TSTP Solution File: SYN204-1 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SYN204-1 : TPTP v3.4.2. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art02.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 17:16:00 EDT 2009
% Result : Unsatisfiable 566.6s
% Output : Refutation 566.6s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 18
% Syntax : Number of formulae : 49 ( 23 unt; 0 def)
% Number of atoms : 94 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 94 ( 49 ~; 45 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 55 ( 9 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(axiom_32,plain,
k0(b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN204-1.tptp',unknown),
[] ).
cnf(162913984,plain,
k0(b),
inference(rewrite,[status(thm)],[axiom_32]),
[] ).
fof(rule_068,plain,
! [A] :
( p1(A,A,A)
| ~ k0(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN204-1.tptp',unknown),
[] ).
cnf(163706136,plain,
( p1(A,A,A)
| ~ k0(A) ),
inference(rewrite,[status(thm)],[rule_068]),
[] ).
fof(axiom_20,plain,
l0(a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN204-1.tptp',unknown),
[] ).
cnf(162853528,plain,
l0(a),
inference(rewrite,[status(thm)],[axiom_20]),
[] ).
fof(rule_050,plain,
! [A,B] :
( n1(A,B,A)
| ~ s0(b)
| ~ l0(A)
| ~ p0(b,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN204-1.tptp',unknown),
[] ).
fof(axiom_14,plain,
! [A] : p0(b,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN204-1.tptp',unknown),
[] ).
cnf(162826400,plain,
p0(b,A),
inference(rewrite,[status(thm)],[axiom_14]),
[] ).
fof(axiom_5,plain,
s0(b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN204-1.tptp',unknown),
[] ).
cnf(162778600,plain,
s0(b),
inference(rewrite,[status(thm)],[axiom_5]),
[] ).
cnf(163474864,plain,
( n1(A,B,A)
| ~ l0(A) ),
inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_050,162826400,162778600]),
[] ).
cnf(175797568,plain,
n1(a,A,a),
inference(resolution,[status(thm)],[163474864,162853528]),
[] ).
fof(rule_054,plain,
! [A,B,C] :
( n1(A,B,B)
| ~ l0(C)
| ~ l1(C,A)
| ~ n1(A,B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN204-1.tptp',unknown),
[] ).
cnf(163540016,plain,
( n1(A,B,B)
| ~ l0(C)
| ~ l1(C,A)
| ~ n1(A,B,A) ),
inference(rewrite,[status(thm)],[rule_054]),
[] ).
fof(axiom_37,plain,
n0(b,a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN204-1.tptp',unknown),
[] ).
cnf(162932696,plain,
n0(b,a),
inference(rewrite,[status(thm)],[axiom_37]),
[] ).
fof(rule_002,plain,
! [A,B] :
( l1(A,A)
| ~ n0(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN204-1.tptp',unknown),
[] ).
cnf(162960120,plain,
( l1(A,A)
| ~ n0(B,A) ),
inference(rewrite,[status(thm)],[rule_002]),
[] ).
cnf(180164712,plain,
l1(a,a),
inference(resolution,[status(thm)],[162932696,162960120]),
[] ).
cnf(668642168,plain,
n1(a,A,A),
inference(forward_subsumption_resolution__resolution,[status(thm)],[162853528,175797568,163540016,180164712]),
[] ).
fof(rule_182,plain,
! [A,B,C] :
( q2(A,B,A)
| ~ p1(A,A,C)
| ~ n1(B,A,C)
| ~ q2(B,C,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN204-1.tptp',unknown),
[] ).
cnf(165037496,plain,
( q2(A,B,A)
| ~ p1(A,A,C)
| ~ n1(B,A,C)
| ~ q2(B,C,A) ),
inference(rewrite,[status(thm)],[rule_182]),
[] ).
fof(rule_177,plain,
! [A,B] :
( q2(A,B,B)
| ~ k0(B)
| ~ p1(A,A,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN204-1.tptp',unknown),
[] ).
cnf(164967072,plain,
( q2(A,B,B)
| ~ k0(B)
| ~ p1(A,A,A) ),
inference(rewrite,[status(thm)],[rule_177]),
[] ).
fof(rule_075,plain,
( p1(a,a,a)
| ~ p0(b,a) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN204-1.tptp',unknown),
[] ).
cnf(163759048,plain,
p1(a,a,a),
inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_075,162826400]),
[] ).
cnf(179114008,plain,
( q2(a,A,A)
| ~ k0(A) ),
inference(resolution,[status(thm)],[164967072,163759048]),
[] ).
cnf(212187060,plain,
( q2(A,a,A)
| ~ k0(A) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[163706136,668642168,165037496,179114008]),
[] ).
fof(rule_273,plain,
! [A,B,C,D] :
( s3(A,B)
| ~ q2(C,A,C)
| ~ s2(A)
| ~ m0(C,D,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN204-1.tptp',unknown),
[] ).
cnf(166320136,plain,
( s3(A,B)
| ~ q2(C,A,C)
| ~ s2(A)
| ~ m0(C,D,B) ),
inference(rewrite,[status(thm)],[rule_273]),
[] ).
fof(axiom_19,plain,
! [A,B] : m0(A,d,B),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN204-1.tptp',unknown),
[] ).
cnf(162849168,plain,
m0(A,d,B),
inference(rewrite,[status(thm)],[axiom_19]),
[] ).
cnf(178717088,plain,
( s3(A,B)
| ~ q2(C,A,C)
| ~ s2(A) ),
inference(resolution,[status(thm)],[166320136,162849168]),
[] ).
fof(rule_181,plain,
! [A] :
( q2(A,A,A)
| ~ p1(A,A,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN204-1.tptp',unknown),
[] ).
cnf(165019072,plain,
( q2(A,A,A)
| ~ p1(A,A,A) ),
inference(rewrite,[status(thm)],[rule_181]),
[] ).
cnf(179103776,plain,
q2(a,a,a),
inference(resolution,[status(thm)],[165019072,163759048]),
[] ).
cnf(189721040,plain,
( s3(a,A)
| ~ s2(a) ),
inference(resolution,[status(thm)],[178717088,179103776]),
[] ).
fof(prove_this,plain,
~ s3(a,c),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN204-1.tptp',unknown),
[] ).
cnf(167123288,plain,
~ s3(a,c),
inference(rewrite,[status(thm)],[prove_this]),
[] ).
cnf(189798680,plain,
~ s2(a),
inference(resolution,[status(thm)],[189721040,167123288]),
[] ).
fof(rule_189,plain,
! [A] :
( s2(A)
| ~ q2(b,A,b)
| ~ s1(b) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN204-1.tptp',unknown),
[] ).
cnf(165147992,plain,
( s2(A)
| ~ q2(b,A,b)
| ~ s1(b) ),
inference(rewrite,[status(thm)],[rule_189]),
[] ).
fof(rule_125,plain,
! [A] :
( s1(A)
| ~ p0(A,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN204-1.tptp',unknown),
[] ).
cnf(164253632,plain,
( s1(A)
| ~ p0(A,A) ),
inference(rewrite,[status(thm)],[rule_125]),
[] ).
cnf(176943752,plain,
s1(b),
inference(resolution,[status(thm)],[164253632,162826400]),
[] ).
cnf(177305136,plain,
( s2(A)
| ~ q2(b,A,b) ),
inference(resolution,[status(thm)],[165147992,176943752]),
[] ).
cnf(189841216,plain,
~ q2(b,a,b),
inference(resolution,[status(thm)],[189798680,177305136]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[162913984,212187060,189841216]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 774 seconds
% START OF PROOF SEQUENCE
% fof(axiom_32,plain,(k0(b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN204-1.tptp',unknown),[]).
%
% cnf(162913984,plain,(k0(b)),inference(rewrite,[status(thm)],[axiom_32]),[]).
%
% fof(rule_068,plain,(p1(A,A,A)|~k0(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN204-1.tptp',unknown),[]).
%
% cnf(163706136,plain,(p1(A,A,A)|~k0(A)),inference(rewrite,[status(thm)],[rule_068]),[]).
%
% fof(axiom_20,plain,(l0(a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN204-1.tptp',unknown),[]).
%
% cnf(162853528,plain,(l0(a)),inference(rewrite,[status(thm)],[axiom_20]),[]).
%
% fof(rule_050,plain,(n1(A,B,A)|~s0(b)|~l0(A)|~p0(b,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN204-1.tptp',unknown),[]).
%
% fof(axiom_14,plain,(p0(b,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN204-1.tptp',unknown),[]).
%
% cnf(162826400,plain,(p0(b,A)),inference(rewrite,[status(thm)],[axiom_14]),[]).
%
% fof(axiom_5,plain,(s0(b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN204-1.tptp',unknown),[]).
%
% cnf(162778600,plain,(s0(b)),inference(rewrite,[status(thm)],[axiom_5]),[]).
%
% cnf(163474864,plain,(n1(A,B,A)|~l0(A)),inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_050,162826400,162778600]),[]).
%
% cnf(175797568,plain,(n1(a,A,a)),inference(resolution,[status(thm)],[163474864,162853528]),[]).
%
% fof(rule_054,plain,(n1(A,B,B)|~l0(C)|~l1(C,A)|~n1(A,B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN204-1.tptp',unknown),[]).
%
% cnf(163540016,plain,(n1(A,B,B)|~l0(C)|~l1(C,A)|~n1(A,B,A)),inference(rewrite,[status(thm)],[rule_054]),[]).
%
% fof(axiom_37,plain,(n0(b,a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN204-1.tptp',unknown),[]).
%
% cnf(162932696,plain,(n0(b,a)),inference(rewrite,[status(thm)],[axiom_37]),[]).
%
% fof(rule_002,plain,(l1(A,A)|~n0(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN204-1.tptp',unknown),[]).
%
% cnf(162960120,plain,(l1(A,A)|~n0(B,A)),inference(rewrite,[status(thm)],[rule_002]),[]).
%
% cnf(180164712,plain,(l1(a,a)),inference(resolution,[status(thm)],[162932696,162960120]),[]).
%
% cnf(668642168,plain,(n1(a,A,A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[162853528,175797568,163540016,180164712]),[]).
%
% fof(rule_182,plain,(q2(A,B,A)|~p1(A,A,C)|~n1(B,A,C)|~q2(B,C,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN204-1.tptp',unknown),[]).
%
% cnf(165037496,plain,(q2(A,B,A)|~p1(A,A,C)|~n1(B,A,C)|~q2(B,C,A)),inference(rewrite,[status(thm)],[rule_182]),[]).
%
% fof(rule_177,plain,(q2(A,B,B)|~k0(B)|~p1(A,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN204-1.tptp',unknown),[]).
%
% cnf(164967072,plain,(q2(A,B,B)|~k0(B)|~p1(A,A,A)),inference(rewrite,[status(thm)],[rule_177]),[]).
%
% fof(rule_075,plain,(p1(a,a,a)|~p0(b,a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN204-1.tptp',unknown),[]).
%
% cnf(163759048,plain,(p1(a,a,a)),inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_075,162826400]),[]).
%
% cnf(179114008,plain,(q2(a,A,A)|~k0(A)),inference(resolution,[status(thm)],[164967072,163759048]),[]).
%
% cnf(212187060,plain,(q2(A,a,A)|~k0(A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[163706136,668642168,165037496,179114008]),[]).
%
% fof(rule_273,plain,(s3(A,B)|~q2(C,A,C)|~s2(A)|~m0(C,D,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN204-1.tptp',unknown),[]).
%
% cnf(166320136,plain,(s3(A,B)|~q2(C,A,C)|~s2(A)|~m0(C,D,B)),inference(rewrite,[status(thm)],[rule_273]),[]).
%
% fof(axiom_19,plain,(m0(A,d,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN204-1.tptp',unknown),[]).
%
% cnf(162849168,plain,(m0(A,d,B)),inference(rewrite,[status(thm)],[axiom_19]),[]).
%
% cnf(178717088,plain,(s3(A,B)|~q2(C,A,C)|~s2(A)),inference(resolution,[status(thm)],[166320136,162849168]),[]).
%
% fof(rule_181,plain,(q2(A,A,A)|~p1(A,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN204-1.tptp',unknown),[]).
%
% cnf(165019072,plain,(q2(A,A,A)|~p1(A,A,A)),inference(rewrite,[status(thm)],[rule_181]),[]).
%
% cnf(179103776,plain,(q2(a,a,a)),inference(resolution,[status(thm)],[165019072,163759048]),[]).
%
% cnf(189721040,plain,(s3(a,A)|~s2(a)),inference(resolution,[status(thm)],[178717088,179103776]),[]).
%
% fof(prove_this,plain,(~s3(a,c)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN204-1.tptp',unknown),[]).
%
% cnf(167123288,plain,(~s3(a,c)),inference(rewrite,[status(thm)],[prove_this]),[]).
%
% cnf(189798680,plain,(~s2(a)),inference(resolution,[status(thm)],[189721040,167123288]),[]).
%
% fof(rule_189,plain,(s2(A)|~q2(b,A,b)|~s1(b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN204-1.tptp',unknown),[]).
%
% cnf(165147992,plain,(s2(A)|~q2(b,A,b)|~s1(b)),inference(rewrite,[status(thm)],[rule_189]),[]).
%
% fof(rule_125,plain,(s1(A)|~p0(A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN204-1.tptp',unknown),[]).
%
% cnf(164253632,plain,(s1(A)|~p0(A,A)),inference(rewrite,[status(thm)],[rule_125]),[]).
%
% cnf(176943752,plain,(s1(b)),inference(resolution,[status(thm)],[164253632,162826400]),[]).
%
% cnf(177305136,plain,(s2(A)|~q2(b,A,b)),inference(resolution,[status(thm)],[165147992,176943752]),[]).
%
% cnf(189841216,plain,(~q2(b,a,b)),inference(resolution,[status(thm)],[189798680,177305136]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[162913984,212187060,189841216]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------