TSTP Solution File: SYN256-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN256-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n018.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 23:54:24 EDT 2022

% Result   : Unsatisfiable 0.20s 0.50s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   41 (  11 unt;   7 typ;   0 def)
%            Number of atoms       :  141 (   0 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  184 (  86   ~;  82   |;   0   &)
%                                         (  16 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :    9 (   9 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   4   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   8 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   90 (  81   !;   0   ?;  90   :)

% Comments : 
%------------------------------------------------------------------------------
tff(n2_type,type,
    n2: $i > $o ).

tff(c_type,type,
    c: $i ).

tff(p1_type,type,
    p1: ( $i * $i * $i ) > $o ).

tff(m0_type,type,
    m0: ( $i * $i * $i ) > $o ).

tff(l0_type,type,
    l0: $i > $o ).

tff(b_type,type,
    b: $i ).

tff(e_type,type,
    e: $i ).

tff(1,plain,
    ( ~ n2(c)
  <=> ~ n2(c) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,axiom,
    ~ n2(c),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).

tff(3,plain,
    ~ n2(c),
    inference(modus_ponens,[status(thm)],[2,1]) ).

tff(4,plain,
    ^ [B: $i,A: $i,C: $i] :
      refl(
        ( ( n2(A)
          | ~ p1(B,C,A) )
      <=> ( n2(A)
          | ~ p1(B,C,A) ) )),
    inference(bind,[status(th)],]) ).

tff(5,plain,
    ( ! [B: $i,A: $i,C: $i] :
        ( n2(A)
        | ~ p1(B,C,A) )
  <=> ! [B: $i,A: $i,C: $i] :
        ( n2(A)
        | ~ p1(B,C,A) ) ),
    inference(quant_intro,[status(thm)],[4]) ).

tff(6,plain,
    ( ! [B: $i,A: $i,C: $i] :
        ( n2(A)
        | ~ p1(B,C,A) )
  <=> ! [B: $i,A: $i,C: $i] :
        ( n2(A)
        | ~ p1(B,C,A) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(7,axiom,
    ! [B: $i,A: $i,C: $i] :
      ( n2(A)
      | ~ p1(B,C,A) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_137) ).

tff(8,plain,
    ! [B: $i,A: $i,C: $i] :
      ( n2(A)
      | ~ p1(B,C,A) ),
    inference(modus_ponens,[status(thm)],[7,6]) ).

tff(9,plain,
    ! [B: $i,A: $i,C: $i] :
      ( n2(A)
      | ~ p1(B,C,A) ),
    inference(skolemize,[status(sab)],[8]) ).

tff(10,plain,
    ! [B: $i,A: $i,C: $i] :
      ( n2(A)
      | ~ p1(B,C,A) ),
    inference(modus_ponens,[status(thm)],[9,5]) ).

tff(11,plain,
    ^ [I: $i,A: $i,J: $i] :
      refl(
        ( ( ~ l0(I)
          | ~ m0(J,A,I)
          | p1(I,I,I) )
      <=> ( ~ l0(I)
          | ~ m0(J,A,I)
          | p1(I,I,I) ) )),
    inference(bind,[status(th)],]) ).

tff(12,plain,
    ( ! [I: $i,A: $i,J: $i] :
        ( ~ l0(I)
        | ~ m0(J,A,I)
        | p1(I,I,I) )
  <=> ! [I: $i,A: $i,J: $i] :
        ( ~ l0(I)
        | ~ m0(J,A,I)
        | p1(I,I,I) ) ),
    inference(quant_intro,[status(thm)],[11]) ).

tff(13,plain,
    ( ! [I: $i,A: $i,J: $i] :
        ( ~ l0(I)
        | ~ m0(J,A,I)
        | p1(I,I,I) )
  <=> ! [I: $i,A: $i,J: $i] :
        ( ~ l0(I)
        | ~ m0(J,A,I)
        | p1(I,I,I) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(14,plain,
    ^ [I: $i,A: $i,J: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( p1(I,I,I)
              | ~ l0(I) )
          <=> ( ~ l0(I)
              | p1(I,I,I) ) )),
          ( ( p1(I,I,I)
            | ~ l0(I)
            | ~ m0(J,A,I) )
        <=> ( ~ l0(I)
            | p1(I,I,I)
            | ~ m0(J,A,I) ) )),
        rewrite(
          ( ( ~ l0(I)
            | p1(I,I,I)
            | ~ m0(J,A,I) )
        <=> ( ~ l0(I)
            | ~ m0(J,A,I)
            | p1(I,I,I) ) )),
        ( ( p1(I,I,I)
          | ~ l0(I)
          | ~ m0(J,A,I) )
      <=> ( ~ l0(I)
          | ~ m0(J,A,I)
          | p1(I,I,I) ) )),
    inference(bind,[status(th)],]) ).

tff(15,plain,
    ( ! [I: $i,A: $i,J: $i] :
        ( p1(I,I,I)
        | ~ l0(I)
        | ~ m0(J,A,I) )
  <=> ! [I: $i,A: $i,J: $i] :
        ( ~ l0(I)
        | ~ m0(J,A,I)
        | p1(I,I,I) ) ),
    inference(quant_intro,[status(thm)],[14]) ).

tff(16,axiom,
    ! [I: $i,A: $i,J: $i] :
      ( p1(I,I,I)
      | ~ l0(I)
      | ~ m0(J,A,I) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_086) ).

tff(17,plain,
    ! [I: $i,A: $i,J: $i] :
      ( ~ l0(I)
      | ~ m0(J,A,I)
      | p1(I,I,I) ),
    inference(modus_ponens,[status(thm)],[16,15]) ).

tff(18,plain,
    ! [I: $i,A: $i,J: $i] :
      ( ~ l0(I)
      | ~ m0(J,A,I)
      | p1(I,I,I) ),
    inference(modus_ponens,[status(thm)],[17,13]) ).

tff(19,plain,
    ! [I: $i,A: $i,J: $i] :
      ( ~ l0(I)
      | ~ m0(J,A,I)
      | p1(I,I,I) ),
    inference(skolemize,[status(sab)],[18]) ).

tff(20,plain,
    ! [I: $i,A: $i,J: $i] :
      ( ~ l0(I)
      | ~ m0(J,A,I)
      | p1(I,I,I) ),
    inference(modus_ponens,[status(thm)],[19,12]) ).

tff(21,plain,
    ( m0(e,b,c)
  <=> m0(e,b,c) ),
    inference(rewrite,[status(thm)],]) ).

tff(22,axiom,
    m0(e,b,c),
    file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_27) ).

tff(23,plain,
    m0(e,b,c),
    inference(modus_ponens,[status(thm)],[22,21]) ).

tff(24,plain,
    ( l0(c)
  <=> l0(c) ),
    inference(rewrite,[status(thm)],]) ).

tff(25,axiom,
    l0(c),
    file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_24) ).

tff(26,plain,
    l0(c),
    inference(modus_ponens,[status(thm)],[25,24]) ).

tff(27,plain,
    ( ( ~ ! [I: $i,A: $i,J: $i] :
            ( ~ l0(I)
            | ~ m0(J,A,I)
            | p1(I,I,I) )
      | ~ l0(c)
      | ~ m0(e,b,c)
      | p1(c,c,c) )
  <=> ( ~ ! [I: $i,A: $i,J: $i] :
            ( ~ l0(I)
            | ~ m0(J,A,I)
            | p1(I,I,I) )
      | ~ l0(c)
      | ~ m0(e,b,c)
      | p1(c,c,c) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(28,plain,
    ( ~ ! [I: $i,A: $i,J: $i] :
          ( ~ l0(I)
          | ~ m0(J,A,I)
          | p1(I,I,I) )
    | ~ l0(c)
    | ~ m0(e,b,c)
    | p1(c,c,c) ),
    inference(quant_inst,[status(thm)],]) ).

tff(29,plain,
    ( ~ ! [I: $i,A: $i,J: $i] :
          ( ~ l0(I)
          | ~ m0(J,A,I)
          | p1(I,I,I) )
    | ~ l0(c)
    | ~ m0(e,b,c)
    | p1(c,c,c) ),
    inference(modus_ponens,[status(thm)],[28,27]) ).

tff(30,plain,
    p1(c,c,c),
    inference(unit_resolution,[status(thm)],[29,26,23,20]) ).

tff(31,plain,
    ( ( ~ ! [B: $i,A: $i,C: $i] :
            ( n2(A)
            | ~ p1(B,C,A) )
      | n2(c)
      | ~ p1(c,c,c) )
  <=> ( ~ ! [B: $i,A: $i,C: $i] :
            ( n2(A)
            | ~ p1(B,C,A) )
      | n2(c)
      | ~ p1(c,c,c) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(32,plain,
    ( ~ ! [B: $i,A: $i,C: $i] :
          ( n2(A)
          | ~ p1(B,C,A) )
    | n2(c)
    | ~ p1(c,c,c) ),
    inference(quant_inst,[status(thm)],]) ).

tff(33,plain,
    ( ~ ! [B: $i,A: $i,C: $i] :
          ( n2(A)
          | ~ p1(B,C,A) )
    | n2(c)
    | ~ p1(c,c,c) ),
    inference(modus_ponens,[status(thm)],[32,31]) ).

tff(34,plain,
    $false,
    inference(unit_resolution,[status(thm)],[33,30,10,3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYN256-1 : TPTP v8.1.0. Released v1.1.0.
% 0.07/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n018.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Mon Sep  5 02:22:46 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35  Usage: tptp [options] [-file:]file
% 0.13/0.35    -h, -?       prints this message.
% 0.13/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.35    -m, -model   generate model.
% 0.13/0.35    -p, -proof   generate proof.
% 0.13/0.35    -c, -core    generate unsat core of named formulas.
% 0.13/0.35    -st, -statistics display statistics.
% 0.13/0.35    -t:timeout   set timeout (in second).
% 0.13/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35    -<param>:<value> configuration parameter and value.
% 0.13/0.35    -o:<output-file> file to place output in.
% 0.20/0.50  % SZS status Unsatisfiable
% 0.20/0.50  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------