%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL401-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 07:58:49 AM UTC 2026
% Result : Unsatisfiable 7.43s 1.36s
% Output : CNFRefutation 7.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% 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 : 206 ( 42 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_67,axiom,
~ is_a_theorem(implies(not(implies(x,y)),not(y))),
file('theBenchmark.p',prove_cn_67) ).
cnf(c_5,plain,
~ is_a_theorem(implies(not(implies(x,y)),not(y))),
inference(clausify,[status(thm)],[prove_cn_67]) ).
cnf(c_4752,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_4752,c_2]) ).
cnf(c_4753,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_4753,c_3]) ).
cnf(c_4754,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_4754,c_4]) ).
cnf(c_4755,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_4755,c_6]) ).
cnf(c_4756,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_4756,c_6]) ).
cnf(c_4757,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_4757,c_9]) ).
cnf(c_4758,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_4758,c_3]) ).
cnf(c_4759,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_4759,c_34]) ).
cnf(c_4760,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_4760,c_29]) ).
cnf(c_4761,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_4761,c_36]) ).
cnf(c_4762,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_4762,c_7]) ).
cnf(c_4763,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_4763,c_44]) ).
cnf(c_4764,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_189,plain,
is_a_theorem(implies(implies(A,B),implies(implies(implies(C,C),A),B))),
inference(resolve,[status(thm)],[c_4764,c_184]) ).
cnf(c_4765,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_4765,c_7]) ).
cnf(c_4766,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_4766,c_205]) ).
cnf(c_4767,plain,
( is_a_theorem(implies(implies(implies(C,C),A),B))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_189]) ).
cnf(c_479,plain,
is_a_theorem(implies(implies(implies(A,A),implies(not(B),B)),B)),
inference(resolve,[status(thm)],[c_4767,c_3]) ).
cnf(c_4768,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_657,plain,
is_a_theorem(implies(implies(not(A),not(implies(B,B))),A)),
inference(resolve,[status(thm)],[c_4768,c_479]) ).
cnf(c_4769,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_4769,c_415]) ).
cnf(c_4770,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_4770,c_907]) ).
cnf(c_4771,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_4771,c_939]) ).
cnf(c_4772,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_4772,c_907]) ).
cnf(c_4773,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_1108,plain,
is_a_theorem(implies(A,implies(not(B),implies(B,C)))),
inference(resolve,[status(thm)],[c_4773,c_1092]) ).
cnf(c_4774,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_4774,c_1092]) ).
cnf(c_4775,plain,
( is_a_theorem(implies(not(B),implies(B,C)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_1108]) ).
cnf(c_1161,plain,
is_a_theorem(implies(not(A),implies(A,B))),
inference(resolve,[status(thm)],[c_4775,c_1108]) ).
cnf(c_4776,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_1181,plain,
is_a_theorem(implies(implies(A,B),implies(not(not(A)),B))),
inference(resolve,[status(thm)],[c_4776,c_1161]) ).
cnf(c_4777,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_4777,c_1111]) ).
cnf(c_4778,plain,
( is_a_theorem(implies(not(A),C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_1111]) ).
cnf(c_1222,plain,
is_a_theorem(implies(not(not(A)),A)),
inference(resolve,[status(thm)],[c_4778,c_657]) ).
cnf(c_4779,plain,
( is_a_theorem(implies(C,implies(B,A)))
| ~ is_a_theorem(implies(not(A),not(B))) ),
inference(resolve,[status(thm)],[c_1,c_907]) ).
cnf(c_1245,plain,
is_a_theorem(implies(A,implies(B,not(not(B))))),
inference(resolve,[status(thm)],[c_4779,c_1222]) ).
cnf(c_4780,plain,
( is_a_theorem(implies(B,not(not(B))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_1245]) ).
cnf(c_1686,plain,
is_a_theorem(implies(A,not(not(A)))),
inference(resolve,[status(thm)],[c_4780,c_1245]) ).
cnf(c_4781,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_1732,plain,
is_a_theorem(implies(A,not(not(implies(B,A))))),
inference(resolve,[status(thm)],[c_4781,c_1686]) ).
cnf(c_4782,plain,
( is_a_theorem(implies(not(not(A)),B))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_1181]) ).
cnf(c_2759,plain,
is_a_theorem(implies(not(not(A)),not(not(implies(B,A))))),
inference(resolve,[status(thm)],[c_4782,c_1732]) ).
cnf(c_4783,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_4783,c_1207]) ).
cnf(c_4784,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_4784,c_907]) ).
cnf(c_4785,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(implies(not(A),not(B))) ),
inference(resolve,[status(thm)],[c_1,c_2934]) ).
cnf(c_4750,plain,
is_a_theorem(implies(not(implies(A,B)),not(B))),
inference(resolve,[status(thm)],[c_4785,c_2759]) ).
cnf(c_4751,plain,
$false,
inference(resolve,[status(thm)],[c_4750,c_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL401-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n009.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Fri Sep 25 22:27:14 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.34 % Process 2717905 was started by sandbox on n009,
% 0.08/0.34 % Fri Sep 25 22:27:14 2026
% 0.08/0.34 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.35
% 0.08/0.35 % From the command line: assign(max_seconds, 300).
% 7.43/1.36
% 7.43/1.36 % SZS status Unsatisfiable for theBenchmark
% 7.43/1.36
% 7.43/1.36 % Proof 1 at 0.66 (+ 0.34) seconds.
% 7.43/1.36 % Length of proof is 40.
% 7.43/1.36 % Level of proof is 19.
% 7.43/1.36 % Maximum clause weight is 62.000.
% 7.43/1.36 % Given clauses 178.
% 7.43/1.36
% 7.43/1.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------