TSTP Solution File: SYN155-1 by Faust---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SYN155-1 : 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 17:01:05 EDT 2009

% Result   : Unsatisfiable 1.5s
% Output   : Refutation 1.5s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   52 (  28 unt;   0 def)
%            Number of atoms       :   88 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   79 (  43   ~;  36   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   16 (  15 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   5 con; 0-0 aty)
%            Number of variables   :   51 (  10 sgn  23   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(axiom_18,plain,
    p0(c,b),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),
    [] ).

cnf(159555984,plain,
    p0(c,b),
    inference(rewrite,[status(thm)],[axiom_18]),
    [] ).

fof(rule_003,plain,
    ! [A,B,C,D] :
      ( l1(A,B)
      | ~ p0(C,A)
      | ~ r0(D)
      | ~ m0(B,A,C) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),
    [] ).

cnf(159804888,plain,
    ( l1(A,B)
    | ~ p0(C,A)
    | ~ r0(D)
    | ~ m0(B,A,C) ),
    inference(rewrite,[status(thm)],[rule_003]),
    [] ).

fof(axiom_9,plain,
    r0(b),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),
    [] ).

cnf(159620000,plain,
    r0(b),
    inference(rewrite,[status(thm)],[axiom_9]),
    [] ).

cnf(172480080,plain,
    ( l1(A,B)
    | ~ p0(C,A)
    | ~ m0(B,A,C) ),
    inference(resolution,[status(thm)],[159804888,159620000]),
    [] ).

fof(axiom_27,plain,
    m0(e,b,c),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),
    [] ).

cnf(159708984,plain,
    m0(e,b,c),
    inference(rewrite,[status(thm)],[axiom_27]),
    [] ).

cnf(200585952,plain,
    l1(b,e),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[159555984,172480080,159708984]),
    [] ).

fof(rule_255,plain,
    ! [A,B,C] :
      ( q3(A,B)
      | ~ q2(C,A,B)
      | ~ n0(C,A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),
    [] ).

cnf(162866160,plain,
    ( q3(A,B)
    | ~ q2(C,A,B)
    | ~ n0(C,A) ),
    inference(rewrite,[status(thm)],[rule_255]),
    [] ).

fof(axiom_30,plain,
    n0(e,e),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),
    [] ).

cnf(159728120,plain,
    n0(e,e),
    inference(rewrite,[status(thm)],[axiom_30]),
    [] ).

cnf(195274592,plain,
    ( q3(e,A)
    | ~ q2(e,e,A) ),
    inference(resolution,[status(thm)],[162866160,159728120]),
    [] ).

fof(rule_274,plain,
    ( k4(c)
    | ~ n0(c,d)
    | ~ q3(e,b)
    | ~ n3(e) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),
    [] ).

fof(axiom_34,plain,
    n0(c,d),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),
    [] ).

cnf(159742984,plain,
    n0(c,d),
    inference(rewrite,[status(thm)],[axiom_34]),
    [] ).

cnf(163155912,plain,
    ( k4(c)
    | ~ q3(e,b)
    | ~ n3(e) ),
    inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_274,159742984]),
    [] ).

fof(rule_236,plain,
    ! [A] :
      ( m3(A,A,A)
      | ~ n2(A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),
    [] ).

cnf(162619832,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/SYN155-1.tptp',unknown),
    [] ).

cnf(161250896,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/SYN155-1.tptp',unknown),
    [] ).

fof(axiom_14,plain,
    ! [A] : p0(b,A),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),
    [] ).

cnf(159647944,plain,
    p0(b,A),
    inference(rewrite,[status(thm)],[axiom_14]),
    [] ).

cnf(160580592,plain,
    p1(a,a,a),
    inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_075,159647944]),
    [] ).

cnf(175840632,plain,
    n2(a),
    inference(resolution,[status(thm)],[161250896,160580592]),
    [] ).

cnf(175892224,plain,
    m3(a,a,a),
    inference(resolution,[status(thm)],[162619832,175840632]),
    [] ).

fof(rule_284,plain,
    ! [A,B] :
      ( n4(A,A)
      | ~ k4(B)
      | ~ m3(A,A,A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),
    [] ).

cnf(163280152,plain,
    ( n4(A,A)
    | ~ k4(B)
    | ~ m3(A,A,A) ),
    inference(rewrite,[status(thm)],[rule_284]),
    [] ).

fof(prove_this,plain,
    ! [A] : ~ n4(A,a),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),
    [] ).

cnf(163944296,plain,
    ~ n4(A,a),
    inference(rewrite,[status(thm)],[prove_this]),
    [] ).

cnf(176055488,plain,
    ~ k4(A),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[175892224,163280152,163944296]),
    [] ).

cnf(176088200,plain,
    ( ~ q3(e,b)
    | ~ n3(e) ),
    inference(resolution,[status(thm)],[163155912,176055488]),
    [] ).

fof(rule_240,plain,
    ! [A,B,C] :
      ( n3(A)
      | ~ p2(B,C,A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),
    [] ).

cnf(162667464,plain,
    ( n3(A)
    | ~ p2(B,C,A) ),
    inference(rewrite,[status(thm)],[rule_240]),
    [] ).

fof(rule_159,plain,
    ! [A] :
      ( p2(A,A,A)
      | ~ k1(A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),
    [] ).

cnf(161560000,plain,
    ( p2(A,A,A)
    | ~ k1(A) ),
    inference(rewrite,[status(thm)],[rule_159]),
    [] ).

fof(rule_001,plain,
    ! [A,B] :
      ( k1(A)
      | ~ n0(B,A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),
    [] ).

cnf(159768208,plain,
    ( k1(A)
    | ~ n0(B,A) ),
    inference(rewrite,[status(thm)],[rule_001]),
    [] ).

fof(axiom_3,plain,
    n0(d,e),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),
    [] ).

cnf(159578368,plain,
    n0(d,e),
    inference(rewrite,[status(thm)],[axiom_3]),
    [] ).

cnf(173110712,plain,
    k1(e),
    inference(resolution,[status(thm)],[159768208,159578368]),
    [] ).

cnf(173235960,plain,
    p2(e,e,e),
    inference(resolution,[status(thm)],[161560000,173110712]),
    [] ).

cnf(176280560,plain,
    n3(e),
    inference(resolution,[status(thm)],[162667464,173235960]),
    [] ).

cnf(178753368,plain,
    ~ q3(e,b),
    inference(resolution,[status(thm)],[176088200,176280560]),
    [] ).

cnf(196232016,plain,
    ~ q2(e,e,b),
    inference(resolution,[status(thm)],[195274592,178753368]),
    [] ).

fof(rule_186,plain,
    ! [A,B] :
      ( q2(A,A,B)
      | ~ l1(B,A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),
    [] ).

cnf(161925448,plain,
    ( q2(A,A,B)
    | ~ l1(B,A) ),
    inference(rewrite,[status(thm)],[rule_186]),
    [] ).

cnf(196313664,plain,
    ~ l1(b,e),
    inference(resolution,[status(thm)],[196232016,161925448]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[200585952,196313664]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 2 seconds
% START OF PROOF SEQUENCE
% fof(axiom_18,plain,(p0(c,b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),[]).
% 
% cnf(159555984,plain,(p0(c,b)),inference(rewrite,[status(thm)],[axiom_18]),[]).
% 
% fof(rule_003,plain,(l1(A,B)|~p0(C,A)|~r0(D)|~m0(B,A,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),[]).
% 
% cnf(159804888,plain,(l1(A,B)|~p0(C,A)|~r0(D)|~m0(B,A,C)),inference(rewrite,[status(thm)],[rule_003]),[]).
% 
% fof(axiom_9,plain,(r0(b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),[]).
% 
% cnf(159620000,plain,(r0(b)),inference(rewrite,[status(thm)],[axiom_9]),[]).
% 
% cnf(172480080,plain,(l1(A,B)|~p0(C,A)|~m0(B,A,C)),inference(resolution,[status(thm)],[159804888,159620000]),[]).
% 
% fof(axiom_27,plain,(m0(e,b,c)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),[]).
% 
% cnf(159708984,plain,(m0(e,b,c)),inference(rewrite,[status(thm)],[axiom_27]),[]).
% 
% cnf(200585952,plain,(l1(b,e)),inference(forward_subsumption_resolution__resolution,[status(thm)],[159555984,172480080,159708984]),[]).
% 
% fof(rule_255,plain,(q3(A,B)|~q2(C,A,B)|~n0(C,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),[]).
% 
% cnf(162866160,plain,(q3(A,B)|~q2(C,A,B)|~n0(C,A)),inference(rewrite,[status(thm)],[rule_255]),[]).
% 
% fof(axiom_30,plain,(n0(e,e)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),[]).
% 
% cnf(159728120,plain,(n0(e,e)),inference(rewrite,[status(thm)],[axiom_30]),[]).
% 
% cnf(195274592,plain,(q3(e,A)|~q2(e,e,A)),inference(resolution,[status(thm)],[162866160,159728120]),[]).
% 
% fof(rule_274,plain,(k4(c)|~n0(c,d)|~q3(e,b)|~n3(e)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),[]).
% 
% fof(axiom_34,plain,(n0(c,d)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),[]).
% 
% cnf(159742984,plain,(n0(c,d)),inference(rewrite,[status(thm)],[axiom_34]),[]).
% 
% cnf(163155912,plain,(k4(c)|~q3(e,b)|~n3(e)),inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_274,159742984]),[]).
% 
% fof(rule_236,plain,(m3(A,A,A)|~n2(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),[]).
% 
% cnf(162619832,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/SYN155-1.tptp',unknown),[]).
% 
% cnf(161250896,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/SYN155-1.tptp',unknown),[]).
% 
% fof(axiom_14,plain,(p0(b,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),[]).
% 
% cnf(159647944,plain,(p0(b,A)),inference(rewrite,[status(thm)],[axiom_14]),[]).
% 
% cnf(160580592,plain,(p1(a,a,a)),inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_075,159647944]),[]).
% 
% cnf(175840632,plain,(n2(a)),inference(resolution,[status(thm)],[161250896,160580592]),[]).
% 
% cnf(175892224,plain,(m3(a,a,a)),inference(resolution,[status(thm)],[162619832,175840632]),[]).
% 
% fof(rule_284,plain,(n4(A,A)|~k4(B)|~m3(A,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),[]).
% 
% cnf(163280152,plain,(n4(A,A)|~k4(B)|~m3(A,A,A)),inference(rewrite,[status(thm)],[rule_284]),[]).
% 
% fof(prove_this,plain,(~n4(A,a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),[]).
% 
% cnf(163944296,plain,(~n4(A,a)),inference(rewrite,[status(thm)],[prove_this]),[]).
% 
% cnf(176055488,plain,(~k4(A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[175892224,163280152,163944296]),[]).
% 
% cnf(176088200,plain,(~q3(e,b)|~n3(e)),inference(resolution,[status(thm)],[163155912,176055488]),[]).
% 
% fof(rule_240,plain,(n3(A)|~p2(B,C,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),[]).
% 
% cnf(162667464,plain,(n3(A)|~p2(B,C,A)),inference(rewrite,[status(thm)],[rule_240]),[]).
% 
% fof(rule_159,plain,(p2(A,A,A)|~k1(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),[]).
% 
% cnf(161560000,plain,(p2(A,A,A)|~k1(A)),inference(rewrite,[status(thm)],[rule_159]),[]).
% 
% fof(rule_001,plain,(k1(A)|~n0(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),[]).
% 
% cnf(159768208,plain,(k1(A)|~n0(B,A)),inference(rewrite,[status(thm)],[rule_001]),[]).
% 
% fof(axiom_3,plain,(n0(d,e)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),[]).
% 
% cnf(159578368,plain,(n0(d,e)),inference(rewrite,[status(thm)],[axiom_3]),[]).
% 
% cnf(173110712,plain,(k1(e)),inference(resolution,[status(thm)],[159768208,159578368]),[]).
% 
% cnf(173235960,plain,(p2(e,e,e)),inference(resolution,[status(thm)],[161560000,173110712]),[]).
% 
% cnf(176280560,plain,(n3(e)),inference(resolution,[status(thm)],[162667464,173235960]),[]).
% 
% cnf(178753368,plain,(~q3(e,b)),inference(resolution,[status(thm)],[176088200,176280560]),[]).
% 
% cnf(196232016,plain,(~q2(e,e,b)),inference(resolution,[status(thm)],[195274592,178753368]),[]).
% 
% fof(rule_186,plain,(q2(A,A,B)|~l1(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),[]).
% 
% cnf(161925448,plain,(q2(A,A,B)|~l1(B,A)),inference(rewrite,[status(thm)],[rule_186]),[]).
% 
% cnf(196313664,plain,(~l1(b,e)),inference(resolution,[status(thm)],[196232016,161925448]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[200585952,196313664]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------