TSTP Solution File: SWC333-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SWC333-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n016.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 : Tue Sep 20 11:57:10 EDT 2022

% Result   : Unsatisfiable 0.19s 0.44s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   51
% Syntax   : Number of formulae    :  111 (  12 unt;   9 typ;   0 def)
%            Number of atoms       :  511 (   0 equ)
%            Maximal formula atoms :   20 (   5 avg)
%            Number of connectives :  749 ( 354   ~; 328   |;   0   &)
%                                         (  67 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :   14 (  14 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   4   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   8 usr;   2 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   5 con; 0-0 aty)
%            Number of variables   :   17 (  15   !;   0   ?;  17   :)

% Comments : 
%------------------------------------------------------------------------------
tff(totalorderedP_type,type,
    totalorderedP: $i > $o ).

tff(sk5_type,type,
    sk5: $i ).

tff(segmentP_type,type,
    segmentP: ( $i * $i ) > $o ).

tff(sk3_type,type,
    sk3: $i ).

tff(sk4_type,type,
    sk4: $i ).

tff(sk1_type,type,
    sk1: $i ).

tff(sk2_type,type,
    sk2: $i ).

tff(neq_type,type,
    neq: ( $i * $i ) > $o ).

tff(ssList_type,type,
    ssList: $i > $o ).

tff(1,plain,
    ( ( totalorderedP(sk5)
      | $false
      | $false )
  <=> totalorderedP(sk5) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,plain,
    ( ~ $true
  <=> $false ),
    inference(rewrite,[status(thm)],]) ).

tff(3,plain,
    ( segmentP(sk4,sk3)
  <=> segmentP(sk4,sk3) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,axiom,
    segmentP(sk4,sk3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).

tff(5,plain,
    segmentP(sk4,sk3),
    inference(modus_ponens,[status(thm)],[4,3]) ).

tff(6,plain,
    ( segmentP(sk4,sk3)
  <=> $true ),
    inference(iff_true,[status(thm)],[5]) ).

tff(7,plain,
    ( ~ segmentP(sk4,sk3)
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[6]) ).

tff(8,plain,
    ( ~ segmentP(sk4,sk3)
  <=> $false ),
    inference(transitivity,[status(thm)],[7,2]) ).

tff(9,plain,
    ( totalorderedP(sk3)
  <=> totalorderedP(sk3) ),
    inference(rewrite,[status(thm)],]) ).

tff(10,axiom,
    totalorderedP(sk3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).

tff(11,plain,
    totalorderedP(sk3),
    inference(modus_ponens,[status(thm)],[10,9]) ).

tff(12,plain,
    ( totalorderedP(sk3)
  <=> $true ),
    inference(iff_true,[status(thm)],[11]) ).

tff(13,plain,
    ( ~ totalorderedP(sk3)
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[12]) ).

tff(14,plain,
    ( ~ totalorderedP(sk3)
  <=> $false ),
    inference(transitivity,[status(thm)],[13,2]) ).

tff(15,plain,
    ( ( totalorderedP(sk5)
      | ~ totalorderedP(sk3)
      | ~ segmentP(sk4,sk3) )
  <=> ( totalorderedP(sk5)
      | $false
      | $false ) ),
    inference(monotonicity,[status(thm)],[14,8]) ).

tff(16,plain,
    ( ( totalorderedP(sk5)
      | ~ totalorderedP(sk3)
      | ~ segmentP(sk4,sk3) )
  <=> totalorderedP(sk5) ),
    inference(transitivity,[status(thm)],[15,1]) ).

tff(17,plain,
    ( ( ~ totalorderedP(sk3)
      | ~ segmentP(sk4,sk3)
      | totalorderedP(sk5) )
  <=> ( totalorderedP(sk5)
      | ~ totalorderedP(sk3)
      | ~ segmentP(sk4,sk3) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(18,plain,
    ( ~ segmentP(sk2,sk1)
  <=> ~ segmentP(sk4,sk3) ),
    inference(rewrite,[status(thm)],]) ).

tff(19,plain,
    ( ~ totalorderedP(sk1)
  <=> ~ totalorderedP(sk3) ),
    inference(rewrite,[status(thm)],]) ).

tff(20,plain,
    ( ( ~ totalorderedP(sk1)
      | ~ segmentP(sk2,sk1)
      | totalorderedP(sk5) )
  <=> ( ~ totalorderedP(sk3)
      | ~ segmentP(sk4,sk3)
      | totalorderedP(sk5) ) ),
    inference(monotonicity,[status(thm)],[19,18]) ).

tff(21,plain,
    ( ( ~ totalorderedP(sk1)
      | ~ segmentP(sk2,sk1)
      | totalorderedP(sk5) )
  <=> ( totalorderedP(sk5)
      | ~ totalorderedP(sk3)
      | ~ segmentP(sk4,sk3) ) ),
    inference(transitivity,[status(thm)],[20,17]) ).

tff(22,plain,
    ( ( ~ totalorderedP(sk1)
      | ~ segmentP(sk2,sk1)
      | totalorderedP(sk5) )
  <=> ( ~ totalorderedP(sk1)
      | ~ segmentP(sk2,sk1)
      | totalorderedP(sk5) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(23,plain,
    ( ( totalorderedP(sk5)
      | ~ segmentP(sk2,sk1)
      | ~ totalorderedP(sk1) )
  <=> ( ~ totalorderedP(sk1)
      | ~ segmentP(sk2,sk1)
      | totalorderedP(sk5) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(24,axiom,
    ( totalorderedP(sk5)
    | ~ segmentP(sk2,sk1)
    | ~ totalorderedP(sk1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).

tff(25,plain,
    ( ~ totalorderedP(sk1)
    | ~ segmentP(sk2,sk1)
    | totalorderedP(sk5) ),
    inference(modus_ponens,[status(thm)],[24,23]) ).

tff(26,plain,
    ( ~ totalorderedP(sk1)
    | ~ segmentP(sk2,sk1)
    | totalorderedP(sk5) ),
    inference(modus_ponens,[status(thm)],[25,22]) ).

tff(27,plain,
    ( ~ totalorderedP(sk1)
    | ~ segmentP(sk2,sk1)
    | totalorderedP(sk5) ),
    inference(modus_ponens,[status(thm)],[26,22]) ).

tff(28,plain,
    ( ~ totalorderedP(sk1)
    | ~ segmentP(sk2,sk1)
    | totalorderedP(sk5) ),
    inference(modus_ponens,[status(thm)],[27,22]) ).

tff(29,plain,
    ( totalorderedP(sk5)
    | ~ totalorderedP(sk3)
    | ~ segmentP(sk4,sk3) ),
    inference(modus_ponens,[status(thm)],[28,21]) ).

tff(30,plain,
    totalorderedP(sk5),
    inference(modus_ponens,[status(thm)],[29,16]) ).

tff(31,plain,
    ( ( $false
      | $false
      | segmentP(sk5,sk3) )
  <=> segmentP(sk5,sk3) ),
    inference(rewrite,[status(thm)],]) ).

tff(32,plain,
    ( ( ~ totalorderedP(sk3)
      | ~ segmentP(sk4,sk3)
      | segmentP(sk5,sk3) )
  <=> ( $false
      | $false
      | segmentP(sk5,sk3) ) ),
    inference(monotonicity,[status(thm)],[14,8]) ).

tff(33,plain,
    ( ( ~ totalorderedP(sk3)
      | ~ segmentP(sk4,sk3)
      | segmentP(sk5,sk3) )
  <=> segmentP(sk5,sk3) ),
    inference(transitivity,[status(thm)],[32,31]) ).

tff(34,plain,
    ( ( ~ totalorderedP(sk1)
      | ~ segmentP(sk2,sk1)
      | segmentP(sk5,sk1) )
  <=> ( ~ totalorderedP(sk3)
      | ~ segmentP(sk4,sk3)
      | segmentP(sk5,sk3) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(35,plain,
    ( ( ~ totalorderedP(sk1)
      | ~ segmentP(sk2,sk1)
      | segmentP(sk5,sk1) )
  <=> ( ~ totalorderedP(sk1)
      | ~ segmentP(sk2,sk1)
      | segmentP(sk5,sk1) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(36,plain,
    ( ( ~ segmentP(sk2,sk1)
      | segmentP(sk5,sk1)
      | ~ totalorderedP(sk1) )
  <=> ( ~ totalorderedP(sk1)
      | ~ segmentP(sk2,sk1)
      | segmentP(sk5,sk1) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(37,plain,
    ( ( segmentP(sk5,sk1)
      | ~ segmentP(sk2,sk1) )
  <=> ( ~ segmentP(sk2,sk1)
      | segmentP(sk5,sk1) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(38,plain,
    ( ( segmentP(sk5,sk1)
      | ~ segmentP(sk2,sk1)
      | ~ totalorderedP(sk1) )
  <=> ( ~ segmentP(sk2,sk1)
      | segmentP(sk5,sk1)
      | ~ totalorderedP(sk1) ) ),
    inference(monotonicity,[status(thm)],[37]) ).

tff(39,plain,
    ( ( segmentP(sk5,sk1)
      | ~ segmentP(sk2,sk1)
      | ~ totalorderedP(sk1) )
  <=> ( ~ totalorderedP(sk1)
      | ~ segmentP(sk2,sk1)
      | segmentP(sk5,sk1) ) ),
    inference(transitivity,[status(thm)],[38,36]) ).

tff(40,axiom,
    ( segmentP(sk5,sk1)
    | ~ segmentP(sk2,sk1)
    | ~ totalorderedP(sk1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).

tff(41,plain,
    ( ~ totalorderedP(sk1)
    | ~ segmentP(sk2,sk1)
    | segmentP(sk5,sk1) ),
    inference(modus_ponens,[status(thm)],[40,39]) ).

tff(42,plain,
    ( ~ totalorderedP(sk1)
    | ~ segmentP(sk2,sk1)
    | segmentP(sk5,sk1) ),
    inference(modus_ponens,[status(thm)],[41,35]) ).

tff(43,plain,
    ( ~ totalorderedP(sk3)
    | ~ segmentP(sk4,sk3)
    | segmentP(sk5,sk3) ),
    inference(modus_ponens,[status(thm)],[42,34]) ).

tff(44,plain,
    segmentP(sk5,sk3),
    inference(modus_ponens,[status(thm)],[43,33]) ).

tff(45,plain,
    ( ( $false
      | $false
      | segmentP(sk4,sk5) )
  <=> segmentP(sk4,sk5) ),
    inference(rewrite,[status(thm)],]) ).

tff(46,plain,
    ( ( ~ totalorderedP(sk3)
      | ~ segmentP(sk4,sk3)
      | segmentP(sk4,sk5) )
  <=> ( $false
      | $false
      | segmentP(sk4,sk5) ) ),
    inference(monotonicity,[status(thm)],[14,8]) ).

tff(47,plain,
    ( ( ~ totalorderedP(sk3)
      | ~ segmentP(sk4,sk3)
      | segmentP(sk4,sk5) )
  <=> segmentP(sk4,sk5) ),
    inference(transitivity,[status(thm)],[46,45]) ).

tff(48,plain,
    ( ( segmentP(sk4,sk5)
      | ~ totalorderedP(sk3)
      | ~ segmentP(sk4,sk3) )
  <=> ( ~ totalorderedP(sk3)
      | ~ segmentP(sk4,sk3)
      | segmentP(sk4,sk5) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(49,plain,
    ( segmentP(sk2,sk5)
  <=> segmentP(sk4,sk5) ),
    inference(rewrite,[status(thm)],]) ).

tff(50,plain,
    ( ( segmentP(sk2,sk5)
      | ~ totalorderedP(sk1)
      | ~ segmentP(sk2,sk1) )
  <=> ( segmentP(sk4,sk5)
      | ~ totalorderedP(sk3)
      | ~ segmentP(sk4,sk3) ) ),
    inference(monotonicity,[status(thm)],[49,19,18]) ).

tff(51,plain,
    ( ( segmentP(sk2,sk5)
      | ~ totalorderedP(sk1)
      | ~ segmentP(sk2,sk1) )
  <=> ( ~ totalorderedP(sk3)
      | ~ segmentP(sk4,sk3)
      | segmentP(sk4,sk5) ) ),
    inference(transitivity,[status(thm)],[50,48]) ).

tff(52,plain,
    ( ( segmentP(sk2,sk5)
      | ~ totalorderedP(sk1)
      | ~ segmentP(sk2,sk1) )
  <=> ( segmentP(sk2,sk5)
      | ~ totalorderedP(sk1)
      | ~ segmentP(sk2,sk1) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(53,plain,
    ( ( segmentP(sk2,sk5)
      | ~ segmentP(sk2,sk1)
      | ~ totalorderedP(sk1) )
  <=> ( segmentP(sk2,sk5)
      | ~ totalorderedP(sk1)
      | ~ segmentP(sk2,sk1) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(54,plain,
    ( ( segmentP(sk2,sk5)
      | ~ segmentP(sk2,sk1) )
  <=> ( segmentP(sk2,sk5)
      | ~ segmentP(sk2,sk1) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(55,plain,
    ( ( segmentP(sk2,sk5)
      | ~ segmentP(sk2,sk1)
      | ~ totalorderedP(sk1) )
  <=> ( segmentP(sk2,sk5)
      | ~ segmentP(sk2,sk1)
      | ~ totalorderedP(sk1) ) ),
    inference(monotonicity,[status(thm)],[54]) ).

tff(56,plain,
    ( ( segmentP(sk2,sk5)
      | ~ segmentP(sk2,sk1)
      | ~ totalorderedP(sk1) )
  <=> ( segmentP(sk2,sk5)
      | ~ totalorderedP(sk1)
      | ~ segmentP(sk2,sk1) ) ),
    inference(transitivity,[status(thm)],[55,53]) ).

tff(57,axiom,
    ( segmentP(sk2,sk5)
    | ~ segmentP(sk2,sk1)
    | ~ totalorderedP(sk1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).

tff(58,plain,
    ( segmentP(sk2,sk5)
    | ~ totalorderedP(sk1)
    | ~ segmentP(sk2,sk1) ),
    inference(modus_ponens,[status(thm)],[57,56]) ).

tff(59,plain,
    ( segmentP(sk2,sk5)
    | ~ totalorderedP(sk1)
    | ~ segmentP(sk2,sk1) ),
    inference(modus_ponens,[status(thm)],[58,52]) ).

tff(60,plain,
    ( segmentP(sk2,sk5)
    | ~ totalorderedP(sk1)
    | ~ segmentP(sk2,sk1) ),
    inference(modus_ponens,[status(thm)],[59,52]) ).

tff(61,plain,
    ( segmentP(sk2,sk5)
    | ~ totalorderedP(sk1)
    | ~ segmentP(sk2,sk1) ),
    inference(modus_ponens,[status(thm)],[60,52]) ).

tff(62,plain,
    ( ~ totalorderedP(sk3)
    | ~ segmentP(sk4,sk3)
    | segmentP(sk4,sk5) ),
    inference(modus_ponens,[status(thm)],[61,51]) ).

tff(63,plain,
    segmentP(sk4,sk5),
    inference(modus_ponens,[status(thm)],[62,47]) ).

tff(64,plain,
    ( ( $false
      | $false
      | neq(sk3,sk5) )
  <=> neq(sk3,sk5) ),
    inference(rewrite,[status(thm)],]) ).

tff(65,plain,
    ( ( ~ totalorderedP(sk3)
      | ~ segmentP(sk4,sk3)
      | neq(sk3,sk5) )
  <=> ( $false
      | $false
      | neq(sk3,sk5) ) ),
    inference(monotonicity,[status(thm)],[14,8]) ).

tff(66,plain,
    ( ( ~ totalorderedP(sk3)
      | ~ segmentP(sk4,sk3)
      | neq(sk3,sk5) )
  <=> neq(sk3,sk5) ),
    inference(transitivity,[status(thm)],[65,64]) ).

tff(67,plain,
    ( ( ~ totalorderedP(sk1)
      | ~ segmentP(sk2,sk1)
      | neq(sk1,sk5) )
  <=> ( ~ totalorderedP(sk3)
      | ~ segmentP(sk4,sk3)
      | neq(sk3,sk5) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(68,plain,
    ( ( ~ totalorderedP(sk1)
      | ~ segmentP(sk2,sk1)
      | neq(sk1,sk5) )
  <=> ( ~ totalorderedP(sk1)
      | ~ segmentP(sk2,sk1)
      | neq(sk1,sk5) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(69,plain,
    ( ( ~ segmentP(sk2,sk1)
      | neq(sk1,sk5)
      | ~ totalorderedP(sk1) )
  <=> ( ~ totalorderedP(sk1)
      | ~ segmentP(sk2,sk1)
      | neq(sk1,sk5) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(70,plain,
    ( ( neq(sk1,sk5)
      | ~ segmentP(sk2,sk1) )
  <=> ( ~ segmentP(sk2,sk1)
      | neq(sk1,sk5) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(71,plain,
    ( ( neq(sk1,sk5)
      | ~ segmentP(sk2,sk1)
      | ~ totalorderedP(sk1) )
  <=> ( ~ segmentP(sk2,sk1)
      | neq(sk1,sk5)
      | ~ totalorderedP(sk1) ) ),
    inference(monotonicity,[status(thm)],[70]) ).

tff(72,plain,
    ( ( neq(sk1,sk5)
      | ~ segmentP(sk2,sk1)
      | ~ totalorderedP(sk1) )
  <=> ( ~ totalorderedP(sk1)
      | ~ segmentP(sk2,sk1)
      | neq(sk1,sk5) ) ),
    inference(transitivity,[status(thm)],[71,69]) ).

tff(73,axiom,
    ( neq(sk1,sk5)
    | ~ segmentP(sk2,sk1)
    | ~ totalorderedP(sk1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).

tff(74,plain,
    ( ~ totalorderedP(sk1)
    | ~ segmentP(sk2,sk1)
    | neq(sk1,sk5) ),
    inference(modus_ponens,[status(thm)],[73,72]) ).

tff(75,plain,
    ( ~ totalorderedP(sk1)
    | ~ segmentP(sk2,sk1)
    | neq(sk1,sk5) ),
    inference(modus_ponens,[status(thm)],[74,68]) ).

tff(76,plain,
    ( ~ totalorderedP(sk3)
    | ~ segmentP(sk4,sk3)
    | neq(sk3,sk5) ),
    inference(modus_ponens,[status(thm)],[75,67]) ).

tff(77,plain,
    neq(sk3,sk5),
    inference(modus_ponens,[status(thm)],[76,66]) ).

tff(78,plain,
    ( ( ssList(sk5)
      | $false
      | $false )
  <=> ssList(sk5) ),
    inference(rewrite,[status(thm)],]) ).

tff(79,plain,
    ( ( ssList(sk5)
      | ~ totalorderedP(sk3)
      | ~ segmentP(sk4,sk3) )
  <=> ( ssList(sk5)
      | $false
      | $false ) ),
    inference(monotonicity,[status(thm)],[14,8]) ).

tff(80,plain,
    ( ( ssList(sk5)
      | ~ totalorderedP(sk3)
      | ~ segmentP(sk4,sk3) )
  <=> ssList(sk5) ),
    inference(transitivity,[status(thm)],[79,78]) ).

tff(81,plain,
    ( ( ssList(sk5)
      | ~ totalorderedP(sk1)
      | ~ segmentP(sk2,sk1) )
  <=> ( ssList(sk5)
      | ~ totalorderedP(sk3)
      | ~ segmentP(sk4,sk3) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(82,plain,
    ( ( ssList(sk5)
      | ~ totalorderedP(sk1)
      | ~ segmentP(sk2,sk1) )
  <=> ( ssList(sk5)
      | ~ totalorderedP(sk1)
      | ~ segmentP(sk2,sk1) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(83,plain,
    ( ( ssList(sk5)
      | ~ segmentP(sk2,sk1)
      | ~ totalorderedP(sk1) )
  <=> ( ssList(sk5)
      | ~ totalorderedP(sk1)
      | ~ segmentP(sk2,sk1) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(84,axiom,
    ( ssList(sk5)
    | ~ segmentP(sk2,sk1)
    | ~ totalorderedP(sk1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).

tff(85,plain,
    ( ssList(sk5)
    | ~ totalorderedP(sk1)
    | ~ segmentP(sk2,sk1) ),
    inference(modus_ponens,[status(thm)],[84,83]) ).

tff(86,plain,
    ( ssList(sk5)
    | ~ totalorderedP(sk1)
    | ~ segmentP(sk2,sk1) ),
    inference(modus_ponens,[status(thm)],[85,82]) ).

tff(87,plain,
    ( ssList(sk5)
    | ~ totalorderedP(sk3)
    | ~ segmentP(sk4,sk3) ),
    inference(modus_ponens,[status(thm)],[86,81]) ).

tff(88,plain,
    ssList(sk5),
    inference(modus_ponens,[status(thm)],[87,80]) ).

tff(89,plain,
    ^ [A: $i] :
      refl(
        ( ( ~ ssList(A)
          | ~ segmentP(A,sk3)
          | ~ segmentP(sk4,A)
          | ~ totalorderedP(A)
          | ~ neq(sk3,A) )
      <=> ( ~ ssList(A)
          | ~ segmentP(A,sk3)
          | ~ segmentP(sk4,A)
          | ~ totalorderedP(A)
          | ~ neq(sk3,A) ) )),
    inference(bind,[status(th)],]) ).

tff(90,plain,
    ( ! [A: $i] :
        ( ~ ssList(A)
        | ~ segmentP(A,sk3)
        | ~ segmentP(sk4,A)
        | ~ totalorderedP(A)
        | ~ neq(sk3,A) )
  <=> ! [A: $i] :
        ( ~ ssList(A)
        | ~ segmentP(A,sk3)
        | ~ segmentP(sk4,A)
        | ~ totalorderedP(A)
        | ~ neq(sk3,A) ) ),
    inference(quant_intro,[status(thm)],[89]) ).

tff(91,plain,
    ( ! [A: $i] :
        ( ~ ssList(A)
        | ~ segmentP(A,sk3)
        | ~ segmentP(sk4,A)
        | ~ totalorderedP(A)
        | ~ neq(sk3,A) )
  <=> ! [A: $i] :
        ( ~ ssList(A)
        | ~ segmentP(A,sk3)
        | ~ segmentP(sk4,A)
        | ~ totalorderedP(A)
        | ~ neq(sk3,A) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(92,plain,
    ^ [A: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              rewrite(
                ( ( ~ ssList(A)
                  | ~ neq(sk3,A)
                  | ~ segmentP(sk4,A) )
              <=> ( ~ ssList(A)
                  | ~ segmentP(sk4,A)
                  | ~ neq(sk3,A) ) )),
              ( ( ~ ssList(A)
                | ~ neq(sk3,A)
                | ~ segmentP(sk4,A)
                | ~ segmentP(A,sk3) )
            <=> ( ~ ssList(A)
                | ~ segmentP(sk4,A)
                | ~ neq(sk3,A)
                | ~ segmentP(A,sk3) ) )),
            rewrite(
              ( ( ~ ssList(A)
                | ~ segmentP(sk4,A)
                | ~ neq(sk3,A)
                | ~ segmentP(A,sk3) )
            <=> ( ~ ssList(A)
                | ~ segmentP(A,sk3)
                | ~ segmentP(sk4,A)
                | ~ neq(sk3,A) ) )),
            ( ( ~ ssList(A)
              | ~ neq(sk3,A)
              | ~ segmentP(sk4,A)
              | ~ segmentP(A,sk3) )
          <=> ( ~ ssList(A)
              | ~ segmentP(A,sk3)
              | ~ segmentP(sk4,A)
              | ~ neq(sk3,A) ) )),
          ( ( ~ ssList(A)
            | ~ neq(sk3,A)
            | ~ segmentP(sk4,A)
            | ~ segmentP(A,sk3)
            | ~ totalorderedP(A) )
        <=> ( ~ ssList(A)
            | ~ segmentP(A,sk3)
            | ~ segmentP(sk4,A)
            | ~ neq(sk3,A)
            | ~ totalorderedP(A) ) )),
        rewrite(
          ( ( ~ ssList(A)
            | ~ segmentP(A,sk3)
            | ~ segmentP(sk4,A)
            | ~ neq(sk3,A)
            | ~ totalorderedP(A) )
        <=> ( ~ ssList(A)
            | ~ segmentP(A,sk3)
            | ~ segmentP(sk4,A)
            | ~ totalorderedP(A)
            | ~ neq(sk3,A) ) )),
        ( ( ~ ssList(A)
          | ~ neq(sk3,A)
          | ~ segmentP(sk4,A)
          | ~ segmentP(A,sk3)
          | ~ totalorderedP(A) )
      <=> ( ~ ssList(A)
          | ~ segmentP(A,sk3)
          | ~ segmentP(sk4,A)
          | ~ totalorderedP(A)
          | ~ neq(sk3,A) ) )),
    inference(bind,[status(th)],]) ).

tff(93,plain,
    ( ! [A: $i] :
        ( ~ ssList(A)
        | ~ neq(sk3,A)
        | ~ segmentP(sk4,A)
        | ~ segmentP(A,sk3)
        | ~ totalorderedP(A) )
  <=> ! [A: $i] :
        ( ~ ssList(A)
        | ~ segmentP(A,sk3)
        | ~ segmentP(sk4,A)
        | ~ totalorderedP(A)
        | ~ neq(sk3,A) ) ),
    inference(quant_intro,[status(thm)],[92]) ).

tff(94,axiom,
    ! [A: $i] :
      ( ~ ssList(A)
      | ~ neq(sk3,A)
      | ~ segmentP(sk4,A)
      | ~ segmentP(A,sk3)
      | ~ totalorderedP(A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).

tff(95,plain,
    ! [A: $i] :
      ( ~ ssList(A)
      | ~ segmentP(A,sk3)
      | ~ segmentP(sk4,A)
      | ~ totalorderedP(A)
      | ~ neq(sk3,A) ),
    inference(modus_ponens,[status(thm)],[94,93]) ).

tff(96,plain,
    ! [A: $i] :
      ( ~ ssList(A)
      | ~ segmentP(A,sk3)
      | ~ segmentP(sk4,A)
      | ~ totalorderedP(A)
      | ~ neq(sk3,A) ),
    inference(modus_ponens,[status(thm)],[95,91]) ).

tff(97,plain,
    ! [A: $i] :
      ( ~ ssList(A)
      | ~ segmentP(A,sk3)
      | ~ segmentP(sk4,A)
      | ~ totalorderedP(A)
      | ~ neq(sk3,A) ),
    inference(skolemize,[status(sab)],[96]) ).

tff(98,plain,
    ! [A: $i] :
      ( ~ ssList(A)
      | ~ segmentP(A,sk3)
      | ~ segmentP(sk4,A)
      | ~ totalorderedP(A)
      | ~ neq(sk3,A) ),
    inference(modus_ponens,[status(thm)],[97,90]) ).

tff(99,plain,
    ( ( ~ ! [A: $i] :
            ( ~ ssList(A)
            | ~ segmentP(A,sk3)
            | ~ segmentP(sk4,A)
            | ~ totalorderedP(A)
            | ~ neq(sk3,A) )
      | ~ ssList(sk5)
      | ~ segmentP(sk5,sk3)
      | ~ segmentP(sk4,sk5)
      | ~ totalorderedP(sk5)
      | ~ neq(sk3,sk5) )
  <=> ( ~ ! [A: $i] :
            ( ~ ssList(A)
            | ~ segmentP(A,sk3)
            | ~ segmentP(sk4,A)
            | ~ totalorderedP(A)
            | ~ neq(sk3,A) )
      | ~ ssList(sk5)
      | ~ segmentP(sk5,sk3)
      | ~ segmentP(sk4,sk5)
      | ~ totalorderedP(sk5)
      | ~ neq(sk3,sk5) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(100,plain,
    ( ~ ! [A: $i] :
          ( ~ ssList(A)
          | ~ segmentP(A,sk3)
          | ~ segmentP(sk4,A)
          | ~ totalorderedP(A)
          | ~ neq(sk3,A) )
    | ~ ssList(sk5)
    | ~ segmentP(sk5,sk3)
    | ~ segmentP(sk4,sk5)
    | ~ totalorderedP(sk5)
    | ~ neq(sk3,sk5) ),
    inference(quant_inst,[status(thm)],]) ).

tff(101,plain,
    ( ~ ! [A: $i] :
          ( ~ ssList(A)
          | ~ segmentP(A,sk3)
          | ~ segmentP(sk4,A)
          | ~ totalorderedP(A)
          | ~ neq(sk3,A) )
    | ~ ssList(sk5)
    | ~ segmentP(sk5,sk3)
    | ~ segmentP(sk4,sk5)
    | ~ totalorderedP(sk5)
    | ~ neq(sk3,sk5) ),
    inference(modus_ponens,[status(thm)],[100,99]) ).

tff(102,plain,
    $false,
    inference(unit_resolution,[status(thm)],[101,98,88,77,63,44,30]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SWC333-1 : TPTP v8.1.0. Released v2.4.0.
% 0.13/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33  % Computer : n016.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Sun Sep  4 00:27:53 EDT 2022
% 0.13/0.33  % 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.
% 0.19/0.44  % SZS status Unsatisfiable
% 0.19/0.44  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------