%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL390-1 : 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 : n026.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 07:58:47 AM UTC 2026
% Result : Unsatisfiable 43.06s 5.98s
% Output : CNFRefutation 43.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 5
% Syntax : Number of formulae : 79 ( 43 unt; 0 def)
% Number of atoms : 117 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 78 ( 40 ~; 38 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 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 : 227 ( 34 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_53,axiom,
~ is_a_theorem(implies(implies(not(x),y),implies(implies(x,y),y))),
file('theBenchmark.p',prove_cn_53) ).
cnf(c_5,plain,
~ is_a_theorem(implies(implies(not(x),y),implies(implies(x,y),y))),
inference(clausify,[status(thm)],[prove_cn_53]) ).
cnf(c_21839,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_21839,c_2]) ).
cnf(c_21840,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_21840,c_3]) ).
cnf(c_21841,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_21841,c_4]) ).
cnf(c_21842,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_21842,c_6]) ).
cnf(c_21843,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_14,plain,
is_a_theorem(implies(implies(implies(implies(A,B),C),D),implies(implies(implies(implies(B,E),implies(A,E)),C),D))),
inference(resolve,[status(thm)],[c_21843,c_6]) ).
cnf(c_21844,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_20,plain,
is_a_theorem(implies(implies(implies(implies(not(A),A),B),C),implies(implies(A,B),C))),
inference(resolve,[status(thm)],[c_21844,c_7]) ).
cnf(c_21845,plain,
( is_a_theorem(implies(implies(not(A),A),B))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_7]) ).
cnf(c_21,plain,
is_a_theorem(implies(implies(not(implies(implies(implies(A,B),implies(C,B)),D)),implies(implies(implies(A,B),implies(C,B)),D)),implies(implies(C,A),D))),
inference(resolve,[status(thm)],[c_21845,c_6]) ).
cnf(c_21846,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_32,plain,
is_a_theorem(implies(implies(A,not(B)),implies(B,implies(A,C)))),
inference(resolve,[status(thm)],[c_21846,c_9]) ).
cnf(c_21847,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_37,plain,
is_a_theorem(implies(A,A)),
inference(resolve,[status(thm)],[c_21847,c_3]) ).
cnf(c_21848,plain,
( is_a_theorem(implies(not(A),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_39,plain,
is_a_theorem(implies(not(implies(A,A)),B)),
inference(resolve,[status(thm)],[c_21848,c_37]) ).
cnf(c_21849,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_46,plain,
is_a_theorem(implies(implies(implies(A,implies(B,C)),D),implies(implies(B,not(A)),D))),
inference(resolve,[status(thm)],[c_21849,c_32]) ).
cnf(c_21850,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,not(B))) ),
inference(resolve,[status(thm)],[c_1,c_32]) ).
cnf(c_47,plain,
is_a_theorem(implies(A,implies(not(implies(B,B)),C))),
inference(resolve,[status(thm)],[c_21850,c_39]) ).
cnf(c_21851,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_80,plain,
is_a_theorem(implies(implies(A,implies(not(B),B)),implies(implies(B,C),implies(A,C)))),
inference(resolve,[status(thm)],[c_21851,c_7]) ).
cnf(c_21852,plain,
( is_a_theorem(implies(implies(implies(implies(B,E),implies(A,E)),C),D))
| ~ is_a_theorem(implies(implies(implies(A,B),C),D)) ),
inference(resolve,[status(thm)],[c_1,c_14]) ).
cnf(c_151,plain,
is_a_theorem(implies(implies(implies(implies(implies(A,B),C),implies(implies(D,B),C)),E),implies(implies(A,D),E))),
inference(resolve,[status(thm)],[c_21852,c_6]) ).
cnf(c_21853,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_80]) ).
cnf(c_240,plain,
is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))),
inference(resolve,[status(thm)],[c_21853,c_47]) ).
cnf(c_21854,plain,
( is_a_theorem(implies(C,B))
| ~ is_a_theorem(implies(implies(A,A),B)) ),
inference(resolve,[status(thm)],[c_1,c_240]) ).
cnf(c_263,plain,
is_a_theorem(implies(A,implies(implies(not(B),B),B))),
inference(resolve,[status(thm)],[c_21854,c_7]) ).
cnf(c_21855,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_518,plain,
is_a_theorem(implies(implies(A,implies(not(B),B)),implies(C,implies(A,B)))),
inference(resolve,[status(thm)],[c_21855,c_263]) ).
cnf(c_21856,plain,
( is_a_theorem(implies(implies(B,not(A)),D))
| ~ is_a_theorem(implies(implies(A,implies(B,C)),D)) ),
inference(resolve,[status(thm)],[c_1,c_46]) ).
cnf(c_1045,plain,
is_a_theorem(implies(implies(not(A),not(B)),implies(C,implies(B,A)))),
inference(resolve,[status(thm)],[c_21856,c_518]) ).
cnf(c_21857,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_1080,plain,
is_a_theorem(implies(A,implies(B,implies(C,A)))),
inference(resolve,[status(thm)],[c_21857,c_1045]) ).
cnf(c_21858,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_80]) ).
cnf(c_1205,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))),
inference(resolve,[status(thm)],[c_21858,c_1080]) ).
cnf(c_21859,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_1205]) ).
cnf(c_1328,plain,
is_a_theorem(implies(not(A),implies(B,implies(A,C)))),
inference(resolve,[status(thm)],[c_21859,c_1045]) ).
cnf(c_21860,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_80]) ).
cnf(c_1348,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(not(A),C))),
inference(resolve,[status(thm)],[c_21860,c_1328]) ).
cnf(c_21861,plain,
( is_a_theorem(implies(C,implies(A,B)))
| ~ is_a_theorem(implies(A,implies(not(B),B))) ),
inference(resolve,[status(thm)],[c_1,c_518]) ).
cnf(c_1552,plain,
is_a_theorem(implies(A,implies(implies(implies(B,C),B),B))),
inference(resolve,[status(thm)],[c_21861,c_1348]) ).
cnf(c_21862,plain,
( is_a_theorem(implies(implies(implies(B,C),B),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_1552]) ).
cnf(c_3068,plain,
is_a_theorem(implies(implies(implies(A,B),A),A)),
inference(resolve,[status(thm)],[c_21862,c_1552]) ).
cnf(c_21863,plain,
( is_a_theorem(implies(implies(C,A),D))
| ~ is_a_theorem(implies(not(implies(implies(implies(A,B),implies(C,B)),D)),implies(implies(implies(A,B),implies(C,B)),D))) ),
inference(resolve,[status(thm)],[c_1,c_21]) ).
cnf(c_3086,plain,
is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))),
inference(resolve,[status(thm)],[c_21863,c_1552]) ).
cnf(c_21864,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_3172,plain,
is_a_theorem(implies(implies(implies(A,B),A),implies(implies(A,B),B))),
inference(resolve,[status(thm)],[c_21864,c_3086]) ).
cnf(c_21865,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_1205]) ).
cnf(c_3394,plain,
is_a_theorem(implies(A,implies(implies(A,B),B))),
inference(resolve,[status(thm)],[c_21865,c_3172]) ).
cnf(c_21866,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_3479,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(B,implies(A,C)))),
inference(resolve,[status(thm)],[c_21866,c_3394]) ).
cnf(c_21867,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_3479]) ).
cnf(c_3965,plain,
is_a_theorem(implies(implies(A,B),implies(implies(C,A),implies(C,B)))),
inference(resolve,[status(thm)],[c_21867,c_2]) ).
cnf(c_21868,plain,
( is_a_theorem(implies(implies(C,A),implies(C,B)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_3965]) ).
cnf(c_4650,plain,
is_a_theorem(implies(implies(A,implies(implies(B,C),B)),implies(A,B))),
inference(resolve,[status(thm)],[c_21868,c_3068]) ).
cnf(c_21869,plain,
( is_a_theorem(implies(implies(A,D),E))
| ~ is_a_theorem(implies(implies(implies(implies(A,B),C),implies(implies(D,B),C)),E)) ),
inference(resolve,[status(thm)],[c_1,c_151]) ).
cnf(c_17623,plain,
is_a_theorem(implies(implies(A,B),implies(implies(implies(A,C),B),B))),
inference(resolve,[status(thm)],[c_21869,c_4650]) ).
cnf(c_21870,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_3479]) ).
cnf(c_21701,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(implies(A,C),C))),
inference(resolve,[status(thm)],[c_21870,c_17623]) ).
cnf(c_21871,plain,
( is_a_theorem(implies(implies(A,B),C))
| ~ is_a_theorem(implies(implies(implies(not(A),A),B),C)) ),
inference(resolve,[status(thm)],[c_1,c_20]) ).
cnf(c_21803,plain,
is_a_theorem(implies(implies(A,B),implies(implies(not(A),B),B))),
inference(resolve,[status(thm)],[c_21871,c_21701]) ).
cnf(c_21872,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_3479]) ).
cnf(c_21837,plain,
is_a_theorem(implies(implies(not(A),B),implies(implies(A,B),B))),
inference(resolve,[status(thm)],[c_21872,c_21803]) ).
cnf(c_21838,plain,
$false,
inference(resolve,[status(thm)],[c_21837,c_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL390-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n026.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Fri Sep 25 22:27:41 UTC 2026
% 0.15/0.38 % CPUTime :
% 0.15/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.38 % Process 3627099 was started by sandbox2 on n026,
% 0.15/0.38 % Fri Sep 25 22:27:41 2026
% 0.15/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.39
% 0.15/0.39 % From the command line: assign(max_seconds, 300).
% 43.06/5.98
% 43.06/5.98 % given #500 (W,wt=37): 7421 is_a_theorem(implies(not(implies(not(A),B)),not(not(implies(A,C))))). [hyper(1,a,4657,a,b,1593,a)].
% 43.06/5.98
% 43.06/5.98 % SZS status Unsatisfiable for theBenchmark
% 43.06/5.98
% 43.06/5.98 % Proof 1 at 4.01 (+ 1.50) seconds.
% 43.06/5.98 % Length of proof is 40.
% 43.06/5.98 % Level of proof is 24.
% 43.06/5.98 % Maximum clause weight is 62.000.
% 43.06/5.98 % Given clauses 634.
% 43.06/5.98
% 43.06/5.98 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------