%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL059-1 : 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 : n019.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 07:57:52 AM UTC 2026
% Result : Unsatisfiable 3.36s 0.85s
% Output : CNFRefutation 3.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 5
% Syntax : Number of formulae : 55 ( 31 unt; 0 def)
% Number of atoms : 81 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 54 ( 28 ~; 26 |; 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 : 148 ( 27 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_49,axiom,
~ is_a_theorem(implies(implies(not(a),not(b)),implies(b,a))),
file('theBenchmark.p',prove_cn_49) ).
cnf(c_5,plain,
~ is_a_theorem(implies(implies(not(a),not(b)),implies(b,a))),
inference(clausify,[status(thm)],[prove_cn_49]) ).
cnf(c_2936,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_2936,c_2]) ).
cnf(c_2937,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_2937,c_3]) ).
cnf(c_2938,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_2938,c_4]) ).
cnf(c_2939,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_2939,c_6]) ).
cnf(c_2940,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_2940,c_6]) ).
cnf(c_2941,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_2941,c_9]) ).
cnf(c_2942,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_2942,c_3]) ).
cnf(c_2943,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_2943,c_34]) ).
cnf(c_2944,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_43,plain,
is_a_theorem(implies(implies(implies(A,implies(B,C)),D),implies(implies(B,not(A)),D))),
inference(resolve,[status(thm)],[c_2944,c_29]) ).
cnf(c_2945,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_2945,c_36]) ).
cnf(c_2946,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_2946,c_7]) ).
cnf(c_2947,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_2947,c_44]) ).
cnf(c_2948,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_2948,c_7]) ).
cnf(c_2949,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_415,plain,
is_a_theorem(implies(implies(A,implies(not(B),B)),implies(C,implies(A,B)))),
inference(resolve,[status(thm)],[c_2949,c_205]) ).
cnf(c_2950,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_43]) ).
cnf(c_907,plain,
is_a_theorem(implies(implies(not(A),not(B)),implies(C,implies(B,A)))),
inference(resolve,[status(thm)],[c_2950,c_415]) ).
cnf(c_2951,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_939,plain,
is_a_theorem(implies(A,implies(B,implies(C,A)))),
inference(resolve,[status(thm)],[c_2951,c_907]) ).
cnf(c_2952,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_980,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))),
inference(resolve,[status(thm)],[c_2952,c_939]) ).
cnf(c_2953,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_980]) ).
cnf(c_1092,plain,
is_a_theorem(implies(not(A),implies(B,implies(A,C)))),
inference(resolve,[status(thm)],[c_2953,c_907]) ).
cnf(c_2954,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_1111,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(not(A),C))),
inference(resolve,[status(thm)],[c_2954,c_1092]) ).
cnf(c_2955,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_415]) ).
cnf(c_1207,plain,
is_a_theorem(implies(A,implies(implies(implies(B,C),B),B))),
inference(resolve,[status(thm)],[c_2955,c_1111]) ).
cnf(c_2956,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_2849,plain,
is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))),
inference(resolve,[status(thm)],[c_2956,c_1207]) ).
cnf(c_2957,plain,
( is_a_theorem(implies(A,B))
| ~ is_a_theorem(implies(A,implies(A,B))) ),
inference(resolve,[status(thm)],[c_1,c_2849]) ).
cnf(c_2934,plain,
is_a_theorem(implies(implies(not(A),not(B)),implies(B,A))),
inference(resolve,[status(thm)],[c_2957,c_907]) ).
cnf(c_2935,plain,
$false,
inference(resolve,[status(thm)],[c_2934,c_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL059-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n019.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 21:47:18 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 3800449 was started by sandbox2 on n019,
% 0.10/0.36 % Fri Sep 25 21:47:18 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 3.36/0.85
% 3.36/0.85 % SZS status Unsatisfiable for theBenchmark
% 3.36/0.85
% 3.36/0.85 % Proof 1 at 0.31 (+ 0.15) seconds.
% 3.36/0.85 % Length of proof is 28.
% 3.36/0.85 % Level of proof is 16.
% 3.36/0.85 % Maximum clause weight is 62.000.
% 3.36/0.85 % Given clauses 132.
% 3.36/0.85
% 3.36/0.85 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------