TSTP Solution File: LCL367-1 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL367-1 : TPTP v3.4.2. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art08.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1003MB
% OS : Linux 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May 6 13:48:39 EDT 2009
% Result : Unsatisfiable 73.7s
% Output : Refutation 73.7s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 50 ( 30 unt; 0 def)
% Number of atoms : 72 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 48 ( 26 ~; 22 |; 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 : 126 ( 38 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(condensed_detachment,plain,
! [A,B] :
( ~ is_a_theorem(implies(A,B))
| ~ is_a_theorem(A)
| is_a_theorem(B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL367-1.tptp',unknown),
[] ).
cnf(149694008,plain,
( ~ is_a_theorem(implies(A,B))
| ~ is_a_theorem(A)
| is_a_theorem(B) ),
inference(rewrite,[status(thm)],[condensed_detachment]),
[] ).
fof(cn_2,plain,
! [A] : is_a_theorem(implies(implies(not(A),A),A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL367-1.tptp',unknown),
[] ).
cnf(149702856,plain,
is_a_theorem(implies(implies(not(A),A),A)),
inference(rewrite,[status(thm)],[cn_2]),
[] ).
cnf(157505256,plain,
( ~ is_a_theorem(implies(implies(implies(not(B),B),B),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[149694008,149702856]),
[] ).
fof(cn_1,plain,
! [A,B,C] : is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL367-1.tptp',unknown),
[] ).
cnf(149698864,plain,
is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))),
inference(rewrite,[status(thm)],[cn_1]),
[] ).
cnf(158237552,plain,
is_a_theorem(implies(implies(A,B),implies(implies(not(A),A),B))),
inference(resolution,[status(thm)],[157505256,149698864]),
[] ).
cnf(157650704,plain,
( ~ is_a_theorem(implies(A,B))
| is_a_theorem(implies(implies(B,C),implies(A,C))) ),
inference(resolution,[status(thm)],[149694008,149698864]),
[] ).
cnf(160432856,plain,
is_a_theorem(implies(implies(implies(implies(not(A),A),B),C),implies(implies(A,B),C))),
inference(resolution,[status(thm)],[158237552,157650704]),
[] ).
cnf(169637256,plain,
( ~ is_a_theorem(implies(implies(implies(not(A),A),B),C))
| is_a_theorem(implies(implies(A,B),C)) ),
inference(resolution,[status(thm)],[149694008,160432856]),
[] ).
fof(cn_3,plain,
! [A,B] : is_a_theorem(implies(A,implies(not(A),B))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL367-1.tptp',unknown),
[] ).
cnf(149706832,plain,
is_a_theorem(implies(A,implies(not(A),B))),
inference(rewrite,[status(thm)],[cn_3]),
[] ).
cnf(157534904,plain,
( ~ is_a_theorem(implies(implies(B,implies(not(B),C)),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[149694008,149706832]),
[] ).
cnf(158567480,plain,
is_a_theorem(implies(implies(implies(not(A),B),C),implies(A,C))),
inference(resolution,[status(thm)],[157534904,149698864]),
[] ).
cnf(163056456,plain,
( ~ is_a_theorem(implies(implies(not(A),B),C))
| is_a_theorem(implies(A,C)) ),
inference(resolution,[status(thm)],[158567480,149694008]),
[] ).
cnf(163105664,plain,
is_a_theorem(implies(A,A)),
inference(resolution,[status(thm)],[158567480,157505256]),
[] ).
cnf(157515584,plain,
( ~ is_a_theorem(A)
| is_a_theorem(implies(not(A),B)) ),
inference(resolution,[status(thm)],[149694008,149706832]),
[] ).
cnf(163436720,plain,
is_a_theorem(implies(not(implies(A,A)),B)),
inference(resolution,[status(thm)],[163105664,157515584]),
[] ).
cnf(163877160,plain,
is_a_theorem(implies(implies(B,C),implies(not(implies(A,A)),C))),
inference(resolution,[status(thm)],[163436720,157650704]),
[] ).
cnf(166553416,plain,
is_a_theorem(implies(A,implies(not(implies(C,C)),B))),
inference(resolution,[status(thm)],[163056456,163877160]),
[] ).
cnf(166659832,plain,
is_a_theorem(implies(implies(implies(not(implies(D,D)),C),B),implies(A,B))),
inference(resolution,[status(thm)],[157650704,166553416]),
[] ).
cnf(179367192,plain,
is_a_theorem(implies(implies(implies(C,C),A),implies(B,A))),
inference(resolution,[status(thm)],[169637256,166659832]),
[] ).
cnf(180003120,plain,
( ~ is_a_theorem(implies(implies(implies(implies(D,D),B),implies(C,B)),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[149694008,179367192]),
[] ).
cnf(159375600,plain,
is_a_theorem(implies(implies(implies(implies(C,D),implies(B,D)),A),implies(implies(B,C),A))),
inference(resolution,[status(thm)],[157650704,149698864]),
[] ).
cnf(180408096,plain,
is_a_theorem(implies(implies(C,B),implies(A,implies(C,B)))),
inference(resolution,[status(thm)],[180003120,159375600]),
[] ).
cnf(181369328,plain,
( ~ is_a_theorem(implies(C,B))
| is_a_theorem(implies(A,implies(C,B))) ),
inference(resolution,[status(thm)],[149694008,180408096]),
[] ).
cnf(163075656,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(A),B),C),implies(A,C)),D))
| is_a_theorem(D) ),
inference(resolution,[status(thm)],[158567480,149694008]),
[] ).
cnf(170419328,plain,
is_a_theorem(implies(implies(C,not(A)),implies(A,implies(C,B)))),
inference(resolution,[status(thm)],[163075656,159375600]),
[] ).
cnf(170760568,plain,
is_a_theorem(implies(A,implies(B,implies(not(A),C)))),
inference(resolution,[status(thm)],[163056456,170419328]),
[] ).
cnf(171112600,plain,
( ~ is_a_theorem(A)
| is_a_theorem(implies(B,implies(not(A),C))) ),
inference(resolution,[status(thm)],[149694008,170760568]),
[] ).
cnf(159389936,plain,
( ~ is_a_theorem(implies(A,implies(not(B),B)))
| is_a_theorem(implies(A,B)) ),
inference(resolution,[status(thm)],[157650704,157505256]),
[] ).
cnf(233615288,plain,
( ~ is_a_theorem(A)
| is_a_theorem(implies(B,A)) ),
inference(resolution,[status(thm)],[171112600,159389936]),
[] ).
cnf(233927696,plain,
( is_a_theorem(implies(A,implies(B,C)))
| ~ is_a_theorem(implies(B,implies(not(C),C))) ),
inference(resolution,[status(thm)],[233615288,159389936]),
[] ).
cnf(171195160,plain,
is_a_theorem(implies(implies(implies(C,implies(not(A),D)),B),implies(A,B))),
inference(resolution,[status(thm)],[157650704,170760568]),
[] ).
cnf(194383200,plain,
( ~ is_a_theorem(implies(implies(C,implies(not(A),D)),B))
| is_a_theorem(implies(A,B)) ),
inference(resolution,[status(thm)],[149694008,171195160]),
[] ).
cnf(170084424,plain,
( ~ is_a_theorem(implies(implies(implies(C,D),implies(B,D)),A))
| is_a_theorem(implies(implies(B,C),A)) ),
inference(resolution,[status(thm)],[149694008,159375600]),
[] ).
cnf(179984016,plain,
( ~ is_a_theorem(implies(implies(C,C),A))
| is_a_theorem(implies(B,A)) ),
inference(resolution,[status(thm)],[149694008,179367192]),
[] ).
cnf(180230264,plain,
is_a_theorem(implies(A,implies(implies(not(B),B),B))),
inference(resolution,[status(thm)],[179984016,158237552]),
[] ).
cnf(180825936,plain,
is_a_theorem(implies(implies(implies(implies(not(C),C),C),B),implies(A,B))),
inference(resolution,[status(thm)],[157650704,180230264]),
[] ).
cnf(214895944,plain,
is_a_theorem(implies(implies(A,implies(not(B),B)),implies(C,implies(A,B)))),
inference(resolution,[status(thm)],[170084424,180825936]),
[] ).
cnf(357581464,plain,
is_a_theorem(implies(A,implies(C,implies(B,A)))),
inference(resolution,[status(thm)],[194383200,214895944]),
[] ).
cnf(360707424,plain,
is_a_theorem(implies(A,implies(B,implies(C,B)))),
inference(resolution,[status(thm)],[233927696,357581464]),
[] ).
cnf(361493304,plain,
is_a_theorem(implies(A,implies(B,implies(C,implies(D,C))))),
inference(resolution,[status(thm)],[181369328,360707424]),
[] ).
fof(prove_cn_17,plain,
~ is_a_theorem(implies(x,implies(implies(y,x),x))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL367-1.tptp',unknown),
[] ).
cnf(149714560,plain,
~ is_a_theorem(implies(x,implies(implies(y,x),x))),
inference(rewrite,[status(thm)],[prove_cn_17]),
[] ).
cnf(157598968,plain,
( ~ is_a_theorem(implies(A,implies(x,implies(implies(y,x),x))))
| ~ is_a_theorem(A) ),
inference(resolution,[status(thm)],[149694008,149714560]),
[] ).
cnf(163564920,plain,
~ is_a_theorem(implies(implies(A,A),implies(x,implies(implies(y,x),x)))),
inference(resolution,[status(thm)],[163105664,157598968]),
[] ).
cnf(157485744,plain,
( ~ is_a_theorem(implies(not(A),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[149694008,149702856]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[361493304,163564920,157485744]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 83 seconds
% START OF PROOF SEQUENCE
% fof(condensed_detachment,plain,(~is_a_theorem(implies(A,B))|~is_a_theorem(A)|is_a_theorem(B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL367-1.tptp',unknown),[]).
%
% cnf(149694008,plain,(~is_a_theorem(implies(A,B))|~is_a_theorem(A)|is_a_theorem(B)),inference(rewrite,[status(thm)],[condensed_detachment]),[]).
%
% fof(cn_2,plain,(is_a_theorem(implies(implies(not(A),A),A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL367-1.tptp',unknown),[]).
%
% cnf(149702856,plain,(is_a_theorem(implies(implies(not(A),A),A))),inference(rewrite,[status(thm)],[cn_2]),[]).
%
% cnf(157505256,plain,(~is_a_theorem(implies(implies(implies(not(B),B),B),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[149694008,149702856]),[]).
%
% fof(cn_1,plain,(is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL367-1.tptp',unknown),[]).
%
% cnf(149698864,plain,(is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C))))),inference(rewrite,[status(thm)],[cn_1]),[]).
%
% cnf(158237552,plain,(is_a_theorem(implies(implies(A,B),implies(implies(not(A),A),B)))),inference(resolution,[status(thm)],[157505256,149698864]),[]).
%
% cnf(157650704,plain,(~is_a_theorem(implies(A,B))|is_a_theorem(implies(implies(B,C),implies(A,C)))),inference(resolution,[status(thm)],[149694008,149698864]),[]).
%
% cnf(160432856,plain,(is_a_theorem(implies(implies(implies(implies(not(A),A),B),C),implies(implies(A,B),C)))),inference(resolution,[status(thm)],[158237552,157650704]),[]).
%
% cnf(169637256,plain,(~is_a_theorem(implies(implies(implies(not(A),A),B),C))|is_a_theorem(implies(implies(A,B),C))),inference(resolution,[status(thm)],[149694008,160432856]),[]).
%
% fof(cn_3,plain,(is_a_theorem(implies(A,implies(not(A),B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL367-1.tptp',unknown),[]).
%
% cnf(149706832,plain,(is_a_theorem(implies(A,implies(not(A),B)))),inference(rewrite,[status(thm)],[cn_3]),[]).
%
% cnf(157534904,plain,(~is_a_theorem(implies(implies(B,implies(not(B),C)),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[149694008,149706832]),[]).
%
% cnf(158567480,plain,(is_a_theorem(implies(implies(implies(not(A),B),C),implies(A,C)))),inference(resolution,[status(thm)],[157534904,149698864]),[]).
%
% cnf(163056456,plain,(~is_a_theorem(implies(implies(not(A),B),C))|is_a_theorem(implies(A,C))),inference(resolution,[status(thm)],[158567480,149694008]),[]).
%
% cnf(163105664,plain,(is_a_theorem(implies(A,A))),inference(resolution,[status(thm)],[158567480,157505256]),[]).
%
% cnf(157515584,plain,(~is_a_theorem(A)|is_a_theorem(implies(not(A),B))),inference(resolution,[status(thm)],[149694008,149706832]),[]).
%
% cnf(163436720,plain,(is_a_theorem(implies(not(implies(A,A)),B))),inference(resolution,[status(thm)],[163105664,157515584]),[]).
%
% cnf(163877160,plain,(is_a_theorem(implies(implies(B,C),implies(not(implies(A,A)),C)))),inference(resolution,[status(thm)],[163436720,157650704]),[]).
%
% cnf(166553416,plain,(is_a_theorem(implies(A,implies(not(implies(C,C)),B)))),inference(resolution,[status(thm)],[163056456,163877160]),[]).
%
% cnf(166659832,plain,(is_a_theorem(implies(implies(implies(not(implies(D,D)),C),B),implies(A,B)))),inference(resolution,[status(thm)],[157650704,166553416]),[]).
%
% cnf(179367192,plain,(is_a_theorem(implies(implies(implies(C,C),A),implies(B,A)))),inference(resolution,[status(thm)],[169637256,166659832]),[]).
%
% cnf(180003120,plain,(~is_a_theorem(implies(implies(implies(implies(D,D),B),implies(C,B)),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[149694008,179367192]),[]).
%
% cnf(159375600,plain,(is_a_theorem(implies(implies(implies(implies(C,D),implies(B,D)),A),implies(implies(B,C),A)))),inference(resolution,[status(thm)],[157650704,149698864]),[]).
%
% cnf(180408096,plain,(is_a_theorem(implies(implies(C,B),implies(A,implies(C,B))))),inference(resolution,[status(thm)],[180003120,159375600]),[]).
%
% cnf(181369328,plain,(~is_a_theorem(implies(C,B))|is_a_theorem(implies(A,implies(C,B)))),inference(resolution,[status(thm)],[149694008,180408096]),[]).
%
% cnf(163075656,plain,(~is_a_theorem(implies(implies(implies(implies(not(A),B),C),implies(A,C)),D))|is_a_theorem(D)),inference(resolution,[status(thm)],[158567480,149694008]),[]).
%
% cnf(170419328,plain,(is_a_theorem(implies(implies(C,not(A)),implies(A,implies(C,B))))),inference(resolution,[status(thm)],[163075656,159375600]),[]).
%
% cnf(170760568,plain,(is_a_theorem(implies(A,implies(B,implies(not(A),C))))),inference(resolution,[status(thm)],[163056456,170419328]),[]).
%
% cnf(171112600,plain,(~is_a_theorem(A)|is_a_theorem(implies(B,implies(not(A),C)))),inference(resolution,[status(thm)],[149694008,170760568]),[]).
%
% cnf(159389936,plain,(~is_a_theorem(implies(A,implies(not(B),B)))|is_a_theorem(implies(A,B))),inference(resolution,[status(thm)],[157650704,157505256]),[]).
%
% cnf(233615288,plain,(~is_a_theorem(A)|is_a_theorem(implies(B,A))),inference(resolution,[status(thm)],[171112600,159389936]),[]).
%
% cnf(233927696,plain,(is_a_theorem(implies(A,implies(B,C)))|~is_a_theorem(implies(B,implies(not(C),C)))),inference(resolution,[status(thm)],[233615288,159389936]),[]).
%
% cnf(171195160,plain,(is_a_theorem(implies(implies(implies(C,implies(not(A),D)),B),implies(A,B)))),inference(resolution,[status(thm)],[157650704,170760568]),[]).
%
% cnf(194383200,plain,(~is_a_theorem(implies(implies(C,implies(not(A),D)),B))|is_a_theorem(implies(A,B))),inference(resolution,[status(thm)],[149694008,171195160]),[]).
%
% cnf(170084424,plain,(~is_a_theorem(implies(implies(implies(C,D),implies(B,D)),A))|is_a_theorem(implies(implies(B,C),A))),inference(resolution,[status(thm)],[149694008,159375600]),[]).
%
% cnf(179984016,plain,(~is_a_theorem(implies(implies(C,C),A))|is_a_theorem(implies(B,A))),inference(resolution,[status(thm)],[149694008,179367192]),[]).
%
% cnf(180230264,plain,(is_a_theorem(implies(A,implies(implies(not(B),B),B)))),inference(resolution,[status(thm)],[179984016,158237552]),[]).
%
% cnf(180825936,plain,(is_a_theorem(implies(implies(implies(implies(not(C),C),C),B),implies(A,B)))),inference(resolution,[status(thm)],[157650704,180230264]),[]).
%
% cnf(214895944,plain,(is_a_theorem(implies(implies(A,implies(not(B),B)),implies(C,implies(A,B))))),inference(resolution,[status(thm)],[170084424,180825936]),[]).
%
% cnf(357581464,plain,(is_a_theorem(implies(A,implies(C,implies(B,A))))),inference(resolution,[status(thm)],[194383200,214895944]),[]).
%
% cnf(360707424,plain,(is_a_theorem(implies(A,implies(B,implies(C,B))))),inference(resolution,[status(thm)],[233927696,357581464]),[]).
%
% cnf(361493304,plain,(is_a_theorem(implies(A,implies(B,implies(C,implies(D,C)))))),inference(resolution,[status(thm)],[181369328,360707424]),[]).
%
% fof(prove_cn_17,plain,(~is_a_theorem(implies(x,implies(implies(y,x),x)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL367-1.tptp',unknown),[]).
%
% cnf(149714560,plain,(~is_a_theorem(implies(x,implies(implies(y,x),x)))),inference(rewrite,[status(thm)],[prove_cn_17]),[]).
%
% cnf(157598968,plain,(~is_a_theorem(implies(A,implies(x,implies(implies(y,x),x))))|~is_a_theorem(A)),inference(resolution,[status(thm)],[149694008,149714560]),[]).
%
% cnf(163564920,plain,(~is_a_theorem(implies(implies(A,A),implies(x,implies(implies(y,x),x))))),inference(resolution,[status(thm)],[163105664,157598968]),[]).
%
% cnf(157485744,plain,(~is_a_theorem(implies(not(A),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[149694008,149702856]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[361493304,163564920,157485744]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------