TSTP Solution File: SYN589-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN589-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n008.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Sep 29 23:56:32 EDT 2022

% Result   : Unsatisfiable 0.12s 0.39s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   30
% Syntax   : Number of formulae    :   41 (   9 unt;  18 typ;   0 def)
%            Number of atoms       :  103 (   0 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  136 (  64   ~;  60   |;   0   &)
%                                         (  12 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    9 (   3 avg)
%            Number of FOOLs       :    8 (   8 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   13 (   9   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :   17 (  17 usr;   9 con; 0-2 aty)
%            Number of variables   :   51 (  45   !;   0   ?;  51   :)

% Comments : 
%------------------------------------------------------------------------------
tff(p7_type,type,
    p7: ( $i * $i ) > $o ).

tff(f8_type,type,
    f8: ( $i * $i ) > $i ).

tff(f9_type,type,
    f9: ( $i * $i ) > $i ).

tff(f10_type,type,
    f10: ( $i * $i ) > $i ).

tff(c22_type,type,
    c22: $i ).

tff(f11_type,type,
    f11: $i > $i ).

tff(f3_type,type,
    f3: $i > $i ).

tff(f4_type,type,
    f4: $i > $i ).

tff(f5_type,type,
    f5: $i > $i ).

tff(c17_type,type,
    c17: $i ).

tff(c24_type,type,
    c24: $i ).

tff(c25_type,type,
    c25: $i ).

tff(c23_type,type,
    c23: $i ).

tff(f12_type,type,
    f12: $i > $i ).

tff(c19_type,type,
    c19: $i ).

tff(c21_type,type,
    c21: $i ).

tff(c18_type,type,
    c18: $i ).

tff(c20_type,type,
    c20: $i ).

tff(1,plain,
    ( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22)))))
  <=> ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22))))) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,axiom,
    ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p7_26) ).

tff(3,plain,
    ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22))))),
    inference(modus_ponens,[status(thm)],[2,1]) ).

tff(4,plain,
    ( p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22)))))
  <=> p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22))))) ),
    inference(rewrite,[status(thm)],]) ).

tff(5,axiom,
    p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7_25) ).

tff(6,plain,
    p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22))))),
    inference(modus_ponens,[status(thm)],[5,4]) ).

tff(7,plain,
    ( p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22)))))
  <=> p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22))))) ),
    inference(rewrite,[status(thm)],]) ).

tff(8,axiom,
    p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7_24) ).

tff(9,plain,
    p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22))))),
    inference(modus_ponens,[status(thm)],[8,7]) ).

tff(10,plain,
    ^ [X25: $i,X27: $i,X26: $i] :
      refl(
        ( ( p7(X26,X27)
          | ~ p7(X25,X27)
          | ~ p7(X25,X26) )
      <=> ( p7(X26,X27)
          | ~ p7(X25,X27)
          | ~ p7(X25,X26) ) )),
    inference(bind,[status(th)],]) ).

tff(11,plain,
    ( ! [X25: $i,X27: $i,X26: $i] :
        ( p7(X26,X27)
        | ~ p7(X25,X27)
        | ~ p7(X25,X26) )
  <=> ! [X25: $i,X27: $i,X26: $i] :
        ( p7(X26,X27)
        | ~ p7(X25,X27)
        | ~ p7(X25,X26) ) ),
    inference(quant_intro,[status(thm)],[10]) ).

tff(12,plain,
    ( ! [X25: $i,X27: $i,X26: $i] :
        ( p7(X26,X27)
        | ~ p7(X25,X27)
        | ~ p7(X25,X26) )
  <=> ! [X25: $i,X27: $i,X26: $i] :
        ( p7(X26,X27)
        | ~ p7(X25,X27)
        | ~ p7(X25,X26) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(13,plain,
    ^ [X25: $i,X27: $i,X26: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( p7(X26,X27)
              | ~ p7(X25,X26) )
          <=> ( p7(X26,X27)
              | ~ p7(X25,X26) ) )),
          ( ( p7(X26,X27)
            | ~ p7(X25,X26)
            | ~ p7(X25,X27) )
        <=> ( p7(X26,X27)
            | ~ p7(X25,X26)
            | ~ p7(X25,X27) ) )),
        rewrite(
          ( ( p7(X26,X27)
            | ~ p7(X25,X26)
            | ~ p7(X25,X27) )
        <=> ( p7(X26,X27)
            | ~ p7(X25,X27)
            | ~ p7(X25,X26) ) )),
        ( ( p7(X26,X27)
          | ~ p7(X25,X26)
          | ~ p7(X25,X27) )
      <=> ( p7(X26,X27)
          | ~ p7(X25,X27)
          | ~ p7(X25,X26) ) )),
    inference(bind,[status(th)],]) ).

tff(14,plain,
    ( ! [X25: $i,X27: $i,X26: $i] :
        ( p7(X26,X27)
        | ~ p7(X25,X26)
        | ~ p7(X25,X27) )
  <=> ! [X25: $i,X27: $i,X26: $i] :
        ( p7(X26,X27)
        | ~ p7(X25,X27)
        | ~ p7(X25,X26) ) ),
    inference(quant_intro,[status(thm)],[13]) ).

tff(15,axiom,
    ! [X25: $i,X27: $i,X26: $i] :
      ( p7(X26,X27)
      | ~ p7(X25,X26)
      | ~ p7(X25,X27) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7_14) ).

tff(16,plain,
    ! [X25: $i,X27: $i,X26: $i] :
      ( p7(X26,X27)
      | ~ p7(X25,X27)
      | ~ p7(X25,X26) ),
    inference(modus_ponens,[status(thm)],[15,14]) ).

tff(17,plain,
    ! [X25: $i,X27: $i,X26: $i] :
      ( p7(X26,X27)
      | ~ p7(X25,X27)
      | ~ p7(X25,X26) ),
    inference(modus_ponens,[status(thm)],[16,12]) ).

tff(18,plain,
    ! [X25: $i,X27: $i,X26: $i] :
      ( p7(X26,X27)
      | ~ p7(X25,X27)
      | ~ p7(X25,X26) ),
    inference(skolemize,[status(sab)],[17]) ).

tff(19,plain,
    ! [X25: $i,X27: $i,X26: $i] :
      ( p7(X26,X27)
      | ~ p7(X25,X27)
      | ~ p7(X25,X26) ),
    inference(modus_ponens,[status(thm)],[18,11]) ).

tff(20,plain,
    ( ( ~ ! [X25: $i,X27: $i,X26: $i] :
            ( p7(X26,X27)
            | ~ p7(X25,X27)
            | ~ p7(X25,X26) )
      | p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22)))))
      | ~ p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22)))))
      | ~ p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22))))) )
  <=> ( ~ ! [X25: $i,X27: $i,X26: $i] :
            ( p7(X26,X27)
            | ~ p7(X25,X27)
            | ~ p7(X25,X26) )
      | p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22)))))
      | ~ p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22)))))
      | ~ p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22))))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(21,plain,
    ( ~ ! [X25: $i,X27: $i,X26: $i] :
          ( p7(X26,X27)
          | ~ p7(X25,X27)
          | ~ p7(X25,X26) )
    | p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22)))))
    | ~ p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22)))))
    | ~ p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22))))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(22,plain,
    ( ~ ! [X25: $i,X27: $i,X26: $i] :
          ( p7(X26,X27)
          | ~ p7(X25,X27)
          | ~ p7(X25,X26) )
    | p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22)))))
    | ~ p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c23),f8(f10(f11(f3(f4(f5(c17)))),c25),f9(f11(c24),f10(f11(f3(f4(f5(c17)))),c22)))))
    | ~ p7(c20,f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),c21),f9(f11(c19),f10(f11(f3(f4(f5(c17)))),c22))))) ),
    inference(modus_ponens,[status(thm)],[21,20]) ).

tff(23,plain,
    $false,
    inference(unit_resolution,[status(thm)],[22,19,9,6,3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SYN589-1 : TPTP v8.1.0. Released v2.5.0.
% 0.06/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34  % Computer : n008.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Mon Sep  5 05:57:55 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34  Usage: tptp [options] [-file:]file
% 0.12/0.34    -h, -?       prints this message.
% 0.12/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.34    -m, -model   generate model.
% 0.12/0.34    -p, -proof   generate proof.
% 0.12/0.34    -c, -core    generate unsat core of named formulas.
% 0.12/0.34    -st, -statistics display statistics.
% 0.12/0.34    -t:timeout   set timeout (in second).
% 0.12/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34    -<param>:<value> configuration parameter and value.
% 0.12/0.34    -o:<output-file> file to place output in.
% 0.12/0.39  % SZS status Unsatisfiable
% 0.12/0.39  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------