%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL113-1 : 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 : n003.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 07:58:01 AM UTC 2026
% Result : Unsatisfiable 271.19s 70.92s
% Output : CNFRefutation 271.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 57 ( 33 unt; 0 def)
% Number of atoms : 83 ( 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 : 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 : 142 ( 16 sgn 11 !; 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(mv_1,axiom,
! [VAR_0,VAR_1] : is_a_theorem(implies(VAR_0,implies(VAR_1,VAR_0))),
file('theBenchmark.p',mv_1) ).
cnf(c_2,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(clausify,[status(thm)],[mv_1]) ).
fof(mv_2,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',mv_2) ).
cnf(c_3,plain,
is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))),
inference(clausify,[status(thm)],[mv_2]) ).
fof(mv_3,axiom,
! [VAR_0,VAR_1] : is_a_theorem(implies(implies(implies(VAR_0,VAR_1),VAR_1),implies(implies(VAR_1,VAR_0),VAR_0))),
file('theBenchmark.p',mv_3) ).
cnf(c_4,plain,
is_a_theorem(implies(implies(implies(A,B),B),implies(implies(B,A),A))),
inference(clausify,[status(thm)],[mv_3]) ).
fof(mv_5,axiom,
! [VAR_0,VAR_1] : is_a_theorem(implies(implies(not(VAR_0),not(VAR_1)),implies(VAR_1,VAR_0))),
file('theBenchmark.p',mv_5) ).
cnf(c_5,plain,
is_a_theorem(implies(implies(not(A),not(B)),implies(B,A))),
inference(clausify,[status(thm)],[mv_5]) ).
fof(prove_mv_33,axiom,
~ is_a_theorem(implies(implies(not(a),b),implies(not(b),a))),
file('theBenchmark.p',prove_mv_33) ).
cnf(c_6,plain,
~ is_a_theorem(implies(implies(not(a),b),implies(not(b),a))),
inference(clausify,[status(thm)],[prove_mv_33]) ).
cnf(c_9229,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_8,plain,
is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),D),implies(implies(C,A),D))),
inference(resolve,[status(thm)],[c_9229,c_3]) ).
cnf(c_9230,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_10,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))),
inference(resolve,[status(thm)],[c_9230,c_2]) ).
cnf(c_9231,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_11,plain,
is_a_theorem(implies(implies(implies(implies(A,B),B),C),implies(implies(implies(B,A),A),C))),
inference(resolve,[status(thm)],[c_9231,c_4]) ).
cnf(c_9232,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_13,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(implies(not(B),not(A)),C))),
inference(resolve,[status(thm)],[c_9232,c_5]) ).
cnf(c_9233,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_14,plain,
is_a_theorem(implies(A,implies(implies(not(B),not(C)),implies(C,B)))),
inference(resolve,[status(thm)],[c_9233,c_5]) ).
cnf(c_9234,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_8]) ).
cnf(c_18,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(D,B),implies(A,implies(D,C))))),
inference(resolve,[status(thm)],[c_9234,c_8]) ).
cnf(c_9235,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_10]) ).
cnf(c_27,plain,
is_a_theorem(implies(not(A),implies(A,B))),
inference(resolve,[status(thm)],[c_9235,c_5]) ).
cnf(c_9236,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_10]) ).
cnf(c_28,plain,
is_a_theorem(implies(A,implies(implies(A,B),B))),
inference(resolve,[status(thm)],[c_9236,c_4]) ).
cnf(c_9237,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_31,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(not(A),C))),
inference(resolve,[status(thm)],[c_9237,c_27]) ).
cnf(c_9238,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_32,plain,
is_a_theorem(implies(A,implies(not(B),implies(B,C)))),
inference(resolve,[status(thm)],[c_9238,c_27]) ).
cnf(c_9239,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_36,plain,
is_a_theorem(implies(implies(implies(implies(A,B),B),C),implies(A,C))),
inference(resolve,[status(thm)],[c_9239,c_28]) ).
cnf(c_9240,plain,
( is_a_theorem(implies(implies(implies(B,A),A),C))
| ~ is_a_theorem(implies(implies(implies(A,B),B),C)) ),
inference(resolve,[status(thm)],[c_1,c_11]) ).
cnf(c_63,plain,
is_a_theorem(implies(implies(implies(A,B),B),implies(A,A))),
inference(resolve,[status(thm)],[c_9240,c_10]) ).
cnf(c_9241,plain,
( is_a_theorem(implies(A,A))
| ~ is_a_theorem(implies(implies(A,B),B)) ),
inference(resolve,[status(thm)],[c_1,c_63]) ).
cnf(c_105,plain,
is_a_theorem(implies(A,A)),
inference(resolve,[status(thm)],[c_9241,c_32]) ).
cnf(c_9242,plain,
( is_a_theorem(implies(implies(A,B),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_28]) ).
cnf(c_108,plain,
is_a_theorem(implies(implies(implies(A,A),B),B)),
inference(resolve,[status(thm)],[c_9242,c_105]) ).
cnf(c_9243,plain,
( is_a_theorem(implies(implies(not(B),not(A)),C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_13]) ).
cnf(c_137,plain,
is_a_theorem(implies(implies(not(A),not(implies(B,B))),A)),
inference(resolve,[status(thm)],[c_9243,c_108]) ).
cnf(c_9244,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_18]) ).
cnf(c_205,plain,
is_a_theorem(implies(implies(A,implies(not(B),not(C))),implies(D,implies(A,implies(C,B))))),
inference(resolve,[status(thm)],[c_9244,c_14]) ).
cnf(c_9245,plain,
( is_a_theorem(implies(A,C))
| ~ is_a_theorem(implies(implies(implies(A,B),B),C)) ),
inference(resolve,[status(thm)],[c_1,c_36]) ).
cnf(c_657,plain,
is_a_theorem(implies(implies(A,B),implies(implies(C,A),implies(C,B)))),
inference(resolve,[status(thm)],[c_9245,c_8]) ).
cnf(c_9246,plain,
( is_a_theorem(implies(not(A),C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_31]) ).
cnf(c_739,plain,
is_a_theorem(implies(not(not(A)),A)),
inference(resolve,[status(thm)],[c_9246,c_137]) ).
cnf(c_9247,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(implies(not(A),not(B))) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_766,plain,
is_a_theorem(implies(A,not(not(A)))),
inference(resolve,[status(thm)],[c_9247,c_739]) ).
cnf(c_9248,plain,
( is_a_theorem(implies(implies(C,A),implies(C,B)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_657]) ).
cnf(c_1565,plain,
is_a_theorem(implies(implies(A,B),implies(A,not(not(B))))),
inference(resolve,[status(thm)],[c_9248,c_766]) ).
cnf(c_9249,plain,
( is_a_theorem(implies(D,implies(A,implies(C,B))))
| ~ is_a_theorem(implies(A,implies(not(B),not(C)))) ),
inference(resolve,[status(thm)],[c_1,c_205]) ).
cnf(c_7132,plain,
is_a_theorem(implies(A,implies(implies(not(B),C),implies(not(C),B)))),
inference(resolve,[status(thm)],[c_9249,c_1565]) ).
cnf(c_9250,plain,
( is_a_theorem(implies(implies(not(B),C),implies(not(C),B)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_7132]) ).
cnf(c_9227,plain,
is_a_theorem(implies(implies(not(A),B),implies(not(B),A))),
inference(resolve,[status(thm)],[c_9250,c_7132]) ).
cnf(c_9228,plain,
$false,
inference(resolve,[status(thm)],[c_9227,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL113-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % 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 21:54:23 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 1192909 was started by sandbox on n003,
% 0.10/0.36 % Fri Sep 25 21:54:23 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 271.19/70.92
% 271.19/70.92 % Assigning unary symbol not kb_weight 0 and highest precedence (5).
% 271.19/70.92
% 271.19/70.92 % SZS status Unsatisfiable for theBenchmark
% 271.19/70.92
% 271.19/70.92 % Proof 1 at 2.20 (+ 1.05) seconds.
% 271.19/70.92 % Length of proof is 29.
% 271.19/70.92 % Level of proof is 12.
% 271.19/70.92 % Maximum clause weight is 26.000.
% 271.19/70.92 % Given clauses 453.
% 271.19/70.92
% 271.19/70.92 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------