TSTP Solution File: SYN270-1 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SYN270-1 : TPTP v3.4.2. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art05.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 17:36:47 EDT 2009
% Result : Unsatisfiable 45.0s
% Output : Refutation 45.0s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 21
% Syntax : Number of formulae : 57 ( 29 unt; 0 def)
% Number of atoms : 104 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 97 ( 50 ~; 47 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 17 ( 16 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 68 ( 12 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(rule_127,plain,
! [A,B,C,D] :
( k2(A,B)
| ~ m1(C,B,A)
| ~ k1(D)
| ~ k2(D,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),
[] ).
cnf(149221944,plain,
( k2(A,B)
| ~ m1(C,B,A)
| ~ k1(D)
| ~ k2(D,B) ),
inference(rewrite,[status(thm)],[rule_127]),
[] ).
fof(rule_007,plain,
! [A,B,C] :
( m1(A,B,A)
| ~ p0(C,B)
| ~ r0(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),
[] ).
cnf(147970784,plain,
( m1(A,B,A)
| ~ p0(C,B)
| ~ r0(A) ),
inference(rewrite,[status(thm)],[rule_007]),
[] ).
fof(axiom_14,plain,
! [A] : p0(b,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),
[] ).
cnf(147767072,plain,
p0(b,A),
inference(rewrite,[status(thm)],[axiom_14]),
[] ).
cnf(161735480,plain,
( m1(A,B,A)
| ~ r0(A) ),
inference(resolution,[status(thm)],[147970784,147767072]),
[] ).
fof(axiom_9,plain,
r0(b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),
[] ).
cnf(147739128,plain,
r0(b),
inference(rewrite,[status(thm)],[axiom_9]),
[] ).
cnf(161739952,plain,
m1(b,A,b),
inference(resolution,[status(thm)],[161735480,147739128]),
[] ).
cnf(423836272,plain,
( k2(b,A)
| ~ k1(B)
| ~ k2(B,A) ),
inference(resolution,[status(thm)],[149221944,161739952]),
[] ).
fof(rule_129,plain,
! [A,B] :
( k2(A,A)
| ~ q1(B,A,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),
[] ).
cnf(149258272,plain,
( k2(A,A)
| ~ q1(B,A,A) ),
inference(rewrite,[status(thm)],[rule_129]),
[] ).
fof(rule_107,plain,
! [A] :
( q1(e,A,A)
| ~ m0(A,d,A)
| ~ m0(e,d,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),
[] ).
fof(axiom_19,plain,
! [A,B] : m0(A,d,B),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),
[] ).
cnf(147789840,plain,
m0(A,d,B),
inference(rewrite,[status(thm)],[axiom_19]),
[] ).
cnf(149047608,plain,
q1(e,A,A),
inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_107,147789840]),
[] ).
cnf(163440696,plain,
k2(A,A),
inference(resolution,[status(thm)],[149258272,149047608]),
[] ).
cnf(428111536,plain,
( k2(b,A)
| ~ k1(A) ),
inference(resolution,[status(thm)],[423836272,163440696]),
[] ).
fof(axiom_26,plain,
n0(d,c),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),
[] ).
cnf(147820328,plain,
n0(d,c),
inference(rewrite,[status(thm)],[axiom_26]),
[] ).
fof(rule_001,plain,
! [A,B] :
( k1(A)
| ~ n0(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),
[] ).
cnf(147887336,plain,
( k1(A)
| ~ n0(B,A) ),
inference(rewrite,[status(thm)],[rule_001]),
[] ).
cnf(163989664,plain,
k1(c),
inference(resolution,[status(thm)],[147820328,147887336]),
[] ).
cnf(428326848,plain,
k2(b,c),
inference(resolution,[status(thm)],[428111536,163989664]),
[] ).
fof(rule_097,plain,
! [A] :
( q1(A,A,A)
| ~ s0(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),
[] ).
cnf(148951216,plain,
( q1(A,A,A)
| ~ s0(A) ),
inference(rewrite,[status(thm)],[rule_097]),
[] ).
fof(axiom_1,plain,
s0(d),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),
[] ).
cnf(147679024,plain,
s0(d),
inference(rewrite,[status(thm)],[axiom_1]),
[] ).
cnf(150098680,plain,
q1(d,d,d),
inference(resolution,[status(thm)],[148951216,147679024]),
[] ).
fof(rule_124,plain,
! [A,B] :
( r1(A)
| ~ q0(A,B)
| ~ s0(d)
| ~ q1(d,B,d) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),
[] ).
cnf(149182128,plain,
( r1(A)
| ~ q0(A,B)
| ~ q1(d,B,d) ),
inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_124,147679024]),
[] ).
fof(axiom_17,plain,
! [A] : q0(A,d),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),
[] ).
cnf(147782360,plain,
q0(A,d),
inference(rewrite,[status(thm)],[axiom_17]),
[] ).
cnf(168212768,plain,
r1(A),
inference(forward_subsumption_resolution__resolution,[status(thm)],[150098680,149182128,147782360]),
[] ).
fof(axiom_24,plain,
l0(c),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),
[] ).
cnf(147816496,plain,
l0(c),
inference(rewrite,[status(thm)],[axiom_24]),
[] ).
fof(rule_188,plain,
! [A] :
( r2(A)
| ~ r1(A)
| ~ l0(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),
[] ).
cnf(150078800,plain,
( r2(A)
| ~ r1(A)
| ~ l0(A) ),
inference(rewrite,[status(thm)],[rule_188]),
[] ).
cnf(164648024,plain,
( r2(c)
| ~ r1(c) ),
inference(resolution,[status(thm)],[147816496,150078800]),
[] ).
cnf(168414720,plain,
r2(c),
inference(resolution,[status(thm)],[168212768,164648024]),
[] ).
fof(rule_020,plain,
( m1(c,c,c)
| ~ l0(c) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),
[] ).
cnf(148113688,plain,
m1(c,c,c),
inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_020,147816496]),
[] ).
fof(rule_176,plain,
! [A,B] :
( p2(A,B,A)
| ~ m1(B,A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),
[] ).
cnf(149900008,plain,
( p2(A,B,A)
| ~ m1(B,A,B) ),
inference(rewrite,[status(thm)],[rule_176]),
[] ).
cnf(165037640,plain,
p2(c,c,c),
inference(resolution,[status(thm)],[148113688,149900008]),
[] ).
fof(rule_267,plain,
! [A,B,C] :
( r3(A,B,A)
| ~ p2(A,C,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),
[] ).
cnf(151145384,plain,
( r3(A,B,A)
| ~ p2(A,C,B) ),
inference(rewrite,[status(thm)],[rule_267]),
[] ).
cnf(165698840,plain,
r3(c,c,c),
inference(resolution,[status(thm)],[165037640,151145384]),
[] ).
fof(rule_272,plain,
! [A,B,C] :
( r3(A,B,C)
| ~ k2(B,C)
| ~ r2(C)
| ~ r3(C,A,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),
[] ).
cnf(151245000,plain,
( r3(A,B,C)
| ~ k2(B,C)
| ~ r2(C)
| ~ r3(C,A,A) ),
inference(rewrite,[status(thm)],[rule_272]),
[] ).
fof(rule_285,plain,
! [A,B] :
( p4(A,A,B)
| ~ r0(A)
| ~ r3(B,A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),
[] ).
cnf(151413984,plain,
( p4(A,A,B)
| ~ r0(A)
| ~ r3(B,A,B) ),
inference(rewrite,[status(thm)],[rule_285]),
[] ).
fof(prove_this,plain,
~ p4(b,b,c),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),
[] ).
cnf(152063296,plain,
~ p4(b,b,c),
inference(rewrite,[status(thm)],[prove_this]),
[] ).
cnf(185669928,plain,
~ r3(c,b,c),
inference(forward_subsumption_resolution__resolution,[status(thm)],[147739128,151413984,152063296]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[428326848,168414720,165698840,151245000,185669928]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 45 seconds
% START OF PROOF SEQUENCE
% fof(rule_127,plain,(k2(A,B)|~m1(C,B,A)|~k1(D)|~k2(D,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),[]).
%
% cnf(149221944,plain,(k2(A,B)|~m1(C,B,A)|~k1(D)|~k2(D,B)),inference(rewrite,[status(thm)],[rule_127]),[]).
%
% fof(rule_007,plain,(m1(A,B,A)|~p0(C,B)|~r0(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),[]).
%
% cnf(147970784,plain,(m1(A,B,A)|~p0(C,B)|~r0(A)),inference(rewrite,[status(thm)],[rule_007]),[]).
%
% fof(axiom_14,plain,(p0(b,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),[]).
%
% cnf(147767072,plain,(p0(b,A)),inference(rewrite,[status(thm)],[axiom_14]),[]).
%
% cnf(161735480,plain,(m1(A,B,A)|~r0(A)),inference(resolution,[status(thm)],[147970784,147767072]),[]).
%
% fof(axiom_9,plain,(r0(b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),[]).
%
% cnf(147739128,plain,(r0(b)),inference(rewrite,[status(thm)],[axiom_9]),[]).
%
% cnf(161739952,plain,(m1(b,A,b)),inference(resolution,[status(thm)],[161735480,147739128]),[]).
%
% cnf(423836272,plain,(k2(b,A)|~k1(B)|~k2(B,A)),inference(resolution,[status(thm)],[149221944,161739952]),[]).
%
% fof(rule_129,plain,(k2(A,A)|~q1(B,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),[]).
%
% cnf(149258272,plain,(k2(A,A)|~q1(B,A,A)),inference(rewrite,[status(thm)],[rule_129]),[]).
%
% fof(rule_107,plain,(q1(e,A,A)|~m0(A,d,A)|~m0(e,d,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),[]).
%
% fof(axiom_19,plain,(m0(A,d,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),[]).
%
% cnf(147789840,plain,(m0(A,d,B)),inference(rewrite,[status(thm)],[axiom_19]),[]).
%
% cnf(149047608,plain,(q1(e,A,A)),inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_107,147789840]),[]).
%
% cnf(163440696,plain,(k2(A,A)),inference(resolution,[status(thm)],[149258272,149047608]),[]).
%
% cnf(428111536,plain,(k2(b,A)|~k1(A)),inference(resolution,[status(thm)],[423836272,163440696]),[]).
%
% fof(axiom_26,plain,(n0(d,c)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),[]).
%
% cnf(147820328,plain,(n0(d,c)),inference(rewrite,[status(thm)],[axiom_26]),[]).
%
% fof(rule_001,plain,(k1(A)|~n0(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),[]).
%
% cnf(147887336,plain,(k1(A)|~n0(B,A)),inference(rewrite,[status(thm)],[rule_001]),[]).
%
% cnf(163989664,plain,(k1(c)),inference(resolution,[status(thm)],[147820328,147887336]),[]).
%
% cnf(428326848,plain,(k2(b,c)),inference(resolution,[status(thm)],[428111536,163989664]),[]).
%
% fof(rule_097,plain,(q1(A,A,A)|~s0(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),[]).
%
% cnf(148951216,plain,(q1(A,A,A)|~s0(A)),inference(rewrite,[status(thm)],[rule_097]),[]).
%
% fof(axiom_1,plain,(s0(d)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),[]).
%
% cnf(147679024,plain,(s0(d)),inference(rewrite,[status(thm)],[axiom_1]),[]).
%
% cnf(150098680,plain,(q1(d,d,d)),inference(resolution,[status(thm)],[148951216,147679024]),[]).
%
% fof(rule_124,plain,(r1(A)|~q0(A,B)|~s0(d)|~q1(d,B,d)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),[]).
%
% cnf(149182128,plain,(r1(A)|~q0(A,B)|~q1(d,B,d)),inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_124,147679024]),[]).
%
% fof(axiom_17,plain,(q0(A,d)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),[]).
%
% cnf(147782360,plain,(q0(A,d)),inference(rewrite,[status(thm)],[axiom_17]),[]).
%
% cnf(168212768,plain,(r1(A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[150098680,149182128,147782360]),[]).
%
% fof(axiom_24,plain,(l0(c)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),[]).
%
% cnf(147816496,plain,(l0(c)),inference(rewrite,[status(thm)],[axiom_24]),[]).
%
% fof(rule_188,plain,(r2(A)|~r1(A)|~l0(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),[]).
%
% cnf(150078800,plain,(r2(A)|~r1(A)|~l0(A)),inference(rewrite,[status(thm)],[rule_188]),[]).
%
% cnf(164648024,plain,(r2(c)|~r1(c)),inference(resolution,[status(thm)],[147816496,150078800]),[]).
%
% cnf(168414720,plain,(r2(c)),inference(resolution,[status(thm)],[168212768,164648024]),[]).
%
% fof(rule_020,plain,(m1(c,c,c)|~l0(c)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),[]).
%
% cnf(148113688,plain,(m1(c,c,c)),inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_020,147816496]),[]).
%
% fof(rule_176,plain,(p2(A,B,A)|~m1(B,A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),[]).
%
% cnf(149900008,plain,(p2(A,B,A)|~m1(B,A,B)),inference(rewrite,[status(thm)],[rule_176]),[]).
%
% cnf(165037640,plain,(p2(c,c,c)),inference(resolution,[status(thm)],[148113688,149900008]),[]).
%
% fof(rule_267,plain,(r3(A,B,A)|~p2(A,C,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),[]).
%
% cnf(151145384,plain,(r3(A,B,A)|~p2(A,C,B)),inference(rewrite,[status(thm)],[rule_267]),[]).
%
% cnf(165698840,plain,(r3(c,c,c)),inference(resolution,[status(thm)],[165037640,151145384]),[]).
%
% fof(rule_272,plain,(r3(A,B,C)|~k2(B,C)|~r2(C)|~r3(C,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),[]).
%
% cnf(151245000,plain,(r3(A,B,C)|~k2(B,C)|~r2(C)|~r3(C,A,A)),inference(rewrite,[status(thm)],[rule_272]),[]).
%
% fof(rule_285,plain,(p4(A,A,B)|~r0(A)|~r3(B,A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),[]).
%
% cnf(151413984,plain,(p4(A,A,B)|~r0(A)|~r3(B,A,B)),inference(rewrite,[status(thm)],[rule_285]),[]).
%
% fof(prove_this,plain,(~p4(b,b,c)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN270-1.tptp',unknown),[]).
%
% cnf(152063296,plain,(~p4(b,b,c)),inference(rewrite,[status(thm)],[prove_this]),[]).
%
% cnf(185669928,plain,(~r3(c,b,c)),inference(forward_subsumption_resolution__resolution,[status(thm)],[147739128,151413984,152063296]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[428326848,168414720,165698840,151245000,185669928]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------