(not(A),B)) | is_a_theorem(implies(not(B),A)). [resolve(14224,a,1,a)].
% 99.51/14.03
% 99.51/14.03 % SZS status Unsatisfiable for theBenchmark
% 99.51/14.03
% 99.51/14.03 % Proof 1 at 3.76 (+ 1.81) seconds.
% 99.51/14.03 % Length of proof is 30.
% 99.51/14.03 % Level of proof is 10.
% 99.51/14.03 % Maximum clause weight is 45.000.
% 99.51/14.03 % Given clauses 660.
% 99.51/14.03
% 99.51/14.03 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------