TSTP Solution File: SYN180-1 by Faust---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SYN180-1 : TPTP v3.4.2. Released v1.1.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art01.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 17:07:55 EDT 2009

% Result   : Unsatisfiable 347.4s
% Output   : Refutation 347.4s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   51 (  25 unt;   0 def)
%            Number of atoms       :   97 (   0 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :   96 (  50   ~;  46   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   16 (  15 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   4 con; 0-0 aty)
%            Number of variables   :   60 (  13 sgn  23   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
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/SYN180-1.tptp',unknown),
    [] ).

cnf(149280192,plain,
    ( q2(A,B,B)
    | ~ k0(B)
    | ~ p1(A,A,A) ),
    inference(rewrite,[status(thm)],[rule_177]),
    [] ).

fof(rule_085,plain,
    ! [A,B] :
      ( p1(A,A,A)
      | ~ p0(B,A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN180-1.tptp',unknown),
    [] ).

cnf(148201168,plain,
    ( p1(A,A,A)
    | ~ p0(B,A) ),
    inference(rewrite,[status(thm)],[rule_085]),
    [] ).

fof(axiom_14,plain,
    ! [A] : p0(b,A),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN180-1.tptp',unknown),
    [] ).

cnf(147139520,plain,
    p0(b,A),
    inference(rewrite,[status(thm)],[axiom_14]),
    [] ).

cnf(161461312,plain,
    p1(A,A,A),
    inference(resolution,[status(thm)],[148201168,147139520]),
    [] ).

cnf(163790312,plain,
    ( q2(A,B,B)
    | ~ k0(B) ),
    inference(resolution,[status(thm)],[149280192,161461312]),
    [] ).

fof(rule_187,plain,
    ! [A,B,C,D] :
      ( q2(A,B,A)
      | ~ r1(B)
      | ~ m0(C,D,A)
      | ~ k0(B)
      | ~ q2(B,B,B) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN180-1.tptp',unknown),
    [] ).

cnf(149437320,plain,
    ( q2(A,B,A)
    | ~ r1(B)
    | ~ m0(C,D,A)
    | ~ k0(B)
    | ~ q2(B,B,B) ),
    inference(rewrite,[status(thm)],[rule_187]),
    [] ).

fof(rule_097,plain,
    ! [A] :
      ( q1(A,A,A)
      | ~ s0(A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN180-1.tptp',unknown),
    [] ).

cnf(148323664,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/SYN180-1.tptp',unknown),
    [] ).

cnf(147051472,plain,
    s0(d),
    inference(rewrite,[status(thm)],[axiom_1]),
    [] ).

cnf(149471144,plain,
    q1(d,d,d),
    inference(resolution,[status(thm)],[148323664,147051472]),
    [] ).

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/SYN180-1.tptp',unknown),
    [] ).

cnf(148554576,plain,
    ( r1(A)
    | ~ q0(A,B)
    | ~ q1(d,B,d) ),
    inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_124,147051472]),
    [] ).

fof(axiom_17,plain,
    ! [A] : q0(A,d),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN180-1.tptp',unknown),
    [] ).

cnf(147154808,plain,
    q0(A,d),
    inference(rewrite,[status(thm)],[axiom_17]),
    [] ).

cnf(161752392,plain,
    r1(A),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[149471144,148554576,147154808]),
    [] ).

cnf(161978728,plain,
    ( q2(A,B,A)
    | ~ m0(C,D,A)
    | ~ k0(B)
    | ~ q2(B,B,B) ),
    inference(resolution,[status(thm)],[149437320,161752392]),
    [] ).

fof(axiom_4,plain,
    m0(e,d,a),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN180-1.tptp',unknown),
    [] ).

cnf(147081104,plain,
    m0(e,d,a),
    inference(rewrite,[status(thm)],[axiom_4]),
    [] ).

cnf(153803397,plain,
    ( q2(a,A,a)
    | ~ k0(A) ),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[163790312,161978728,147081104]),
    [] ).

fof(axiom_28,plain,
    k0(e),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN180-1.tptp',unknown),
    [] ).

cnf(147205080,plain,
    k0(e),
    inference(rewrite,[status(thm)],[axiom_28]),
    [] ).

cnf(153804848,plain,
    q2(a,e,a),
    inference(resolution,[status(thm)],[153803397,147205080]),
    [] ).

fof(rule_295,plain,
    ! [A,B,C,D,E] :
      ( q4(A,B)
      | ~ k3(C,C,A)
      | ~ q2(D,B,A)
      | ~ m3(D,E,D) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN180-1.tptp',unknown),
    [] ).

cnf(150920080,plain,
    ( q4(A,B)
    | ~ k3(C,C,A)
    | ~ q2(D,B,A)
    | ~ m3(D,E,D) ),
    inference(rewrite,[status(thm)],[rule_295]),
    [] ).

fof(prove_this,plain,
    ~ q4(a,e),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN180-1.tptp',unknown),
    [] ).

cnf(151435720,plain,
    ~ q4(a,e),
    inference(rewrite,[status(thm)],[prove_this]),
    [] ).

cnf(163366032,plain,
    ( ~ k3(A,A,a)
    | ~ q2(B,e,a)
    | ~ m3(B,C,B) ),
    inference(resolution,[status(thm)],[150920080,151435720]),
    [] ).

fof(rule_236,plain,
    ! [A] :
      ( m3(A,A,A)
      | ~ n2(A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN180-1.tptp',unknown),
    [] ).

cnf(150111408,plain,
    ( m3(A,A,A)
    | ~ n2(A) ),
    inference(rewrite,[status(thm)],[rule_236]),
    [] ).

fof(rule_137,plain,
    ! [A,B,C] :
      ( n2(A)
      | ~ p1(B,C,A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN180-1.tptp',unknown),
    [] ).

cnf(148742472,plain,
    ( n2(A)
    | ~ p1(B,C,A) ),
    inference(rewrite,[status(thm)],[rule_137]),
    [] ).

fof(rule_075,plain,
    ( p1(a,a,a)
    | ~ p0(b,a) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN180-1.tptp',unknown),
    [] ).

cnf(148072168,plain,
    p1(a,a,a),
    inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_075,147139520]),
    [] ).

cnf(163147040,plain,
    n2(a),
    inference(resolution,[status(thm)],[148742472,148072168]),
    [] ).

cnf(163255896,plain,
    m3(a,a,a),
    inference(resolution,[status(thm)],[150111408,163147040]),
    [] ).

cnf(184740989,plain,
    ~ k3(A,A,a),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[153804848,163366032,163255896]),
    [] ).

fof(rule_204,plain,
    ( k3(a,a,a)
    | ~ r2(a) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN180-1.tptp',unknown),
    [] ).

cnf(149692056,plain,
    ( k3(a,a,a)
    | ~ r2(a) ),
    inference(rewrite,[status(thm)],[rule_204]),
    [] ).

fof(rule_188,plain,
    ! [A] :
      ( r2(A)
      | ~ r1(A)
      | ~ l0(A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN180-1.tptp',unknown),
    [] ).

cnf(149451248,plain,
    ( r2(A)
    | ~ r1(A)
    | ~ l0(A) ),
    inference(rewrite,[status(thm)],[rule_188]),
    [] ).

cnf(161894328,plain,
    ( r2(A)
    | ~ l0(A) ),
    inference(resolution,[status(thm)],[149451248,161752392]),
    [] ).

fof(axiom_20,plain,
    l0(a),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN180-1.tptp',unknown),
    [] ).

cnf(147166648,plain,
    l0(a),
    inference(rewrite,[status(thm)],[axiom_20]),
    [] ).

cnf(161904776,plain,
    r2(a),
    inference(resolution,[status(thm)],[161894328,147166648]),
    [] ).

cnf(162012328,plain,
    k3(a,a,a),
    inference(resolution,[status(thm)],[149692056,161904776]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[184740989,162012328]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 447 seconds
% START OF PROOF SEQUENCE
% fof(rule_177,plain,(q2(A,B,B)|~k0(B)|~p1(A,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN180-1.tptp',unknown),[]).
% 
% cnf(149280192,plain,(q2(A,B,B)|~k0(B)|~p1(A,A,A)),inference(rewrite,[status(thm)],[rule_177]),[]).
% 
% fof(rule_085,plain,(p1(A,A,A)|~p0(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN180-1.tptp',unknown),[]).
% 
% cnf(148201168,plain,(p1(A,A,A)|~p0(B,A)),inference(rewrite,[status(thm)],[rule_085]),[]).
% 
% fof(axiom_14,plain,(p0(b,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN180-1.tptp',unknown),[]).
% 
% cnf(147139520,plain,(p0(b,A)),inference(rewrite,[status(thm)],[axiom_14]),[]).
% 
% cnf(161461312,plain,(p1(A,A,A)),inference(resolution,[status(thm)],[148201168,147139520]),[]).
% 
% cnf(163790312,plain,(q2(A,B,B)|~k0(B)),inference(resolution,[status(thm)],[149280192,161461312]),[]).
% 
% fof(rule_187,plain,(q2(A,B,A)|~r1(B)|~m0(C,D,A)|~k0(B)|~q2(B,B,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN180-1.tptp',unknown),[]).
% 
% cnf(149437320,plain,(q2(A,B,A)|~r1(B)|~m0(C,D,A)|~k0(B)|~q2(B,B,B)),inference(rewrite,[status(thm)],[rule_187]),[]).
% 
% fof(rule_097,plain,(q1(A,A,A)|~s0(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN180-1.tptp',unknown),[]).
% 
% cnf(148323664,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/SYN180-1.tptp',unknown),[]).
% 
% cnf(147051472,plain,(s0(d)),inference(rewrite,[status(thm)],[axiom_1]),[]).
% 
% cnf(149471144,plain,(q1(d,d,d)),inference(resolution,[status(thm)],[148323664,147051472]),[]).
% 
% fof(rule_124,plain,(r1(A)|~q0(A,B)|~s0(d)|~q1(d,B,d)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN180-1.tptp',unknown),[]).
% 
% cnf(148554576,plain,(r1(A)|~q0(A,B)|~q1(d,B,d)),inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_124,147051472]),[]).
% 
% fof(axiom_17,plain,(q0(A,d)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN180-1.tptp',unknown),[]).
% 
% cnf(147154808,plain,(q0(A,d)),inference(rewrite,[status(thm)],[axiom_17]),[]).
% 
% cnf(161752392,plain,(r1(A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[149471144,148554576,147154808]),[]).
% 
% cnf(161978728,plain,(q2(A,B,A)|~m0(C,D,A)|~k0(B)|~q2(B,B,B)),inference(resolution,[status(thm)],[149437320,161752392]),[]).
% 
% fof(axiom_4,plain,(m0(e,d,a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN180-1.tptp',unknown),[]).
% 
% cnf(147081104,plain,(m0(e,d,a)),inference(rewrite,[status(thm)],[axiom_4]),[]).
% 
% cnf(153803397,plain,(q2(a,A,a)|~k0(A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[163790312,161978728,147081104]),[]).
% 
% fof(axiom_28,plain,(k0(e)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN180-1.tptp',unknown),[]).
% 
% cnf(147205080,plain,(k0(e)),inference(rewrite,[status(thm)],[axiom_28]),[]).
% 
% cnf(153804848,plain,(q2(a,e,a)),inference(resolution,[status(thm)],[153803397,147205080]),[]).
% 
% fof(rule_295,plain,(q4(A,B)|~k3(C,C,A)|~q2(D,B,A)|~m3(D,E,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN180-1.tptp',unknown),[]).
% 
% cnf(150920080,plain,(q4(A,B)|~k3(C,C,A)|~q2(D,B,A)|~m3(D,E,D)),inference(rewrite,[status(thm)],[rule_295]),[]).
% 
% fof(prove_this,plain,(~q4(a,e)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN180-1.tptp',unknown),[]).
% 
% cnf(151435720,plain,(~q4(a,e)),inference(rewrite,[status(thm)],[prove_this]),[]).
% 
% cnf(163366032,plain,(~k3(A,A,a)|~q2(B,e,a)|~m3(B,C,B)),inference(resolution,[status(thm)],[150920080,151435720]),[]).
% 
% fof(rule_236,plain,(m3(A,A,A)|~n2(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN180-1.tptp',unknown),[]).
% 
% cnf(150111408,plain,(m3(A,A,A)|~n2(A)),inference(rewrite,[status(thm)],[rule_236]),[]).
% 
% fof(rule_137,plain,(n2(A)|~p1(B,C,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN180-1.tptp',unknown),[]).
% 
% cnf(148742472,plain,(n2(A)|~p1(B,C,A)),inference(rewrite,[status(thm)],[rule_137]),[]).
% 
% fof(rule_075,plain,(p1(a,a,a)|~p0(b,a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN180-1.tptp',unknown),[]).
% 
% cnf(148072168,plain,(p1(a,a,a)),inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_075,147139520]),[]).
% 
% cnf(163147040,plain,(n2(a)),inference(resolution,[status(thm)],[148742472,148072168]),[]).
% 
% cnf(163255896,plain,(m3(a,a,a)),inference(resolution,[status(thm)],[150111408,163147040]),[]).
% 
% cnf(184740989,plain,(~k3(A,A,a)),inference(forward_subsumption_resolution__resolution,[status(thm)],[153804848,163366032,163255896]),[]).
% 
% fof(rule_204,plain,(k3(a,a,a)|~r2(a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN180-1.tptp',unknown),[]).
% 
% cnf(149692056,plain,(k3(a,a,a)|~r2(a)),inference(rewrite,[status(thm)],[rule_204]),[]).
% 
% fof(rule_188,plain,(r2(A)|~r1(A)|~l0(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN180-1.tptp',unknown),[]).
% 
% cnf(149451248,plain,(r2(A)|~r1(A)|~l0(A)),inference(rewrite,[status(thm)],[rule_188]),[]).
% 
% cnf(161894328,plain,(r2(A)|~l0(A)),inference(resolution,[status(thm)],[149451248,161752392]),[]).
% 
% fof(axiom_20,plain,(l0(a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN180-1.tptp',unknown),[]).
% 
% cnf(147166648,plain,(l0(a)),inference(rewrite,[status(thm)],[axiom_20]),[]).
% 
% cnf(161904776,plain,(r2(a)),inference(resolution,[status(thm)],[161894328,147166648]),[]).
% 
% cnf(162012328,plain,(k3(a,a,a)),inference(resolution,[status(thm)],[149692056,161904776]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[184740989,162012328]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------