TSTP Solution File: LDA001-1 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LDA001-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art09.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 13:58:09 EDT 2009
% Result : Unsatisfiable 16.1s
% Output : Refutation 16.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 35 unt; 0 def)
% Number of atoms : 35 ( 0 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 26 ( 26 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 6 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(a1,plain,
! [A,B,C] : $equal(f(f(A,B),f(A,C)),f(A,f(B,C))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LDA/LDA001-1.tptp',unknown),
[] ).
cnf(168479392,plain,
$equal(f(f(A,B),f(A,C)),f(A,f(B,C))),
inference(rewrite,[status(thm)],[a1]),
[] ).
fof(prove_equation,plain,
~ $equal(f(f(u,u),u),f(f(n3,n2),u)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LDA/LDA001-1.tptp',unknown),
[] ).
cnf(168495856,plain,
~ $equal(f(f(u,u),u),f(f(n3,n2),u)),
inference(rewrite,[status(thm)],[prove_equation]),
[] ).
fof(clause_4,plain,
$equal(f(n2,n2),u),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LDA/LDA001-1.tptp',unknown),
[] ).
cnf(168491176,plain,
$equal(f(n2,n2),u),
inference(rewrite,[status(thm)],[clause_4]),
[] ).
cnf(176399984,plain,
~ $equal(f(f(u,u),u),f(f(n3,n2),f(n2,n2))),
inference(paramodulation,[status(thm)],[168495856,168491176,theory(equality)]),
[] ).
fof(clause_2,plain,
$equal(f(n1,n1),n2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LDA/LDA001-1.tptp',unknown),
[] ).
cnf(168483448,plain,
$equal(f(n1,n1),n2),
inference(rewrite,[status(thm)],[clause_2]),
[] ).
cnf(176995016,plain,
~ $equal(f(f(u,u),u),f(f(n3,n2),f(n2,f(n1,n1)))),
inference(paramodulation,[status(thm)],[176399984,168483448,theory(equality)]),
[] ).
cnf(179064688,plain,
~ $equal(f(f(u,u),u),f(f(n3,n2),f(f(n2,n1),f(n2,n1)))),
inference(paramodulation,[status(thm)],[176995016,168479392,theory(equality)]),
[] ).
fof(clause_3,plain,
$equal(f(n2,n1),n3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LDA/LDA001-1.tptp',unknown),
[] ).
cnf(168487360,plain,
$equal(f(n2,n1),n3),
inference(rewrite,[status(thm)],[clause_3]),
[] ).
cnf(189710696,plain,
~ $equal(f(f(u,u),u),f(f(n3,n2),f(n3,f(n2,n1)))),
inference(paramodulation,[status(thm)],[179064688,168487360,theory(equality)]),
[] ).
cnf(193536784,plain,
~ $equal(f(f(u,u),u),f(f(n3,n2),f(n3,n3))),
inference(paramodulation,[status(thm)],[189710696,168487360,theory(equality)]),
[] ).
cnf(193761152,plain,
~ $equal(f(f(u,u),u),f(n3,f(n2,n3))),
inference(paramodulation,[status(thm)],[193536784,168479392,theory(equality)]),
[] ).
cnf(193836528,plain,
~ $equal(f(f(f(n2,n2),u),u),f(n3,f(n2,n3))),
inference(paramodulation,[status(thm)],[193761152,168491176,theory(equality)]),
[] ).
cnf(194293544,plain,
~ $equal(f(f(f(n2,n2),f(n2,n2)),u),f(n3,f(n2,n3))),
inference(paramodulation,[status(thm)],[193836528,168491176,theory(equality)]),
[] ).
cnf(203602096,plain,
~ $equal(f(f(n2,f(n2,n2)),u),f(n3,f(n2,n3))),
inference(paramodulation,[status(thm)],[194293544,168479392,theory(equality)]),
[] ).
cnf(203715800,plain,
~ $equal(f(f(n2,u),u),f(n3,f(n2,n3))),
inference(paramodulation,[status(thm)],[203602096,168491176,theory(equality)]),
[] ).
cnf(203785848,plain,
~ $equal(f(f(n2,u),u),f(f(n2,n1),f(n2,n3))),
inference(paramodulation,[status(thm)],[203715800,168487360,theory(equality)]),
[] ).
cnf(204027560,plain,
~ $equal(f(f(n2,u),u),f(n2,f(n1,n3))),
inference(paramodulation,[status(thm)],[203785848,168479392,theory(equality)]),
[] ).
cnf(204072312,plain,
~ $equal(f(f(n2,u),u),f(f(n1,n1),f(n1,n3))),
inference(paramodulation,[status(thm)],[204027560,168483448,theory(equality)]),
[] ).
cnf(204495608,plain,
~ $equal(f(f(n2,u),u),f(n1,f(n1,n3))),
inference(paramodulation,[status(thm)],[204072312,168479392,theory(equality)]),
[] ).
cnf(204569824,plain,
~ $equal(f(f(n2,u),f(n2,n2)),f(n1,f(n1,n3))),
inference(paramodulation,[status(thm)],[204495608,168491176,theory(equality)]),
[] ).
cnf(205410912,plain,
~ $equal(f(n2,f(u,n2)),f(n1,f(n1,n3))),
inference(paramodulation,[status(thm)],[204569824,168479392,theory(equality)]),
[] ).
cnf(205485000,plain,
~ $equal(f(n2,f(f(n2,n2),n2)),f(n1,f(n1,n3))),
inference(paramodulation,[status(thm)],[205410912,168491176,theory(equality)]),
[] ).
cnf(190607992,plain,
~ $equal(f(n2,f(f(f(n1,n1),n2),n2)),f(n1,f(n1,n3))),
inference(paramodulation,[status(thm)],[205485000,168483448,theory(equality)]),
[] ).
cnf(229013208,plain,
~ $equal(f(n2,f(f(f(n1,n1),f(n1,n1)),n2)),f(n1,f(n1,n3))),
inference(paramodulation,[status(thm)],[190607992,168483448,theory(equality)]),
[] ).
cnf(350582232,plain,
~ $equal(f(n2,f(f(n1,f(n1,n1)),n2)),f(n1,f(n1,n3))),
inference(paramodulation,[status(thm)],[229013208,168479392,theory(equality)]),
[] ).
cnf(369211272,plain,
~ $equal(f(n2,f(f(n1,n2),n2)),f(n1,f(n1,n3))),
inference(paramodulation,[status(thm)],[350582232,168483448,theory(equality)]),
[] ).
cnf(369282192,plain,
~ $equal(f(n2,f(f(n1,n2),f(n1,n1))),f(n1,f(n1,n3))),
inference(paramodulation,[status(thm)],[369211272,168483448,theory(equality)]),
[] ).
cnf(383788536,plain,
~ $equal(f(n2,f(n1,f(n2,n1))),f(n1,f(n1,n3))),
inference(paramodulation,[status(thm)],[369282192,168479392,theory(equality)]),
[] ).
cnf(383841664,plain,
~ $equal(f(n2,f(n1,n3)),f(n1,f(n1,n3))),
inference(paramodulation,[status(thm)],[383788536,168487360,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[168479392,383841664,168483448,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 15 seconds
% START OF PROOF SEQUENCE
% fof(a1,plain,($equal(f(f(A,B),f(A,C)),f(A,f(B,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LDA/LDA001-1.tptp',unknown),[]).
%
% cnf(168479392,plain,($equal(f(f(A,B),f(A,C)),f(A,f(B,C)))),inference(rewrite,[status(thm)],[a1]),[]).
%
% fof(prove_equation,plain,(~$equal(f(f(u,u),u),f(f(n3,n2),u))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LDA/LDA001-1.tptp',unknown),[]).
%
% cnf(168495856,plain,(~$equal(f(f(u,u),u),f(f(n3,n2),u))),inference(rewrite,[status(thm)],[prove_equation]),[]).
%
% fof(clause_4,plain,($equal(f(n2,n2),u)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LDA/LDA001-1.tptp',unknown),[]).
%
% cnf(168491176,plain,($equal(f(n2,n2),u)),inference(rewrite,[status(thm)],[clause_4]),[]).
%
% cnf(176399984,plain,(~$equal(f(f(u,u),u),f(f(n3,n2),f(n2,n2)))),inference(paramodulation,[status(thm)],[168495856,168491176,theory(equality)]),[]).
%
% fof(clause_2,plain,($equal(f(n1,n1),n2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LDA/LDA001-1.tptp',unknown),[]).
%
% cnf(168483448,plain,($equal(f(n1,n1),n2)),inference(rewrite,[status(thm)],[clause_2]),[]).
%
% cnf(176995016,plain,(~$equal(f(f(u,u),u),f(f(n3,n2),f(n2,f(n1,n1))))),inference(paramodulation,[status(thm)],[176399984,168483448,theory(equality)]),[]).
%
% cnf(179064688,plain,(~$equal(f(f(u,u),u),f(f(n3,n2),f(f(n2,n1),f(n2,n1))))),inference(paramodulation,[status(thm)],[176995016,168479392,theory(equality)]),[]).
%
% fof(clause_3,plain,($equal(f(n2,n1),n3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LDA/LDA001-1.tptp',unknown),[]).
%
% cnf(168487360,plain,($equal(f(n2,n1),n3)),inference(rewrite,[status(thm)],[clause_3]),[]).
%
% cnf(189710696,plain,(~$equal(f(f(u,u),u),f(f(n3,n2),f(n3,f(n2,n1))))),inference(paramodulation,[status(thm)],[179064688,168487360,theory(equality)]),[]).
%
% cnf(193536784,plain,(~$equal(f(f(u,u),u),f(f(n3,n2),f(n3,n3)))),inference(paramodulation,[status(thm)],[189710696,168487360,theory(equality)]),[]).
%
% cnf(193761152,plain,(~$equal(f(f(u,u),u),f(n3,f(n2,n3)))),inference(paramodulation,[status(thm)],[193536784,168479392,theory(equality)]),[]).
%
% cnf(193836528,plain,(~$equal(f(f(f(n2,n2),u),u),f(n3,f(n2,n3)))),inference(paramodulation,[status(thm)],[193761152,168491176,theory(equality)]),[]).
%
% cnf(194293544,plain,(~$equal(f(f(f(n2,n2),f(n2,n2)),u),f(n3,f(n2,n3)))),inference(paramodulation,[status(thm)],[193836528,168491176,theory(equality)]),[]).
%
% cnf(203602096,plain,(~$equal(f(f(n2,f(n2,n2)),u),f(n3,f(n2,n3)))),inference(paramodulation,[status(thm)],[194293544,168479392,theory(equality)]),[]).
%
% cnf(203715800,plain,(~$equal(f(f(n2,u),u),f(n3,f(n2,n3)))),inference(paramodulation,[status(thm)],[203602096,168491176,theory(equality)]),[]).
%
% cnf(203785848,plain,(~$equal(f(f(n2,u),u),f(f(n2,n1),f(n2,n3)))),inference(paramodulation,[status(thm)],[203715800,168487360,theory(equality)]),[]).
%
% cnf(204027560,plain,(~$equal(f(f(n2,u),u),f(n2,f(n1,n3)))),inference(paramodulation,[status(thm)],[203785848,168479392,theory(equality)]),[]).
%
% cnf(204072312,plain,(~$equal(f(f(n2,u),u),f(f(n1,n1),f(n1,n3)))),inference(paramodulation,[status(thm)],[204027560,168483448,theory(equality)]),[]).
%
% cnf(204495608,plain,(~$equal(f(f(n2,u),u),f(n1,f(n1,n3)))),inference(paramodulation,[status(thm)],[204072312,168479392,theory(equality)]),[]).
%
% cnf(204569824,plain,(~$equal(f(f(n2,u),f(n2,n2)),f(n1,f(n1,n3)))),inference(paramodulation,[status(thm)],[204495608,168491176,theory(equality)]),[]).
%
% cnf(205410912,plain,(~$equal(f(n2,f(u,n2)),f(n1,f(n1,n3)))),inference(paramodulation,[status(thm)],[204569824,168479392,theory(equality)]),[]).
%
% cnf(205485000,plain,(~$equal(f(n2,f(f(n2,n2),n2)),f(n1,f(n1,n3)))),inference(paramodulation,[status(thm)],[205410912,168491176,theory(equality)]),[]).
%
% cnf(190607992,plain,(~$equal(f(n2,f(f(f(n1,n1),n2),n2)),f(n1,f(n1,n3)))),inference(paramodulation,[status(thm)],[205485000,168483448,theory(equality)]),[]).
%
% cnf(229013208,plain,(~$equal(f(n2,f(f(f(n1,n1),f(n1,n1)),n2)),f(n1,f(n1,n3)))),inference(paramodulation,[status(thm)],[190607992,168483448,theory(equality)]),[]).
%
% cnf(350582232,plain,(~$equal(f(n2,f(f(n1,f(n1,n1)),n2)),f(n1,f(n1,n3)))),inference(paramodulation,[status(thm)],[229013208,168479392,theory(equality)]),[]).
%
% cnf(369211272,plain,(~$equal(f(n2,f(f(n1,n2),n2)),f(n1,f(n1,n3)))),inference(paramodulation,[status(thm)],[350582232,168483448,theory(equality)]),[]).
%
% cnf(369282192,plain,(~$equal(f(n2,f(f(n1,n2),f(n1,n1))),f(n1,f(n1,n3)))),inference(paramodulation,[status(thm)],[369211272,168483448,theory(equality)]),[]).
%
% cnf(383788536,plain,(~$equal(f(n2,f(n1,f(n2,n1))),f(n1,f(n1,n3)))),inference(paramodulation,[status(thm)],[369282192,168479392,theory(equality)]),[]).
%
% cnf(383841664,plain,(~$equal(f(n2,f(n1,n3)),f(n1,f(n1,n3)))),inference(paramodulation,[status(thm)],[383788536,168487360,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[168479392,383841664,168483448,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------