TSTP Solution File: SYN711-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN711-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n017.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 23:57:02 EDT 2022

% Result   : Unsatisfiable 0.20s 0.42s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   32
% Syntax   : Number of formulae    :   52 (  11 unt;  13 typ;   0 def)
%            Number of atoms       :  175 (   0 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  238 ( 111   ~; 107   |;   0   &)
%                                         (  20 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :   11 (   4 avg)
%            Number of FOOLs       :    9 (   9 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   13 (  10   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   3 con; 0-2 aty)
%            Number of variables   :   94 (  87   !;   0   ?;  94   :)

% Comments : 
%------------------------------------------------------------------------------
tff(p42_type,type,
    p42: ( $i * $i ) > $o ).

tff(f13_type,type,
    f13: $i > $i ).

tff(f14_type,type,
    f14: ( $i * $i ) > $i ).

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

tff(f15_type,type,
    f15: $i > $i ).

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

tff(c49_type,type,
    c49: $i ).

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

tff(f16_type,type,
    f16: $i > $i ).

tff(f7_type,type,
    f7: $i > $i ).

tff(c46_type,type,
    c46: $i ).

tff(p41_type,type,
    p41: ( $i * $i ) > $o ).

tff(c62_type,type,
    c62: $i ).

tff(1,plain,
    ( p41(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49)))))))))))
  <=> p41(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,axiom,
    p41(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p41_80) ).

tff(3,plain,
    p41(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))),
    inference(modus_ponens,[status(thm)],[2,1]) ).

tff(4,plain,
    ^ [X73: $i,X74: $i] :
      refl(
        ( ( ~ p41(X73,X74)
          | p42(X73,X74) )
      <=> ( ~ p41(X73,X74)
          | p42(X73,X74) ) )),
    inference(bind,[status(th)],]) ).

tff(5,plain,
    ( ! [X73: $i,X74: $i] :
        ( ~ p41(X73,X74)
        | p42(X73,X74) )
  <=> ! [X73: $i,X74: $i] :
        ( ~ p41(X73,X74)
        | p42(X73,X74) ) ),
    inference(quant_intro,[status(thm)],[4]) ).

tff(6,plain,
    ( ! [X73: $i,X74: $i] :
        ( ~ p41(X73,X74)
        | p42(X73,X74) )
  <=> ! [X73: $i,X74: $i] :
        ( ~ p41(X73,X74)
        | p42(X73,X74) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(7,plain,
    ^ [X73: $i,X74: $i] :
      rewrite(
        ( ( p42(X73,X74)
          | ~ p41(X73,X74) )
      <=> ( ~ p41(X73,X74)
          | p42(X73,X74) ) )),
    inference(bind,[status(th)],]) ).

tff(8,plain,
    ( ! [X73: $i,X74: $i] :
        ( p42(X73,X74)
        | ~ p41(X73,X74) )
  <=> ! [X73: $i,X74: $i] :
        ( ~ p41(X73,X74)
        | p42(X73,X74) ) ),
    inference(quant_intro,[status(thm)],[7]) ).

tff(9,axiom,
    ! [X73: $i,X74: $i] :
      ( p42(X73,X74)
      | ~ p41(X73,X74) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p42_26) ).

tff(10,plain,
    ! [X73: $i,X74: $i] :
      ( ~ p41(X73,X74)
      | p42(X73,X74) ),
    inference(modus_ponens,[status(thm)],[9,8]) ).

tff(11,plain,
    ! [X73: $i,X74: $i] :
      ( ~ p41(X73,X74)
      | p42(X73,X74) ),
    inference(modus_ponens,[status(thm)],[10,6]) ).

tff(12,plain,
    ! [X73: $i,X74: $i] :
      ( ~ p41(X73,X74)
      | p42(X73,X74) ),
    inference(skolemize,[status(sab)],[11]) ).

tff(13,plain,
    ! [X73: $i,X74: $i] :
      ( ~ p41(X73,X74)
      | p42(X73,X74) ),
    inference(modus_ponens,[status(thm)],[12,5]) ).

tff(14,plain,
    ( ( ~ ! [X73: $i,X74: $i] :
            ( ~ p41(X73,X74)
            | p42(X73,X74) )
      | ~ p41(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49)))))))))))
      | p42(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))) )
  <=> ( ~ ! [X73: $i,X74: $i] :
            ( ~ p41(X73,X74)
            | p42(X73,X74) )
      | ~ p41(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49)))))))))))
      | p42(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(15,plain,
    ( ~ ! [X73: $i,X74: $i] :
          ( ~ p41(X73,X74)
          | p42(X73,X74) )
    | ~ p41(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49)))))))))))
    | p42(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(16,plain,
    ( ~ ! [X73: $i,X74: $i] :
          ( ~ p41(X73,X74)
          | p42(X73,X74) )
    | ~ p41(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49)))))))))))
    | p42(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))) ),
    inference(modus_ponens,[status(thm)],[15,14]) ).

tff(17,plain,
    p42(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))),
    inference(unit_resolution,[status(thm)],[16,13,3]) ).

tff(18,plain,
    ( ~ p42(f16(c62),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49)))))))))))
  <=> ~ p42(f16(c62),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))) ),
    inference(rewrite,[status(thm)],]) ).

tff(19,axiom,
    ~ p42(f16(c62),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p42_78) ).

tff(20,plain,
    ~ p42(f16(c62),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))),
    inference(modus_ponens,[status(thm)],[19,18]) ).

tff(21,plain,
    ( ! [X76: $i,X75: $i,X77: $i] :
        ( ~ p42(X77,X76)
        | ~ p42(X75,X77)
        | p42(X75,X76) )
  <=> ! [X76: $i,X75: $i,X77: $i] :
        ( ~ p42(X77,X76)
        | ~ p42(X75,X77)
        | p42(X75,X76) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(22,plain,
    ( ! [X76: $i,X75: $i,X77: $i] :
        ( ~ p42(X77,X76)
        | ~ p42(X75,X77)
        | p42(X75,X76) )
  <=> ! [X76: $i,X75: $i,X77: $i] :
        ( ~ p42(X77,X76)
        | ~ p42(X75,X77)
        | p42(X75,X76) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(23,plain,
    ^ [X76: $i,X75: $i,X77: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( p42(X75,X76)
              | ~ p42(X75,X77) )
          <=> ( ~ p42(X75,X77)
              | p42(X75,X76) ) )),
          ( ( p42(X75,X76)
            | ~ p42(X75,X77)
            | ~ p42(X77,X76) )
        <=> ( ~ p42(X75,X77)
            | p42(X75,X76)
            | ~ p42(X77,X76) ) )),
        rewrite(
          ( ( ~ p42(X75,X77)
            | p42(X75,X76)
            | ~ p42(X77,X76) )
        <=> ( ~ p42(X77,X76)
            | ~ p42(X75,X77)
            | p42(X75,X76) ) )),
        ( ( p42(X75,X76)
          | ~ p42(X75,X77)
          | ~ p42(X77,X76) )
      <=> ( ~ p42(X77,X76)
          | ~ p42(X75,X77)
          | p42(X75,X76) ) )),
    inference(bind,[status(th)],]) ).

tff(24,plain,
    ( ! [X76: $i,X75: $i,X77: $i] :
        ( p42(X75,X76)
        | ~ p42(X75,X77)
        | ~ p42(X77,X76) )
  <=> ! [X76: $i,X75: $i,X77: $i] :
        ( ~ p42(X77,X76)
        | ~ p42(X75,X77)
        | p42(X75,X76) ) ),
    inference(quant_intro,[status(thm)],[23]) ).

tff(25,axiom,
    ! [X76: $i,X75: $i,X77: $i] :
      ( p42(X75,X76)
      | ~ p42(X75,X77)
      | ~ p42(X77,X76) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p42_47) ).

tff(26,plain,
    ! [X76: $i,X75: $i,X77: $i] :
      ( ~ p42(X77,X76)
      | ~ p42(X75,X77)
      | p42(X75,X76) ),
    inference(modus_ponens,[status(thm)],[25,24]) ).

tff(27,plain,
    ! [X76: $i,X75: $i,X77: $i] :
      ( ~ p42(X77,X76)
      | ~ p42(X75,X77)
      | p42(X75,X76) ),
    inference(modus_ponens,[status(thm)],[26,22]) ).

tff(28,plain,
    ! [X76: $i,X75: $i,X77: $i] :
      ( ~ p42(X77,X76)
      | ~ p42(X75,X77)
      | p42(X75,X76) ),
    inference(skolemize,[status(sab)],[27]) ).

tff(29,plain,
    ! [X76: $i,X75: $i,X77: $i] :
      ( ~ p42(X77,X76)
      | ~ p42(X75,X77)
      | p42(X75,X76) ),
    inference(modus_ponens,[status(thm)],[28,21]) ).

tff(30,plain,
    ( p42(f16(c62),f16(f7(c46)))
  <=> p42(f16(c62),f16(f7(c46))) ),
    inference(rewrite,[status(thm)],]) ).

tff(31,axiom,
    p42(f16(c62),f16(f7(c46))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p42_25) ).

tff(32,plain,
    p42(f16(c62),f16(f7(c46))),
    inference(modus_ponens,[status(thm)],[31,30]) ).

tff(33,plain,
    ( ( ~ ! [X76: $i,X75: $i,X77: $i] :
            ( ~ p42(X77,X76)
            | ~ p42(X75,X77)
            | p42(X75,X76) )
      | p42(f16(c62),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49)))))))))))
      | ~ p42(f16(c62),f16(f7(c46)))
      | ~ p42(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))) )
  <=> ( ~ ! [X76: $i,X75: $i,X77: $i] :
            ( ~ p42(X77,X76)
            | ~ p42(X75,X77)
            | p42(X75,X76) )
      | p42(f16(c62),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49)))))))))))
      | ~ p42(f16(c62),f16(f7(c46)))
      | ~ p42(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(34,plain,
    ( ( ~ p42(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49)))))))))))
      | ~ p42(f16(c62),f16(f7(c46)))
      | p42(f16(c62),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))) )
  <=> ( p42(f16(c62),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49)))))))))))
      | ~ p42(f16(c62),f16(f7(c46)))
      | ~ p42(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(35,plain,
    ( ( ~ ! [X76: $i,X75: $i,X77: $i] :
            ( ~ p42(X77,X76)
            | ~ p42(X75,X77)
            | p42(X75,X76) )
      | ~ p42(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49)))))))))))
      | ~ p42(f16(c62),f16(f7(c46)))
      | p42(f16(c62),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))) )
  <=> ( ~ ! [X76: $i,X75: $i,X77: $i] :
            ( ~ p42(X77,X76)
            | ~ p42(X75,X77)
            | p42(X75,X76) )
      | p42(f16(c62),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49)))))))))))
      | ~ p42(f16(c62),f16(f7(c46)))
      | ~ p42(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))) ) ),
    inference(monotonicity,[status(thm)],[34]) ).

tff(36,plain,
    ( ( ~ ! [X76: $i,X75: $i,X77: $i] :
            ( ~ p42(X77,X76)
            | ~ p42(X75,X77)
            | p42(X75,X76) )
      | ~ p42(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49)))))))))))
      | ~ p42(f16(c62),f16(f7(c46)))
      | p42(f16(c62),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))) )
  <=> ( ~ ! [X76: $i,X75: $i,X77: $i] :
            ( ~ p42(X77,X76)
            | ~ p42(X75,X77)
            | p42(X75,X76) )
      | p42(f16(c62),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49)))))))))))
      | ~ p42(f16(c62),f16(f7(c46)))
      | ~ p42(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))) ) ),
    inference(transitivity,[status(thm)],[35,33]) ).

tff(37,plain,
    ( ~ ! [X76: $i,X75: $i,X77: $i] :
          ( ~ p42(X77,X76)
          | ~ p42(X75,X77)
          | p42(X75,X76) )
    | ~ p42(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49)))))))))))
    | ~ p42(f16(c62),f16(f7(c46)))
    | p42(f16(c62),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(38,plain,
    ( ~ ! [X76: $i,X75: $i,X77: $i] :
          ( ~ p42(X77,X76)
          | ~ p42(X75,X77)
          | p42(X75,X76) )
    | p42(f16(c62),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49)))))))))))
    | ~ p42(f16(c62),f16(f7(c46)))
    | ~ p42(f16(f7(c46)),f13(f14(f10(f11(f15(f12(c49)))),f11(f15(f15(f15(f15(f12(f15(f12(c49))))))))))) ),
    inference(modus_ponens,[status(thm)],[37,36]) ).

tff(39,plain,
    $false,
    inference(unit_resolution,[status(thm)],[38,32,29,20,17]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SYN711-1 : TPTP v8.1.0. Released v2.5.0.
% 0.04/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n017.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 06:05:40 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.
% 0.20/0.42  % SZS status Unsatisfiable
% 0.20/0.42  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------