%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL072-1 : 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 : 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 07:57:54 AM UTC 2026
% Result : Unsatisfiable 2.10s 0.76s
% Output : CNFRefutation 2.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 18 unt; 0 def)
% Number of atoms : 42 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 15 ~; 13 |; 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 : 77 ( 15 sgn 12 !; 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_19,axiom,
! [VAR_0,VAR_1,VAR_2] : is_a_theorem(implies(implies(implies(VAR_0,VAR_1),VAR_2),implies(VAR_1,VAR_2))),
file('theBenchmark.p',cn_19) ).
cnf(c_2,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))),
inference(clausify,[status(thm)],[cn_19]) ).
fof(cn_37,axiom,
! [VAR_0,VAR_1,VAR_2] : is_a_theorem(implies(implies(implies(VAR_0,VAR_1),VAR_2),implies(not(VAR_0),VAR_2))),
file('theBenchmark.p',cn_37) ).
cnf(c_3,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(not(A),C))),
inference(clausify,[status(thm)],[cn_37]) ).
fof(cn_60,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : is_a_theorem(implies(implies(VAR_0,implies(not(VAR_1),VAR_2)),implies(VAR_0,implies(implies(VAR_3,VAR_2),implies(implies(VAR_1,VAR_3),VAR_2))))),
file('theBenchmark.p',cn_60) ).
cnf(c_4,plain,
is_a_theorem(implies(implies(A,implies(not(B),C)),implies(A,implies(implies(D,C),implies(implies(B,D),C))))),
inference(clausify,[status(thm)],[cn_60]) ).
fof(prove_cn_3,axiom,
~ is_a_theorem(implies(a,implies(not(a),b))),
file('theBenchmark.p',prove_cn_3) ).
cnf(c_5,plain,
~ is_a_theorem(implies(a,implies(not(a),b))),
inference(clausify,[status(thm)],[prove_cn_3]) ).
cnf(c_1034,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_7,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(resolve,[status(thm)],[c_1034,c_2]) ).
cnf(c_8,plain,
( is_a_theorem(implies(not(A),C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_3,c_1]) ).
cnf(c_1035,plain,
( is_a_theorem(implies(A,implies(implies(D,C),implies(implies(B,D),C))))
| ~ is_a_theorem(implies(A,implies(not(B),C))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_15,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(implies(D,C),implies(implies(A,D),C)))),
inference(resolve,[status(thm)],[c_1035,c_3]) ).
cnf(c_1036,plain,
( is_a_theorem(implies(implies(D,C),implies(implies(A,D),C)))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_15]) ).
cnf(c_72,plain,
is_a_theorem(implies(implies(A,implies(B,implies(C,D))),implies(implies(C,A),implies(B,implies(C,D))))),
inference(resolve,[status(thm)],[c_1036,c_7]) ).
cnf(c_1037,plain,
( is_a_theorem(implies(implies(C,A),implies(B,implies(C,D))))
| ~ is_a_theorem(implies(A,implies(B,implies(C,D)))) ),
inference(resolve,[status(thm)],[c_1,c_72]) ).
cnf(c_613,plain,
is_a_theorem(implies(implies(A,implies(A,B)),implies(C,implies(A,B)))),
inference(resolve,[status(thm)],[c_1037,c_7]) ).
cnf(c_1038,plain,
( is_a_theorem(implies(C,implies(A,B)))
| ~ is_a_theorem(implies(A,implies(A,B))) ),
inference(resolve,[status(thm)],[c_1,c_613]) ).
cnf(c_677,plain,
is_a_theorem(implies(A,implies(B,B))),
inference(resolve,[status(thm)],[c_1038,c_7]) ).
cnf(c_1039,plain,
( is_a_theorem(implies(B,B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_677]) ).
cnf(c_690,plain,
is_a_theorem(implies(A,A)),
inference(resolve,[status(thm)],[c_1039,c_677]) ).
cnf(c_696,plain,
is_a_theorem(implies(not(A),implies(A,B))),
inference(resolve,[status(thm)],[c_690,c_8]) ).
cnf(c_1040,plain,
( is_a_theorem(implies(implies(C,A),implies(B,implies(C,D))))
| ~ is_a_theorem(implies(A,implies(B,implies(C,D)))) ),
inference(resolve,[status(thm)],[c_1,c_72]) ).
cnf(c_714,plain,
is_a_theorem(implies(implies(A,not(B)),implies(B,implies(A,C)))),
inference(resolve,[status(thm)],[c_1040,c_696]) ).
cnf(c_1041,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,not(B))) ),
inference(resolve,[status(thm)],[c_1,c_714]) ).
cnf(c_1032,plain,
is_a_theorem(implies(A,implies(not(A),B))),
inference(resolve,[status(thm)],[c_1041,c_690]) ).
cnf(c_1033,plain,
$false,
inference(resolve,[status(thm)],[c_1032,c_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL072-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n002.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Fri Sep 25 21:51:35 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 65451 was started by sandbox2 on n002,
% 0.18/0.45 % Fri Sep 25 21:51:35 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 2.10/0.76
% 2.10/0.76 % SZS status Unsatisfiable for theBenchmark
% 2.10/0.76
% 2.10/0.76 % Proof 1 at 0.18 (+ 0.11) seconds.
% 2.10/0.76 % Length of proof is 16.
% 2.10/0.76 % Level of proof is 9.
% 2.10/0.76 % Maximum clause weight is 63.000.
% 2.10/0.76 % Given clauses 157.
% 2.10/0.76
% 2.10/0.76 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------