TSTP Solution File: KRS156+1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : KRS156+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n003.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 : Sat Sep 17 17:45:00 EDT 2022

% Result   : Theorem 0.19s 0.45s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   47
% Syntax   : Number of formulae    :   91 (  16 unt;  11 typ;   0 def)
%            Number of atoms       :  397 (   0 equ)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  578 ( 267   ~;  98   |;  97   &)
%                                         ( 116 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :    6 (   6 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   13 (  12 usr;   1 prp; 0-1 aty)
%            Number of functors    :    1 (   1 usr;   1 con; 0-0 aty)
%            Number of variables   :   69 (  63   !;   0   ?;  69   :)

% Comments : 
%------------------------------------------------------------------------------
tff(cC138_type,type,
    cC138: $i > $o ).

tff(iV5475_type,type,
    iV5475: $i ).

tff(cC116_type,type,
    cC116: $i > $o ).

tff(cTOP_type,type,
    cTOP: $i > $o ).

tff(cC114xcomp_type,type,
    cC114xcomp: $i > $o ).

tff(cC140_type,type,
    cC140: $i > $o ).

tff(cTEST_type,type,
    cTEST: $i > $o ).

tff(cowlThing_type,type,
    cowlThing: $i > $o ).

tff(xsd_integer_type,type,
    xsd_integer: $i > $o ).

tff(xsd_string_type,type,
    xsd_string: $i > $o ).

tff(cowlNothing_type,type,
    cowlNothing: $i > $o ).

tff(1,plain,
    ^ [X: $i] :
      refl(
        ( ( cC116(X)
        <=> ~ ( ~ cC114xcomp(X)
              | ~ cTOP(X) ) )
      <=> ( cC116(X)
        <=> ~ ( ~ cC114xcomp(X)
              | ~ cTOP(X) ) ) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [X: $i] :
        ( cC116(X)
      <=> ~ ( ~ cC114xcomp(X)
            | ~ cTOP(X) ) )
  <=> ! [X: $i] :
        ( cC116(X)
      <=> ~ ( ~ cC114xcomp(X)
            | ~ cTOP(X) ) ) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ^ [X: $i] :
      rewrite(
        ( ( cC116(X)
        <=> ( cTOP(X)
            & cC114xcomp(X) ) )
      <=> ( cC116(X)
        <=> ~ ( ~ cC114xcomp(X)
              | ~ cTOP(X) ) ) )),
    inference(bind,[status(th)],]) ).

tff(4,plain,
    ( ! [X: $i] :
        ( cC116(X)
      <=> ( cTOP(X)
          & cC114xcomp(X) ) )
  <=> ! [X: $i] :
        ( cC116(X)
      <=> ~ ( ~ cC114xcomp(X)
            | ~ cTOP(X) ) ) ),
    inference(quant_intro,[status(thm)],[3]) ).

tff(5,plain,
    ( ! [X: $i] :
        ( cC116(X)
      <=> ( cTOP(X)
          & cC114xcomp(X) ) )
  <=> ! [X: $i] :
        ( cC116(X)
      <=> ( cTOP(X)
          & cC114xcomp(X) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(6,axiom,
    ! [X: $i] :
      ( cC116(X)
    <=> ( cTOP(X)
        & cC114xcomp(X) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_25) ).

tff(7,plain,
    ! [X: $i] :
      ( cC116(X)
    <=> ( cTOP(X)
        & cC114xcomp(X) ) ),
    inference(modus_ponens,[status(thm)],[6,5]) ).

tff(8,plain,
    ! [X: $i] :
      ( cC116(X)
    <=> ( cTOP(X)
        & cC114xcomp(X) ) ),
    inference(skolemize,[status(sab)],[7]) ).

tff(9,plain,
    ! [X: $i] :
      ( cC116(X)
    <=> ~ ( ~ cC114xcomp(X)
          | ~ cTOP(X) ) ),
    inference(modus_ponens,[status(thm)],[8,4]) ).

tff(10,plain,
    ! [X: $i] :
      ( cC116(X)
    <=> ~ ( ~ cC114xcomp(X)
          | ~ cTOP(X) ) ),
    inference(modus_ponens,[status(thm)],[9,2]) ).

tff(11,plain,
    ( ~ ! [X: $i] :
          ( cC116(X)
        <=> ~ ( ~ cC114xcomp(X)
              | ~ cTOP(X) ) )
    | ( cC116(iV5475)
    <=> ~ ( ~ cC114xcomp(iV5475)
          | ~ cTOP(iV5475) ) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(12,plain,
    ( cC116(iV5475)
  <=> ~ ( ~ cC114xcomp(iV5475)
        | ~ cTOP(iV5475) ) ),
    inference(unit_resolution,[status(thm)],[11,10]) ).

tff(13,plain,
    ( cC114xcomp(iV5475)
  <=> cC114xcomp(iV5475) ),
    inference(rewrite,[status(thm)],]) ).

tff(14,axiom,
    cC114xcomp(iV5475),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_130) ).

tff(15,plain,
    cC114xcomp(iV5475),
    inference(modus_ponens,[status(thm)],[14,13]) ).

tff(16,plain,
    ( cTOP(iV5475)
  <=> cTOP(iV5475) ),
    inference(rewrite,[status(thm)],]) ).

tff(17,axiom,
    cTOP(iV5475),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_128) ).

tff(18,plain,
    cTOP(iV5475),
    inference(modus_ponens,[status(thm)],[17,16]) ).

tff(19,plain,
    ( ~ ( ~ cC114xcomp(iV5475)
        | ~ cTOP(iV5475) )
    | ~ cC114xcomp(iV5475)
    | ~ cTOP(iV5475) ),
    inference(tautology,[status(thm)],]) ).

tff(20,plain,
    ~ ( ~ cC114xcomp(iV5475)
      | ~ cTOP(iV5475) ),
    inference(unit_resolution,[status(thm)],[19,18,15]) ).

tff(21,plain,
    ( ~ ( cC116(iV5475)
      <=> ~ ( ~ cC114xcomp(iV5475)
            | ~ cTOP(iV5475) ) )
    | cC116(iV5475)
    | ~ cC114xcomp(iV5475)
    | ~ cTOP(iV5475) ),
    inference(tautology,[status(thm)],]) ).

tff(22,plain,
    ( ~ ( cC116(iV5475)
      <=> ~ ( ~ cC114xcomp(iV5475)
            | ~ cTOP(iV5475) ) )
    | cC116(iV5475) ),
    inference(unit_resolution,[status(thm)],[21,20]) ).

tff(23,plain,
    cC116(iV5475),
    inference(unit_resolution,[status(thm)],[22,12]) ).

tff(24,plain,
    ^ [X: $i] :
      refl(
        ( ( cTEST(X)
        <=> ~ ( ~ cC140(X)
              | ~ cC116(X) ) )
      <=> ( cTEST(X)
        <=> ~ ( ~ cC140(X)
              | ~ cC116(X) ) ) )),
    inference(bind,[status(th)],]) ).

tff(25,plain,
    ( ! [X: $i] :
        ( cTEST(X)
      <=> ~ ( ~ cC140(X)
            | ~ cC116(X) ) )
  <=> ! [X: $i] :
        ( cTEST(X)
      <=> ~ ( ~ cC140(X)
            | ~ cC116(X) ) ) ),
    inference(quant_intro,[status(thm)],[24]) ).

tff(26,plain,
    ^ [X: $i] :
      rewrite(
        ( ( cTEST(X)
        <=> ( cC140(X)
            & cC116(X) ) )
      <=> ( cTEST(X)
        <=> ~ ( ~ cC140(X)
              | ~ cC116(X) ) ) )),
    inference(bind,[status(th)],]) ).

tff(27,plain,
    ( ! [X: $i] :
        ( cTEST(X)
      <=> ( cC140(X)
          & cC116(X) ) )
  <=> ! [X: $i] :
        ( cTEST(X)
      <=> ~ ( ~ cC140(X)
            | ~ cC116(X) ) ) ),
    inference(quant_intro,[status(thm)],[26]) ).

tff(28,plain,
    ( ! [X: $i] :
        ( cTEST(X)
      <=> ( cC140(X)
          & cC116(X) ) )
  <=> ! [X: $i] :
        ( cTEST(X)
      <=> ( cC140(X)
          & cC116(X) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(29,axiom,
    ! [X: $i] :
      ( cTEST(X)
    <=> ( cC140(X)
        & cC116(X) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_127) ).

tff(30,plain,
    ! [X: $i] :
      ( cTEST(X)
    <=> ( cC140(X)
        & cC116(X) ) ),
    inference(modus_ponens,[status(thm)],[29,28]) ).

tff(31,plain,
    ! [X: $i] :
      ( cTEST(X)
    <=> ( cC140(X)
        & cC116(X) ) ),
    inference(skolemize,[status(sab)],[30]) ).

tff(32,plain,
    ! [X: $i] :
      ( cTEST(X)
    <=> ~ ( ~ cC140(X)
          | ~ cC116(X) ) ),
    inference(modus_ponens,[status(thm)],[31,27]) ).

tff(33,plain,
    ! [X: $i] :
      ( cTEST(X)
    <=> ~ ( ~ cC140(X)
          | ~ cC116(X) ) ),
    inference(modus_ponens,[status(thm)],[32,25]) ).

tff(34,plain,
    ( ( ~ ! [X: $i] :
            ( cTEST(X)
          <=> ~ ( ~ cC140(X)
                | ~ cC116(X) ) )
      | ( cTEST(iV5475)
      <=> ~ ( ~ cC116(iV5475)
            | ~ cC140(iV5475) ) ) )
  <=> ( ~ ! [X: $i] :
            ( cTEST(X)
          <=> ~ ( ~ cC140(X)
                | ~ cC116(X) ) )
      | ( cTEST(iV5475)
      <=> ~ ( ~ cC116(iV5475)
            | ~ cC140(iV5475) ) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(35,plain,
    ( ( cTEST(iV5475)
    <=> ~ ( ~ cC140(iV5475)
          | ~ cC116(iV5475) ) )
  <=> ( cTEST(iV5475)
    <=> ~ ( ~ cC116(iV5475)
          | ~ cC140(iV5475) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(36,plain,
    ( ( ~ ! [X: $i] :
            ( cTEST(X)
          <=> ~ ( ~ cC140(X)
                | ~ cC116(X) ) )
      | ( cTEST(iV5475)
      <=> ~ ( ~ cC140(iV5475)
            | ~ cC116(iV5475) ) ) )
  <=> ( ~ ! [X: $i] :
            ( cTEST(X)
          <=> ~ ( ~ cC140(X)
                | ~ cC116(X) ) )
      | ( cTEST(iV5475)
      <=> ~ ( ~ cC116(iV5475)
            | ~ cC140(iV5475) ) ) ) ),
    inference(monotonicity,[status(thm)],[35]) ).

tff(37,plain,
    ( ( ~ ! [X: $i] :
            ( cTEST(X)
          <=> ~ ( ~ cC140(X)
                | ~ cC116(X) ) )
      | ( cTEST(iV5475)
      <=> ~ ( ~ cC140(iV5475)
            | ~ cC116(iV5475) ) ) )
  <=> ( ~ ! [X: $i] :
            ( cTEST(X)
          <=> ~ ( ~ cC140(X)
                | ~ cC116(X) ) )
      | ( cTEST(iV5475)
      <=> ~ ( ~ cC116(iV5475)
            | ~ cC140(iV5475) ) ) ) ),
    inference(transitivity,[status(thm)],[36,34]) ).

tff(38,plain,
    ( ~ ! [X: $i] :
          ( cTEST(X)
        <=> ~ ( ~ cC140(X)
              | ~ cC116(X) ) )
    | ( cTEST(iV5475)
    <=> ~ ( ~ cC140(iV5475)
          | ~ cC116(iV5475) ) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(39,plain,
    ( ~ ! [X: $i] :
          ( cTEST(X)
        <=> ~ ( ~ cC140(X)
              | ~ cC116(X) ) )
    | ( cTEST(iV5475)
    <=> ~ ( ~ cC116(iV5475)
          | ~ cC140(iV5475) ) ) ),
    inference(modus_ponens,[status(thm)],[38,37]) ).

tff(40,plain,
    ( cTEST(iV5475)
  <=> ~ ( ~ cC116(iV5475)
        | ~ cC140(iV5475) ) ),
    inference(unit_resolution,[status(thm)],[39,33]) ).

tff(41,plain,
    ( cTEST(iV5475)
  <=> cTEST(iV5475) ),
    inference(rewrite,[status(thm)],]) ).

tff(42,axiom,
    cTEST(iV5475),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_131) ).

tff(43,plain,
    cTEST(iV5475),
    inference(modus_ponens,[status(thm)],[42,41]) ).

tff(44,plain,
    ( ~ ( cTEST(iV5475)
      <=> ~ ( ~ cC116(iV5475)
            | ~ cC140(iV5475) ) )
    | ~ cTEST(iV5475)
    | ~ ( ~ cC116(iV5475)
        | ~ cC140(iV5475) ) ),
    inference(tautology,[status(thm)],]) ).

tff(45,plain,
    ( ~ ( cTEST(iV5475)
      <=> ~ ( ~ cC116(iV5475)
            | ~ cC140(iV5475) ) )
    | ~ ( ~ cC116(iV5475)
        | ~ cC140(iV5475) ) ),
    inference(unit_resolution,[status(thm)],[44,43]) ).

tff(46,plain,
    ~ ( ~ cC116(iV5475)
      | ~ cC140(iV5475) ),
    inference(unit_resolution,[status(thm)],[45,40]) ).

tff(47,plain,
    ( ~ cC116(iV5475)
    | ~ cC140(iV5475)
    | cC140(iV5475) ),
    inference(tautology,[status(thm)],]) ).

tff(48,plain,
    cC140(iV5475),
    inference(unit_resolution,[status(thm)],[47,46]) ).

tff(49,plain,
    ( ~ ~ ( ~ cC116(iV5475)
          | ~ cC140(iV5475)
          | ~ cC138(iV5475) )
  <=> ( ~ cC116(iV5475)
      | ~ cC140(iV5475)
      | ~ cC138(iV5475) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(50,plain,
    ( ( cC116(iV5475)
      & cC140(iV5475)
      & cC138(iV5475) )
  <=> ~ ( ~ cC116(iV5475)
        | ~ cC140(iV5475)
        | ~ cC138(iV5475) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(51,plain,
    ( ~ ( cC116(iV5475)
        & cC140(iV5475)
        & cC138(iV5475) )
  <=> ~ ~ ( ~ cC116(iV5475)
          | ~ cC140(iV5475)
          | ~ cC138(iV5475) ) ),
    inference(monotonicity,[status(thm)],[50]) ).

tff(52,plain,
    ( ~ ( cC116(iV5475)
        & cC140(iV5475)
        & cC138(iV5475) )
  <=> ( ~ cC116(iV5475)
      | ~ cC140(iV5475)
      | ~ cC138(iV5475) ) ),
    inference(transitivity,[status(thm)],[51,49]) ).

tff(53,plain,
    ( ~ ( cC116(iV5475)
        & cC140(iV5475)
        & cC138(iV5475) )
  <=> ~ ( cC116(iV5475)
        & cC140(iV5475)
        & cC138(iV5475) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(54,plain,
    ( ~ ( ! [X: $i] :
            ( cowlThing(X)
            & ~ cowlNothing(X) )
        & ! [X: $i] :
            ( xsd_string(X)
          <=> ~ xsd_integer(X) )
        & cC116(iV5475)
        & cC140(iV5475)
        & cowlThing(iV5475)
        & cC138(iV5475) )
  <=> ~ ( cC116(iV5475)
        & cC140(iV5475)
        & cC138(iV5475) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(55,plain,
    ( ( ! [X: $i] :
          ( cowlThing(X)
          & ~ cowlNothing(X) )
      & ! [X: $i] :
          ( xsd_string(X)
        <=> ~ xsd_integer(X) )
      & cC116(iV5475)
      & cC140(iV5475)
      & cowlThing(iV5475)
      & cC138(iV5475) )
  <=> ( ! [X: $i] :
          ( cowlThing(X)
          & ~ cowlNothing(X) )
      & ! [X: $i] :
          ( xsd_string(X)
        <=> ~ xsd_integer(X) )
      & cC116(iV5475)
      & cC140(iV5475)
      & cowlThing(iV5475)
      & cC138(iV5475) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(56,plain,
    ( ~ ( ! [X: $i] :
            ( cowlThing(X)
            & ~ cowlNothing(X) )
        & ! [X: $i] :
            ( xsd_string(X)
          <=> ~ xsd_integer(X) )
        & cC116(iV5475)
        & cC140(iV5475)
        & cowlThing(iV5475)
        & cC138(iV5475) )
  <=> ~ ( ! [X: $i] :
            ( cowlThing(X)
            & ~ cowlNothing(X) )
        & ! [X: $i] :
            ( xsd_string(X)
          <=> ~ xsd_integer(X) )
        & cC116(iV5475)
        & cC140(iV5475)
        & cowlThing(iV5475)
        & cC138(iV5475) ) ),
    inference(monotonicity,[status(thm)],[55]) ).

tff(57,plain,
    ( ~ ( ! [X: $i] :
            ( cowlThing(X)
            & ~ cowlNothing(X) )
        & ! [X: $i] :
            ( xsd_string(X)
          <=> ~ xsd_integer(X) )
        & cC116(iV5475)
        & cC140(iV5475)
        & cowlThing(iV5475)
        & cC138(iV5475) )
  <=> ~ ( ! [X: $i] :
            ( cowlThing(X)
            & ~ cowlNothing(X) )
        & ! [X: $i] :
            ( xsd_string(X)
          <=> ~ xsd_integer(X) )
        & cC116(iV5475)
        & cC140(iV5475)
        & cowlThing(iV5475)
        & cC138(iV5475) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(58,axiom,
    ~ ( ! [X: $i] :
          ( cowlThing(X)
          & ~ cowlNothing(X) )
      & ! [X: $i] :
          ( xsd_string(X)
        <=> ~ xsd_integer(X) )
      & cC116(iV5475)
      & cC140(iV5475)
      & cowlThing(iV5475)
      & cC138(iV5475) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',the_axiom) ).

tff(59,plain,
    ~ ( ! [X: $i] :
          ( cowlThing(X)
          & ~ cowlNothing(X) )
      & ! [X: $i] :
          ( xsd_string(X)
        <=> ~ xsd_integer(X) )
      & cC116(iV5475)
      & cC140(iV5475)
      & cowlThing(iV5475)
      & cC138(iV5475) ),
    inference(modus_ponens,[status(thm)],[58,57]) ).

tff(60,plain,
    ~ ( ! [X: $i] :
          ( cowlThing(X)
          & ~ cowlNothing(X) )
      & ! [X: $i] :
          ( xsd_string(X)
        <=> ~ xsd_integer(X) )
      & cC116(iV5475)
      & cC140(iV5475)
      & cowlThing(iV5475)
      & cC138(iV5475) ),
    inference(modus_ponens,[status(thm)],[59,56]) ).

tff(61,plain,
    ~ ( cC116(iV5475)
      & cC140(iV5475)
      & cC138(iV5475) ),
    inference(modus_ponens,[status(thm)],[60,54]) ).

tff(62,plain,
    ~ ( cC116(iV5475)
      & cC140(iV5475)
      & cC138(iV5475) ),
    inference(modus_ponens,[status(thm)],[61,53]) ).

tff(63,plain,
    ( ~ cC116(iV5475)
    | ~ cC140(iV5475)
    | ~ cC138(iV5475) ),
    inference(modus_ponens,[status(thm)],[62,52]) ).

tff(64,plain,
    ~ cC138(iV5475),
    inference(unit_resolution,[status(thm)],[63,48,23]) ).

tff(65,plain,
    ^ [X: $i] :
      refl(
        ( ( cC140(X)
        <=> ~ ( ~ cC138(X)
              | ~ cTOP(X) ) )
      <=> ( cC140(X)
        <=> ~ ( ~ cC138(X)
              | ~ cTOP(X) ) ) )),
    inference(bind,[status(th)],]) ).

tff(66,plain,
    ( ! [X: $i] :
        ( cC140(X)
      <=> ~ ( ~ cC138(X)
            | ~ cTOP(X) ) )
  <=> ! [X: $i] :
        ( cC140(X)
      <=> ~ ( ~ cC138(X)
            | ~ cTOP(X) ) ) ),
    inference(quant_intro,[status(thm)],[65]) ).

tff(67,plain,
    ^ [X: $i] :
      rewrite(
        ( ( cC140(X)
        <=> ( cTOP(X)
            & cC138(X) ) )
      <=> ( cC140(X)
        <=> ~ ( ~ cC138(X)
              | ~ cTOP(X) ) ) )),
    inference(bind,[status(th)],]) ).

tff(68,plain,
    ( ! [X: $i] :
        ( cC140(X)
      <=> ( cTOP(X)
          & cC138(X) ) )
  <=> ! [X: $i] :
        ( cC140(X)
      <=> ~ ( ~ cC138(X)
            | ~ cTOP(X) ) ) ),
    inference(quant_intro,[status(thm)],[67]) ).

tff(69,plain,
    ( ! [X: $i] :
        ( cC140(X)
      <=> ( cTOP(X)
          & cC138(X) ) )
  <=> ! [X: $i] :
        ( cC140(X)
      <=> ( cTOP(X)
          & cC138(X) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(70,axiom,
    ! [X: $i] :
      ( cC140(X)
    <=> ( cTOP(X)
        & cC138(X) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_49) ).

tff(71,plain,
    ! [X: $i] :
      ( cC140(X)
    <=> ( cTOP(X)
        & cC138(X) ) ),
    inference(modus_ponens,[status(thm)],[70,69]) ).

tff(72,plain,
    ! [X: $i] :
      ( cC140(X)
    <=> ( cTOP(X)
        & cC138(X) ) ),
    inference(skolemize,[status(sab)],[71]) ).

tff(73,plain,
    ! [X: $i] :
      ( cC140(X)
    <=> ~ ( ~ cC138(X)
          | ~ cTOP(X) ) ),
    inference(modus_ponens,[status(thm)],[72,68]) ).

tff(74,plain,
    ! [X: $i] :
      ( cC140(X)
    <=> ~ ( ~ cC138(X)
          | ~ cTOP(X) ) ),
    inference(modus_ponens,[status(thm)],[73,66]) ).

tff(75,plain,
    ( ~ ! [X: $i] :
          ( cC140(X)
        <=> ~ ( ~ cC138(X)
              | ~ cTOP(X) ) )
    | ( cC140(iV5475)
    <=> ~ ( ~ cC138(iV5475)
          | ~ cTOP(iV5475) ) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(76,plain,
    ( cC140(iV5475)
  <=> ~ ( ~ cC138(iV5475)
        | ~ cTOP(iV5475) ) ),
    inference(unit_resolution,[status(thm)],[75,74]) ).

tff(77,plain,
    ( ~ ( cC140(iV5475)
      <=> ~ ( ~ cC138(iV5475)
            | ~ cTOP(iV5475) ) )
    | ~ cC140(iV5475)
    | ~ ( ~ cC138(iV5475)
        | ~ cTOP(iV5475) ) ),
    inference(tautology,[status(thm)],]) ).

tff(78,plain,
    ~ ( ~ cC138(iV5475)
      | ~ cTOP(iV5475) ),
    inference(unit_resolution,[status(thm)],[77,48,76]) ).

tff(79,plain,
    ( ~ cC138(iV5475)
    | ~ cTOP(iV5475)
    | cC138(iV5475) ),
    inference(tautology,[status(thm)],]) ).

tff(80,plain,
    $false,
    inference(unit_resolution,[status(thm)],[79,78,64]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12  % Problem  : KRS156+1 : TPTP v8.1.0. Released v3.1.0.
% 0.05/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n003.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 : Thu Sep  1 09:40:09 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34  Usage: tptp [options] [-file:]file
% 0.13/0.34    -h, -?       prints this message.
% 0.13/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.34    -m, -model   generate model.
% 0.13/0.34    -p, -proof   generate proof.
% 0.13/0.34    -c, -core    generate unsat core of named formulas.
% 0.13/0.34    -st, -statistics display statistics.
% 0.13/0.34    -t:timeout   set timeout (in second).
% 0.13/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34    -<param>:<value> configuration parameter and value.
% 0.13/0.34    -o:<output-file> file to place output in.
% 0.19/0.45  % SZS status Theorem
% 0.19/0.45  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------