TSTP Solution File: SYN090-1.008 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN090-1.008 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n013.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 23:53:42 EDT 2022

% Result   : Unsatisfiable 0.16s 0.35s
% Output   : Proof 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   90
%            Number of leaves      :  130
% Syntax   : Number of formulae    :  359 (  26 unt;  25 typ;   0 def)
%            Number of atoms       : 1090 (   0 equ)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives : 1228 ( 472   ~; 483   |;   0   &)
%                                         ( 273 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   4 avg)
%            Maximal term depth    :    0 (   0 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   27 (  25 usr;  27 prp; 0-0 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :    0 (   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(q_0_type,type,
    q_0: $o ).

tff(p_0_type,type,
    p_0: $o ).

tff(p_1_type,type,
    p_1: $o ).

tff(p_2_type,type,
    p_2: $o ).

tff(p_3_type,type,
    p_3: $o ).

tff(p_4_type,type,
    p_4: $o ).

tff(p_5_type,type,
    p_5: $o ).

tff(p_6_type,type,
    p_6: $o ).

tff(p_7_type,type,
    p_7: $o ).

tff(p_9_type,type,
    p_9: $o ).

tff(p_8_type,type,
    p_8: $o ).

tff(q_11_type,type,
    q_11: $o ).

tff(q_10_type,type,
    q_10: $o ).

tff(p_12_type,type,
    p_12: $o ).

tff(q_14_type,type,
    q_14: $o ).

tff(q_13_type,type,
    q_13: $o ).

tff(p_15_type,type,
    p_15: $o ).

tff(p_11_type,type,
    p_11: $o ).

tff(q_12_type,type,
    q_12: $o ).

tff(p_14_type,type,
    p_14: $o ).

tff(q_9_type,type,
    q_9: $o ).

tff(q_2_type,type,
    q_2: $o ).

tff(q_4_type,type,
    q_4: $o ).

tff(q_6_type,type,
    q_6: $o ).

tff(q_8_type,type,
    q_8: $o ).

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

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

tff(3,plain,
    ( ( q_0
    <=> $true )
  <=> q_0 ),
    inference(rewrite,[status(thm)],]) ).

tff(4,plain,
    ( q_0
  <=> ( q_0
    <=> $true ) ),
    inference(symmetry,[status(thm)],[3]) ).

tff(5,plain,
    ( ( q_0
      | $false )
  <=> q_0 ),
    inference(rewrite,[status(thm)],]) ).

tff(6,plain,
    ( ( p_1
    <=> $true )
  <=> p_1 ),
    inference(rewrite,[status(thm)],]) ).

tff(7,plain,
    ( p_1
  <=> ( p_1
    <=> $true ) ),
    inference(symmetry,[status(thm)],[6]) ).

tff(8,plain,
    ( ( p_1
      | $false )
  <=> p_1 ),
    inference(rewrite,[status(thm)],]) ).

tff(9,plain,
    ( ( p_2
    <=> $true )
  <=> p_2 ),
    inference(rewrite,[status(thm)],]) ).

tff(10,plain,
    ( p_2
  <=> ( p_2
    <=> $true ) ),
    inference(symmetry,[status(thm)],[9]) ).

tff(11,plain,
    ( ( p_2
      | $false )
  <=> p_2 ),
    inference(rewrite,[status(thm)],]) ).

tff(12,plain,
    ( ( p_3
    <=> $true )
  <=> p_3 ),
    inference(rewrite,[status(thm)],]) ).

tff(13,plain,
    ( p_3
  <=> ( p_3
    <=> $true ) ),
    inference(symmetry,[status(thm)],[12]) ).

tff(14,plain,
    ( ( p_3
      | $false )
  <=> p_3 ),
    inference(rewrite,[status(thm)],]) ).

tff(15,plain,
    ( ( p_4
    <=> $true )
  <=> p_4 ),
    inference(rewrite,[status(thm)],]) ).

tff(16,plain,
    ( p_4
  <=> ( p_4
    <=> $true ) ),
    inference(symmetry,[status(thm)],[15]) ).

tff(17,plain,
    ( ( p_4
      | $false )
  <=> p_4 ),
    inference(rewrite,[status(thm)],]) ).

tff(18,plain,
    ( ( p_5
    <=> $true )
  <=> p_5 ),
    inference(rewrite,[status(thm)],]) ).

tff(19,plain,
    ( p_5
  <=> ( p_5
    <=> $true ) ),
    inference(symmetry,[status(thm)],[18]) ).

tff(20,plain,
    ( ( p_5
      | $false )
  <=> p_5 ),
    inference(rewrite,[status(thm)],]) ).

tff(21,plain,
    ( ( p_6
    <=> $true )
  <=> p_6 ),
    inference(rewrite,[status(thm)],]) ).

tff(22,plain,
    ( p_6
  <=> ( p_6
    <=> $true ) ),
    inference(symmetry,[status(thm)],[21]) ).

tff(23,plain,
    ( ( p_6
      | $false )
  <=> p_6 ),
    inference(rewrite,[status(thm)],]) ).

tff(24,plain,
    ( ( p_7
    <=> $true )
  <=> p_7 ),
    inference(rewrite,[status(thm)],]) ).

tff(25,plain,
    ( p_7
  <=> ( p_7
    <=> $true ) ),
    inference(symmetry,[status(thm)],[24]) ).

tff(26,plain,
    ( ( p_7
      | $false
      | $false )
  <=> p_7 ),
    inference(rewrite,[status(thm)],]) ).

tff(27,plain,
    ( ( p_9
    <=> $true )
  <=> p_9 ),
    inference(rewrite,[status(thm)],]) ).

tff(28,plain,
    ( p_9
  <=> ( p_9
    <=> $true ) ),
    inference(symmetry,[status(thm)],[27]) ).

tff(29,plain,
    ( ( p_9
      | $false
      | $false )
  <=> p_9 ),
    inference(rewrite,[status(thm)],]) ).

tff(30,plain,
    ( ( q_11
      | $false )
  <=> q_11 ),
    inference(rewrite,[status(thm)],]) ).

tff(31,plain,
    ( ( p_12
      | $false
      | $false )
  <=> p_12 ),
    inference(rewrite,[status(thm)],]) ).

tff(32,axiom,
    q_14,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_3) ).

tff(33,plain,
    ( q_14
  <=> $true ),
    inference(iff_true,[status(thm)],[32]) ).

tff(34,plain,
    ( ~ q_14
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[33]) ).

tff(35,plain,
    ( ~ q_14
  <=> $false ),
    inference(transitivity,[status(thm)],[34,2]) ).

tff(36,plain,
    ( ( q_13
      | $false
      | $false )
  <=> q_13 ),
    inference(rewrite,[status(thm)],]) ).

tff(37,axiom,
    p_15,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_2) ).

tff(38,plain,
    ( p_15
  <=> $true ),
    inference(iff_true,[status(thm)],[37]) ).

tff(39,plain,
    ( ~ p_15
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[38]) ).

tff(40,plain,
    ( ~ p_15
  <=> $false ),
    inference(transitivity,[status(thm)],[39,2]) ).

tff(41,plain,
    ( ( q_13
      | ~ q_14
      | ~ p_15 )
  <=> ( q_13
      | $false
      | $false ) ),
    inference(monotonicity,[status(thm)],[35,40]) ).

tff(42,plain,
    ( ( q_13
      | ~ q_14
      | ~ p_15 )
  <=> q_13 ),
    inference(transitivity,[status(thm)],[41,36]) ).

tff(43,plain,
    ( ( q_13
      | ~ q_14
      | ~ p_15 )
  <=> ( q_13
      | ~ q_14
      | ~ p_15 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(44,plain,
    ( ( q_13
      | ~ q_14
      | ~ p_15 )
  <=> ( q_13
      | ~ q_14
      | ~ p_15 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(45,axiom,
    ( q_13
    | ~ q_14
    | ~ p_15 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_type12_28) ).

tff(46,plain,
    ( q_13
    | ~ q_14
    | ~ p_15 ),
    inference(modus_ponens,[status(thm)],[45,44]) ).

tff(47,plain,
    ( q_13
    | ~ q_14
    | ~ p_15 ),
    inference(modus_ponens,[status(thm)],[46,43]) ).

tff(48,plain,
    q_13,
    inference(modus_ponens,[status(thm)],[47,42]) ).

tff(49,plain,
    ( q_13
  <=> $true ),
    inference(iff_true,[status(thm)],[48]) ).

tff(50,plain,
    ( ~ q_13
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[49]) ).

tff(51,plain,
    ( ~ q_13
  <=> $false ),
    inference(transitivity,[status(thm)],[50,2]) ).

tff(52,plain,
    ( ( p_12
      | ~ q_13
      | ~ q_14 )
  <=> ( p_12
      | $false
      | $false ) ),
    inference(monotonicity,[status(thm)],[51,35]) ).

tff(53,plain,
    ( ( p_12
      | ~ q_13
      | ~ q_14 )
  <=> p_12 ),
    inference(transitivity,[status(thm)],[52,31]) ).

tff(54,plain,
    ( ( p_12
      | ~ q_13
      | ~ q_14 )
  <=> ( p_12
      | ~ q_13
      | ~ q_14 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(55,axiom,
    ( p_12
    | ~ q_13
    | ~ q_14 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_type11_26) ).

tff(56,plain,
    ( p_12
    | ~ q_13
    | ~ q_14 ),
    inference(modus_ponens,[status(thm)],[55,54]) ).

tff(57,plain,
    p_12,
    inference(modus_ponens,[status(thm)],[56,53]) ).

tff(58,plain,
    ( p_12
  <=> $true ),
    inference(iff_true,[status(thm)],[57]) ).

tff(59,plain,
    ( ~ p_12
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[58]) ).

tff(60,plain,
    ( ~ p_12
  <=> $false ),
    inference(transitivity,[status(thm)],[59,2]) ).

tff(61,plain,
    ( ( q_11
      | ~ p_12 )
  <=> ( q_11
      | $false ) ),
    inference(monotonicity,[status(thm)],[60]) ).

tff(62,plain,
    ( ( q_11
      | ~ p_12 )
  <=> q_11 ),
    inference(transitivity,[status(thm)],[61,30]) ).

tff(63,plain,
    ( ( q_11
      | ~ p_12
      | $false )
  <=> ( q_11
      | ~ p_12 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(64,plain,
    ( ( q_11
      | ~ p_12
      | ~ q_13 )
  <=> ( q_11
      | ~ p_12
      | $false ) ),
    inference(monotonicity,[status(thm)],[51]) ).

tff(65,plain,
    ( ( q_11
      | ~ p_12
      | ~ q_13 )
  <=> ( q_11
      | ~ p_12 ) ),
    inference(transitivity,[status(thm)],[64,63]) ).

tff(66,plain,
    ( ( q_11
      | ~ p_12
      | ~ q_13 )
  <=> ( q_11
      | ~ p_12
      | ~ q_13 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(67,axiom,
    ( q_11
    | ~ p_12
    | ~ q_13 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_type12_23) ).

tff(68,plain,
    ( q_11
    | ~ p_12
    | ~ q_13 ),
    inference(modus_ponens,[status(thm)],[67,66]) ).

tff(69,plain,
    ( q_11
    | ~ p_12 ),
    inference(modus_ponens,[status(thm)],[68,65]) ).

tff(70,plain,
    q_11,
    inference(modus_ponens,[status(thm)],[69,62]) ).

tff(71,plain,
    ( q_11
  <=> $true ),
    inference(iff_true,[status(thm)],[70]) ).

tff(72,plain,
    ( ~ q_11
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[71]) ).

tff(73,plain,
    ( ~ q_11
  <=> $false ),
    inference(transitivity,[status(thm)],[72,2]) ).

tff(74,plain,
    ( ( q_10
      | $false )
  <=> q_10 ),
    inference(rewrite,[status(thm)],]) ).

tff(75,plain,
    ( ( p_11
      | $false
      | $false )
  <=> p_11 ),
    inference(rewrite,[status(thm)],]) ).

tff(76,plain,
    ( ( q_12
      | $false
      | $false )
  <=> q_12 ),
    inference(rewrite,[status(thm)],]) ).

tff(77,axiom,
    p_14,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_1) ).

tff(78,plain,
    ( p_14
  <=> $true ),
    inference(iff_true,[status(thm)],[77]) ).

tff(79,plain,
    ( ~ p_14
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[78]) ).

tff(80,plain,
    ( ~ p_14
  <=> $false ),
    inference(transitivity,[status(thm)],[79,2]) ).

tff(81,plain,
    ( ( q_12
      | ~ q_13
      | ~ p_14 )
  <=> ( q_12
      | $false
      | $false ) ),
    inference(monotonicity,[status(thm)],[51,80]) ).

tff(82,plain,
    ( ( q_12
      | ~ q_13
      | ~ p_14 )
  <=> q_12 ),
    inference(transitivity,[status(thm)],[81,76]) ).

tff(83,plain,
    ( ( q_12
      | ~ q_13
      | ~ p_14 )
  <=> ( q_12
      | ~ q_13
      | ~ p_14 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(84,plain,
    ( ( q_12
      | ~ q_13
      | ~ p_14 )
  <=> ( q_12
      | ~ q_13
      | ~ p_14 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(85,axiom,
    ( q_12
    | ~ q_13
    | ~ p_14 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_type12_26) ).

tff(86,plain,
    ( q_12
    | ~ q_13
    | ~ p_14 ),
    inference(modus_ponens,[status(thm)],[85,84]) ).

tff(87,plain,
    ( q_12
    | ~ q_13
    | ~ p_14 ),
    inference(modus_ponens,[status(thm)],[86,83]) ).

tff(88,plain,
    q_12,
    inference(modus_ponens,[status(thm)],[87,82]) ).

tff(89,plain,
    ( q_12
  <=> $true ),
    inference(iff_true,[status(thm)],[88]) ).

tff(90,plain,
    ( ~ q_12
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[89]) ).

tff(91,plain,
    ( ~ q_12
  <=> $false ),
    inference(transitivity,[status(thm)],[90,2]) ).

tff(92,plain,
    ( ( p_11
      | ~ q_12
      | ~ q_13 )
  <=> ( p_11
      | $false
      | $false ) ),
    inference(monotonicity,[status(thm)],[91,51]) ).

tff(93,plain,
    ( ( p_11
      | ~ q_12
      | ~ q_13 )
  <=> p_11 ),
    inference(transitivity,[status(thm)],[92,75]) ).

tff(94,plain,
    ( ( p_11
      | ~ q_12
      | ~ q_13 )
  <=> ( p_11
      | ~ q_12
      | ~ q_13 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(95,axiom,
    ( p_11
    | ~ q_12
    | ~ q_13 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_type11_24) ).

tff(96,plain,
    ( p_11
    | ~ q_12
    | ~ q_13 ),
    inference(modus_ponens,[status(thm)],[95,94]) ).

tff(97,plain,
    p_11,
    inference(modus_ponens,[status(thm)],[96,93]) ).

tff(98,plain,
    ( p_11
  <=> $true ),
    inference(iff_true,[status(thm)],[97]) ).

tff(99,plain,
    ( ~ p_11
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[98]) ).

tff(100,plain,
    ( ~ p_11
  <=> $false ),
    inference(transitivity,[status(thm)],[99,2]) ).

tff(101,plain,
    ( ( q_10
      | ~ p_11 )
  <=> ( q_10
      | $false ) ),
    inference(monotonicity,[status(thm)],[100]) ).

tff(102,plain,
    ( ( q_10
      | ~ p_11 )
  <=> q_10 ),
    inference(transitivity,[status(thm)],[101,74]) ).

tff(103,plain,
    ( ( q_10
      | ~ p_11
      | $false )
  <=> ( q_10
      | ~ p_11 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(104,plain,
    ( ( q_10
      | ~ p_11
      | ~ q_12 )
  <=> ( q_10
      | ~ p_11
      | $false ) ),
    inference(monotonicity,[status(thm)],[91]) ).

tff(105,plain,
    ( ( q_10
      | ~ p_11
      | ~ q_12 )
  <=> ( q_10
      | ~ p_11 ) ),
    inference(transitivity,[status(thm)],[104,103]) ).

tff(106,plain,
    ( ( q_10
      | ~ p_11
      | ~ q_12 )
  <=> ( q_10
      | ~ p_11
      | ~ q_12 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(107,axiom,
    ( q_10
    | ~ p_11
    | ~ q_12 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_type12_21) ).

tff(108,plain,
    ( q_10
    | ~ p_11
    | ~ q_12 ),
    inference(modus_ponens,[status(thm)],[107,106]) ).

tff(109,plain,
    ( q_10
    | ~ p_11 ),
    inference(modus_ponens,[status(thm)],[108,105]) ).

tff(110,plain,
    q_10,
    inference(modus_ponens,[status(thm)],[109,102]) ).

tff(111,plain,
    ( q_10
  <=> $true ),
    inference(iff_true,[status(thm)],[110]) ).

tff(112,plain,
    ( ~ q_10
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[111]) ).

tff(113,plain,
    ( ~ q_10
  <=> $false ),
    inference(transitivity,[status(thm)],[112,2]) ).

tff(114,plain,
    ( ( p_9
      | ~ q_10
      | ~ q_11 )
  <=> ( p_9
      | $false
      | $false ) ),
    inference(monotonicity,[status(thm)],[113,73]) ).

tff(115,plain,
    ( ( p_9
      | ~ q_10
      | ~ q_11 )
  <=> p_9 ),
    inference(transitivity,[status(thm)],[114,29]) ).

tff(116,plain,
    ( ( p_9
      | ~ q_10
      | ~ q_11 )
  <=> ( p_9
      | ~ q_10
      | ~ q_11 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(117,axiom,
    ( p_9
    | ~ q_10
    | ~ q_11 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_type11_20) ).

tff(118,plain,
    ( p_9
    | ~ q_10
    | ~ q_11 ),
    inference(modus_ponens,[status(thm)],[117,116]) ).

tff(119,plain,
    p_9,
    inference(modus_ponens,[status(thm)],[118,115]) ).

tff(120,plain,
    ( p_9
  <=> $true ),
    inference(modus_ponens,[status(thm)],[119,28]) ).

tff(121,plain,
    ( ~ p_9
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[120]) ).

tff(122,plain,
    ( ~ p_9
  <=> $false ),
    inference(transitivity,[status(thm)],[121,2]) ).

tff(123,plain,
    ( ( p_8
    <=> $true )
  <=> p_8 ),
    inference(rewrite,[status(thm)],]) ).

tff(124,plain,
    ( p_8
  <=> ( p_8
    <=> $true ) ),
    inference(symmetry,[status(thm)],[123]) ).

tff(125,plain,
    ( ( p_8
      | $false
      | $false )
  <=> p_8 ),
    inference(rewrite,[status(thm)],]) ).

tff(126,plain,
    ( ( q_9
      | $false )
  <=> q_9 ),
    inference(rewrite,[status(thm)],]) ).

tff(127,plain,
    ( ( q_9
      | ~ q_10 )
  <=> ( q_9
      | $false ) ),
    inference(monotonicity,[status(thm)],[113]) ).

tff(128,plain,
    ( ( q_9
      | ~ q_10 )
  <=> q_9 ),
    inference(transitivity,[status(thm)],[127,126]) ).

tff(129,plain,
    ( ( q_9
      | ~ q_10
      | $false )
  <=> ( q_9
      | ~ q_10 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(130,plain,
    ( ( q_9
      | ~ q_10
      | ~ p_11 )
  <=> ( q_9
      | ~ q_10
      | $false ) ),
    inference(monotonicity,[status(thm)],[100]) ).

tff(131,plain,
    ( ( q_9
      | ~ q_10
      | ~ p_11 )
  <=> ( q_9
      | ~ q_10 ) ),
    inference(transitivity,[status(thm)],[130,129]) ).

tff(132,plain,
    ( ( q_9
      | ~ q_10
      | ~ p_11 )
  <=> ( q_9
      | ~ q_10
      | ~ p_11 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(133,plain,
    ( ( q_9
      | ~ q_10
      | ~ p_11 )
  <=> ( q_9
      | ~ q_10
      | ~ p_11 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(134,axiom,
    ( q_9
    | ~ q_10
    | ~ p_11 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_type12_20) ).

tff(135,plain,
    ( q_9
    | ~ q_10
    | ~ p_11 ),
    inference(modus_ponens,[status(thm)],[134,133]) ).

tff(136,plain,
    ( q_9
    | ~ q_10
    | ~ p_11 ),
    inference(modus_ponens,[status(thm)],[135,132]) ).

tff(137,plain,
    ( q_9
    | ~ q_10
    | ~ p_11 ),
    inference(modus_ponens,[status(thm)],[136,132]) ).

tff(138,plain,
    ( q_9
    | ~ q_10 ),
    inference(modus_ponens,[status(thm)],[137,131]) ).

tff(139,plain,
    q_9,
    inference(modus_ponens,[status(thm)],[138,128]) ).

tff(140,plain,
    ( q_9
  <=> $true ),
    inference(iff_true,[status(thm)],[139]) ).

tff(141,plain,
    ( ~ q_9
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[140]) ).

tff(142,plain,
    ( ~ q_9
  <=> $false ),
    inference(transitivity,[status(thm)],[141,2]) ).

tff(143,plain,
    ( ( p_8
      | ~ q_9
      | ~ q_10 )
  <=> ( p_8
      | $false
      | $false ) ),
    inference(monotonicity,[status(thm)],[142,113]) ).

tff(144,plain,
    ( ( p_8
      | ~ q_9
      | ~ q_10 )
  <=> p_8 ),
    inference(transitivity,[status(thm)],[143,125]) ).

tff(145,plain,
    ( ( p_8
      | ~ q_9
      | ~ q_10 )
  <=> ( p_8
      | ~ q_9
      | ~ q_10 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(146,plain,
    ( ( p_8
      | ~ q_9
      | ~ q_10 )
  <=> ( p_8
      | ~ q_9
      | ~ q_10 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(147,axiom,
    ( p_8
    | ~ q_9
    | ~ q_10 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_type11_18) ).

tff(148,plain,
    ( p_8
    | ~ q_9
    | ~ q_10 ),
    inference(modus_ponens,[status(thm)],[147,146]) ).

tff(149,plain,
    ( p_8
    | ~ q_9
    | ~ q_10 ),
    inference(modus_ponens,[status(thm)],[148,145]) ).

tff(150,plain,
    ( p_8
    | ~ q_9
    | ~ q_10 ),
    inference(modus_ponens,[status(thm)],[149,145]) ).

tff(151,plain,
    p_8,
    inference(modus_ponens,[status(thm)],[150,144]) ).

tff(152,plain,
    ( p_8
  <=> $true ),
    inference(modus_ponens,[status(thm)],[151,124]) ).

tff(153,plain,
    ( ~ p_8
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[152]) ).

tff(154,plain,
    ( ~ p_8
  <=> $false ),
    inference(transitivity,[status(thm)],[153,2]) ).

tff(155,plain,
    ( ( p_7
      | ~ p_8
      | ~ p_9 )
  <=> ( p_7
      | $false
      | $false ) ),
    inference(monotonicity,[status(thm)],[154,122]) ).

tff(156,plain,
    ( ( p_7
      | ~ p_8
      | ~ p_9 )
  <=> p_7 ),
    inference(transitivity,[status(thm)],[155,26]) ).

tff(157,plain,
    ( ( p_7
      | ~ p_8
      | ~ p_9 )
  <=> ( p_7
      | ~ p_8
      | ~ p_9 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(158,axiom,
    ( p_7
    | ~ p_8
    | ~ p_9 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_type11_15) ).

tff(159,plain,
    ( p_7
    | ~ p_8
    | ~ p_9 ),
    inference(modus_ponens,[status(thm)],[158,157]) ).

tff(160,plain,
    p_7,
    inference(modus_ponens,[status(thm)],[159,156]) ).

tff(161,plain,
    ( p_7
  <=> $true ),
    inference(modus_ponens,[status(thm)],[160,25]) ).

tff(162,plain,
    ( ~ p_7
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[161]) ).

tff(163,plain,
    ( ~ p_7
  <=> $false ),
    inference(transitivity,[status(thm)],[162,2]) ).

tff(164,plain,
    ( ( p_6
      | ~ p_7 )
  <=> ( p_6
      | $false ) ),
    inference(monotonicity,[status(thm)],[163]) ).

tff(165,plain,
    ( ( p_6
      | ~ p_7 )
  <=> p_6 ),
    inference(transitivity,[status(thm)],[164,23]) ).

tff(166,plain,
    ( ( p_6
      | ~ p_7
      | $false )
  <=> ( p_6
      | ~ p_7 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(167,plain,
    ( ( p_6
      | ~ p_7
      | ~ p_8 )
  <=> ( p_6
      | ~ p_7
      | $false ) ),
    inference(monotonicity,[status(thm)],[154]) ).

tff(168,plain,
    ( ( p_6
      | ~ p_7
      | ~ p_8 )
  <=> ( p_6
      | ~ p_7 ) ),
    inference(transitivity,[status(thm)],[167,166]) ).

tff(169,plain,
    ( ( p_6
      | ~ p_7
      | ~ p_8 )
  <=> ( p_6
      | ~ p_7
      | ~ p_8 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(170,axiom,
    ( p_6
    | ~ p_7
    | ~ p_8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_type11_13) ).

tff(171,plain,
    ( p_6
    | ~ p_7
    | ~ p_8 ),
    inference(modus_ponens,[status(thm)],[170,169]) ).

tff(172,plain,
    ( p_6
    | ~ p_7 ),
    inference(modus_ponens,[status(thm)],[171,168]) ).

tff(173,plain,
    p_6,
    inference(modus_ponens,[status(thm)],[172,165]) ).

tff(174,plain,
    ( p_6
  <=> $true ),
    inference(modus_ponens,[status(thm)],[173,22]) ).

tff(175,plain,
    ( ~ p_6
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[174]) ).

tff(176,plain,
    ( ~ p_6
  <=> $false ),
    inference(transitivity,[status(thm)],[175,2]) ).

tff(177,plain,
    ( ( p_5
      | ~ p_6 )
  <=> ( p_5
      | $false ) ),
    inference(monotonicity,[status(thm)],[176]) ).

tff(178,plain,
    ( ( p_5
      | ~ p_6 )
  <=> p_5 ),
    inference(transitivity,[status(thm)],[177,20]) ).

tff(179,plain,
    ( ( p_5
      | ~ p_6
      | $false )
  <=> ( p_5
      | ~ p_6 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(180,plain,
    ( ( p_5
      | ~ p_6
      | ~ p_7 )
  <=> ( p_5
      | ~ p_6
      | $false ) ),
    inference(monotonicity,[status(thm)],[163]) ).

tff(181,plain,
    ( ( p_5
      | ~ p_6
      | ~ p_7 )
  <=> ( p_5
      | ~ p_6 ) ),
    inference(transitivity,[status(thm)],[180,179]) ).

tff(182,plain,
    ( ( p_5
      | ~ p_6
      | ~ p_7 )
  <=> ( p_5
      | ~ p_6
      | ~ p_7 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(183,axiom,
    ( p_5
    | ~ p_6
    | ~ p_7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_type11_11) ).

tff(184,plain,
    ( p_5
    | ~ p_6
    | ~ p_7 ),
    inference(modus_ponens,[status(thm)],[183,182]) ).

tff(185,plain,
    ( p_5
    | ~ p_6 ),
    inference(modus_ponens,[status(thm)],[184,181]) ).

tff(186,plain,
    p_5,
    inference(modus_ponens,[status(thm)],[185,178]) ).

tff(187,plain,
    ( p_5
  <=> $true ),
    inference(modus_ponens,[status(thm)],[186,19]) ).

tff(188,plain,
    ( ~ p_5
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[187]) ).

tff(189,plain,
    ( ~ p_5
  <=> $false ),
    inference(transitivity,[status(thm)],[188,2]) ).

tff(190,plain,
    ( ( p_4
      | ~ p_5 )
  <=> ( p_4
      | $false ) ),
    inference(monotonicity,[status(thm)],[189]) ).

tff(191,plain,
    ( ( p_4
      | ~ p_5 )
  <=> p_4 ),
    inference(transitivity,[status(thm)],[190,17]) ).

tff(192,plain,
    ( ( p_4
      | ~ p_5
      | $false )
  <=> ( p_4
      | ~ p_5 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(193,plain,
    ( ( p_4
      | ~ p_5
      | ~ p_6 )
  <=> ( p_4
      | ~ p_5
      | $false ) ),
    inference(monotonicity,[status(thm)],[176]) ).

tff(194,plain,
    ( ( p_4
      | ~ p_5
      | ~ p_6 )
  <=> ( p_4
      | ~ p_5 ) ),
    inference(transitivity,[status(thm)],[193,192]) ).

tff(195,plain,
    ( ( p_4
      | ~ p_5
      | ~ p_6 )
  <=> ( p_4
      | ~ p_5
      | ~ p_6 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(196,axiom,
    ( p_4
    | ~ p_5
    | ~ p_6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_type11_9) ).

tff(197,plain,
    ( p_4
    | ~ p_5
    | ~ p_6 ),
    inference(modus_ponens,[status(thm)],[196,195]) ).

tff(198,plain,
    ( p_4
    | ~ p_5 ),
    inference(modus_ponens,[status(thm)],[197,194]) ).

tff(199,plain,
    p_4,
    inference(modus_ponens,[status(thm)],[198,191]) ).

tff(200,plain,
    ( p_4
  <=> $true ),
    inference(modus_ponens,[status(thm)],[199,16]) ).

tff(201,plain,
    ( ~ p_4
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[200]) ).

tff(202,plain,
    ( ~ p_4
  <=> $false ),
    inference(transitivity,[status(thm)],[201,2]) ).

tff(203,plain,
    ( ( p_3
      | ~ p_4 )
  <=> ( p_3
      | $false ) ),
    inference(monotonicity,[status(thm)],[202]) ).

tff(204,plain,
    ( ( p_3
      | ~ p_4 )
  <=> p_3 ),
    inference(transitivity,[status(thm)],[203,14]) ).

tff(205,plain,
    ( ( p_3
      | ~ p_4
      | $false )
  <=> ( p_3
      | ~ p_4 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(206,plain,
    ( ( p_3
      | ~ p_4
      | ~ p_5 )
  <=> ( p_3
      | ~ p_4
      | $false ) ),
    inference(monotonicity,[status(thm)],[189]) ).

tff(207,plain,
    ( ( p_3
      | ~ p_4
      | ~ p_5 )
  <=> ( p_3
      | ~ p_4 ) ),
    inference(transitivity,[status(thm)],[206,205]) ).

tff(208,plain,
    ( ( p_3
      | ~ p_4
      | ~ p_5 )
  <=> ( p_3
      | ~ p_4
      | ~ p_5 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(209,axiom,
    ( p_3
    | ~ p_4
    | ~ p_5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_type11_7) ).

tff(210,plain,
    ( p_3
    | ~ p_4
    | ~ p_5 ),
    inference(modus_ponens,[status(thm)],[209,208]) ).

tff(211,plain,
    ( p_3
    | ~ p_4 ),
    inference(modus_ponens,[status(thm)],[210,207]) ).

tff(212,plain,
    p_3,
    inference(modus_ponens,[status(thm)],[211,204]) ).

tff(213,plain,
    ( p_3
  <=> $true ),
    inference(modus_ponens,[status(thm)],[212,13]) ).

tff(214,plain,
    ( ~ p_3
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[213]) ).

tff(215,plain,
    ( ~ p_3
  <=> $false ),
    inference(transitivity,[status(thm)],[214,2]) ).

tff(216,plain,
    ( ( p_2
      | ~ p_3 )
  <=> ( p_2
      | $false ) ),
    inference(monotonicity,[status(thm)],[215]) ).

tff(217,plain,
    ( ( p_2
      | ~ p_3 )
  <=> p_2 ),
    inference(transitivity,[status(thm)],[216,11]) ).

tff(218,plain,
    ( ( p_2
      | ~ p_3
      | $false )
  <=> ( p_2
      | ~ p_3 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(219,plain,
    ( ( p_2
      | ~ p_3
      | ~ p_4 )
  <=> ( p_2
      | ~ p_3
      | $false ) ),
    inference(monotonicity,[status(thm)],[202]) ).

tff(220,plain,
    ( ( p_2
      | ~ p_3
      | ~ p_4 )
  <=> ( p_2
      | ~ p_3 ) ),
    inference(transitivity,[status(thm)],[219,218]) ).

tff(221,plain,
    ( ( p_2
      | ~ p_3
      | ~ p_4 )
  <=> ( p_2
      | ~ p_3
      | ~ p_4 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(222,axiom,
    ( p_2
    | ~ p_3
    | ~ p_4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_type11_5) ).

tff(223,plain,
    ( p_2
    | ~ p_3
    | ~ p_4 ),
    inference(modus_ponens,[status(thm)],[222,221]) ).

tff(224,plain,
    ( p_2
    | ~ p_3 ),
    inference(modus_ponens,[status(thm)],[223,220]) ).

tff(225,plain,
    p_2,
    inference(modus_ponens,[status(thm)],[224,217]) ).

tff(226,plain,
    ( p_2
  <=> $true ),
    inference(modus_ponens,[status(thm)],[225,10]) ).

tff(227,plain,
    ( ~ p_2
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[226]) ).

tff(228,plain,
    ( ~ p_2
  <=> $false ),
    inference(transitivity,[status(thm)],[227,2]) ).

tff(229,plain,
    ( ( p_1
      | ~ p_2 )
  <=> ( p_1
      | $false ) ),
    inference(monotonicity,[status(thm)],[228]) ).

tff(230,plain,
    ( ( p_1
      | ~ p_2 )
  <=> p_1 ),
    inference(transitivity,[status(thm)],[229,8]) ).

tff(231,plain,
    ( ( p_1
      | ~ p_2
      | $false )
  <=> ( p_1
      | ~ p_2 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(232,plain,
    ( ( p_1
      | ~ p_2
      | ~ p_3 )
  <=> ( p_1
      | ~ p_2
      | $false ) ),
    inference(monotonicity,[status(thm)],[215]) ).

tff(233,plain,
    ( ( p_1
      | ~ p_2
      | ~ p_3 )
  <=> ( p_1
      | ~ p_2 ) ),
    inference(transitivity,[status(thm)],[232,231]) ).

tff(234,plain,
    ( ( p_1
      | ~ p_2
      | ~ p_3 )
  <=> ( p_1
      | ~ p_2
      | ~ p_3 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(235,axiom,
    ( p_1
    | ~ p_2
    | ~ p_3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_type11_3) ).

tff(236,plain,
    ( p_1
    | ~ p_2
    | ~ p_3 ),
    inference(modus_ponens,[status(thm)],[235,234]) ).

tff(237,plain,
    ( p_1
    | ~ p_2 ),
    inference(modus_ponens,[status(thm)],[236,233]) ).

tff(238,plain,
    p_1,
    inference(modus_ponens,[status(thm)],[237,230]) ).

tff(239,plain,
    ( p_1
  <=> $true ),
    inference(modus_ponens,[status(thm)],[238,7]) ).

tff(240,plain,
    ( ~ p_1
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[239]) ).

tff(241,plain,
    ( ~ p_1
  <=> $false ),
    inference(transitivity,[status(thm)],[240,2]) ).

tff(242,plain,
    ( ( q_0
      | ~ p_1 )
  <=> ( q_0
      | $false ) ),
    inference(monotonicity,[status(thm)],[241]) ).

tff(243,plain,
    ( ( q_0
      | ~ p_1 )
  <=> q_0 ),
    inference(transitivity,[status(thm)],[242,5]) ).

tff(244,plain,
    ( ( q_0
      | ~ p_1
      | $false )
  <=> ( q_0
      | ~ p_1 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(245,plain,
    ( ( q_2
    <=> $true )
  <=> q_2 ),
    inference(rewrite,[status(thm)],]) ).

tff(246,plain,
    ( q_2
  <=> ( q_2
    <=> $true ) ),
    inference(symmetry,[status(thm)],[245]) ).

tff(247,plain,
    ( ( q_2
      | $false )
  <=> q_2 ),
    inference(rewrite,[status(thm)],]) ).

tff(248,plain,
    ( ( q_2
      | ~ p_3 )
  <=> ( q_2
      | $false ) ),
    inference(monotonicity,[status(thm)],[215]) ).

tff(249,plain,
    ( ( q_2
      | ~ p_3 )
  <=> q_2 ),
    inference(transitivity,[status(thm)],[248,247]) ).

tff(250,plain,
    ( ( q_2
      | ~ p_3
      | $false )
  <=> ( q_2
      | ~ p_3 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(251,plain,
    ( ( q_4
    <=> $true )
  <=> q_4 ),
    inference(rewrite,[status(thm)],]) ).

tff(252,plain,
    ( q_4
  <=> ( q_4
    <=> $true ) ),
    inference(symmetry,[status(thm)],[251]) ).

tff(253,plain,
    ( ( q_4
      | $false )
  <=> q_4 ),
    inference(rewrite,[status(thm)],]) ).

tff(254,plain,
    ( ( q_4
      | ~ p_5 )
  <=> ( q_4
      | $false ) ),
    inference(monotonicity,[status(thm)],[189]) ).

tff(255,plain,
    ( ( q_4
      | ~ p_5 )
  <=> q_4 ),
    inference(transitivity,[status(thm)],[254,253]) ).

tff(256,plain,
    ( ( q_4
      | ~ p_5
      | $false )
  <=> ( q_4
      | ~ p_5 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(257,plain,
    ( ( q_6
    <=> $true )
  <=> q_6 ),
    inference(rewrite,[status(thm)],]) ).

tff(258,plain,
    ( q_6
  <=> ( q_6
    <=> $true ) ),
    inference(symmetry,[status(thm)],[257]) ).

tff(259,plain,
    ( ( q_6
      | $false
      | $false )
  <=> q_6 ),
    inference(rewrite,[status(thm)],]) ).

tff(260,plain,
    ( ( q_8
    <=> $true )
  <=> q_8 ),
    inference(rewrite,[status(thm)],]) ).

tff(261,plain,
    ( q_8
  <=> ( q_8
    <=> $true ) ),
    inference(symmetry,[status(thm)],[260]) ).

tff(262,plain,
    ( ( q_8
      | $false )
  <=> q_8 ),
    inference(rewrite,[status(thm)],]) ).

tff(263,plain,
    ( ( q_8
      | ~ p_9 )
  <=> ( q_8
      | $false ) ),
    inference(monotonicity,[status(thm)],[122]) ).

tff(264,plain,
    ( ( q_8
      | ~ p_9 )
  <=> q_8 ),
    inference(transitivity,[status(thm)],[263,262]) ).

tff(265,plain,
    ( ( q_8
      | ~ p_9
      | $false )
  <=> ( q_8
      | ~ p_9 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(266,plain,
    ( ( q_8
      | ~ p_9
      | ~ q_10 )
  <=> ( q_8
      | ~ p_9
      | $false ) ),
    inference(monotonicity,[status(thm)],[113]) ).

tff(267,plain,
    ( ( q_8
      | ~ p_9
      | ~ q_10 )
  <=> ( q_8
      | ~ p_9 ) ),
    inference(transitivity,[status(thm)],[266,265]) ).

tff(268,plain,
    ( ( q_8
      | ~ p_9
      | ~ q_10 )
  <=> ( q_8
      | ~ p_9
      | ~ q_10 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(269,axiom,
    ( q_8
    | ~ p_9
    | ~ q_10 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_type12_17) ).

tff(270,plain,
    ( q_8
    | ~ p_9
    | ~ q_10 ),
    inference(modus_ponens,[status(thm)],[269,268]) ).

tff(271,plain,
    ( q_8
    | ~ p_9 ),
    inference(modus_ponens,[status(thm)],[270,267]) ).

tff(272,plain,
    q_8,
    inference(modus_ponens,[status(thm)],[271,264]) ).

tff(273,plain,
    ( q_8
  <=> $true ),
    inference(modus_ponens,[status(thm)],[272,261]) ).

tff(274,plain,
    ( ~ q_8
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[273]) ).

tff(275,plain,
    ( ~ q_8
  <=> $false ),
    inference(transitivity,[status(thm)],[274,2]) ).

tff(276,plain,
    ( ( q_6
      | ~ p_7
      | ~ q_8 )
  <=> ( q_6
      | $false
      | $false ) ),
    inference(monotonicity,[status(thm)],[163,275]) ).

tff(277,plain,
    ( ( q_6
      | ~ p_7
      | ~ q_8 )
  <=> q_6 ),
    inference(transitivity,[status(thm)],[276,259]) ).

tff(278,plain,
    ( ( q_6
      | ~ p_7
      | ~ q_8 )
  <=> ( q_6
      | ~ p_7
      | ~ q_8 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(279,axiom,
    ( q_6
    | ~ p_7
    | ~ q_8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_type12_13) ).

tff(280,plain,
    ( q_6
    | ~ p_7
    | ~ q_8 ),
    inference(modus_ponens,[status(thm)],[279,278]) ).

tff(281,plain,
    q_6,
    inference(modus_ponens,[status(thm)],[280,277]) ).

tff(282,plain,
    ( q_6
  <=> $true ),
    inference(modus_ponens,[status(thm)],[281,258]) ).

tff(283,plain,
    ( ~ q_6
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[282]) ).

tff(284,plain,
    ( ~ q_6
  <=> $false ),
    inference(transitivity,[status(thm)],[283,2]) ).

tff(285,plain,
    ( ( q_4
      | ~ p_5
      | ~ q_6 )
  <=> ( q_4
      | ~ p_5
      | $false ) ),
    inference(monotonicity,[status(thm)],[284]) ).

tff(286,plain,
    ( ( q_4
      | ~ p_5
      | ~ q_6 )
  <=> ( q_4
      | ~ p_5 ) ),
    inference(transitivity,[status(thm)],[285,256]) ).

tff(287,plain,
    ( ( q_4
      | ~ p_5
      | ~ q_6 )
  <=> ( q_4
      | ~ p_5
      | ~ q_6 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(288,axiom,
    ( q_4
    | ~ p_5
    | ~ q_6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_type12_9) ).

tff(289,plain,
    ( q_4
    | ~ p_5
    | ~ q_6 ),
    inference(modus_ponens,[status(thm)],[288,287]) ).

tff(290,plain,
    ( q_4
    | ~ p_5 ),
    inference(modus_ponens,[status(thm)],[289,286]) ).

tff(291,plain,
    q_4,
    inference(modus_ponens,[status(thm)],[290,255]) ).

tff(292,plain,
    ( q_4
  <=> $true ),
    inference(modus_ponens,[status(thm)],[291,252]) ).

tff(293,plain,
    ( ~ q_4
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[292]) ).

tff(294,plain,
    ( ~ q_4
  <=> $false ),
    inference(transitivity,[status(thm)],[293,2]) ).

tff(295,plain,
    ( ( q_2
      | ~ p_3
      | ~ q_4 )
  <=> ( q_2
      | ~ p_3
      | $false ) ),
    inference(monotonicity,[status(thm)],[294]) ).

tff(296,plain,
    ( ( q_2
      | ~ p_3
      | ~ q_4 )
  <=> ( q_2
      | ~ p_3 ) ),
    inference(transitivity,[status(thm)],[295,250]) ).

tff(297,plain,
    ( ( q_2
      | ~ p_3
      | ~ q_4 )
  <=> ( q_2
      | ~ p_3
      | ~ q_4 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(298,axiom,
    ( q_2
    | ~ p_3
    | ~ q_4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_type12_5) ).

tff(299,plain,
    ( q_2
    | ~ p_3
    | ~ q_4 ),
    inference(modus_ponens,[status(thm)],[298,297]) ).

tff(300,plain,
    ( q_2
    | ~ p_3 ),
    inference(modus_ponens,[status(thm)],[299,296]) ).

tff(301,plain,
    q_2,
    inference(modus_ponens,[status(thm)],[300,249]) ).

tff(302,plain,
    ( q_2
  <=> $true ),
    inference(modus_ponens,[status(thm)],[301,246]) ).

tff(303,plain,
    ( ~ q_2
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[302]) ).

tff(304,plain,
    ( ~ q_2
  <=> $false ),
    inference(transitivity,[status(thm)],[303,2]) ).

tff(305,plain,
    ( ( q_0
      | ~ p_1
      | ~ q_2 )
  <=> ( q_0
      | ~ p_1
      | $false ) ),
    inference(monotonicity,[status(thm)],[304]) ).

tff(306,plain,
    ( ( q_0
      | ~ p_1
      | ~ q_2 )
  <=> ( q_0
      | ~ p_1 ) ),
    inference(transitivity,[status(thm)],[305,244]) ).

tff(307,plain,
    ( ( q_0
      | ~ p_1
      | ~ q_2 )
  <=> ( q_0
      | ~ p_1
      | ~ q_2 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(308,axiom,
    ( q_0
    | ~ p_1
    | ~ q_2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_type12_1) ).

tff(309,plain,
    ( q_0
    | ~ p_1
    | ~ q_2 ),
    inference(modus_ponens,[status(thm)],[308,307]) ).

tff(310,plain,
    ( q_0
    | ~ p_1 ),
    inference(modus_ponens,[status(thm)],[309,306]) ).

tff(311,plain,
    q_0,
    inference(modus_ponens,[status(thm)],[310,243]) ).

tff(312,plain,
    ( q_0
  <=> $true ),
    inference(modus_ponens,[status(thm)],[311,4]) ).

tff(313,plain,
    ( ~ q_0
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[312]) ).

tff(314,plain,
    ( ~ q_0
  <=> $false ),
    inference(transitivity,[status(thm)],[313,2]) ).

tff(315,plain,
    ( ( p_0
    <=> $true )
  <=> p_0 ),
    inference(rewrite,[status(thm)],]) ).

tff(316,plain,
    ( p_0
  <=> ( p_0
    <=> $true ) ),
    inference(symmetry,[status(thm)],[315]) ).

tff(317,plain,
    ( ( p_0
      | $false )
  <=> p_0 ),
    inference(rewrite,[status(thm)],]) ).

tff(318,plain,
    ( ( p_0
      | ~ p_1 )
  <=> ( p_0
      | $false ) ),
    inference(monotonicity,[status(thm)],[241]) ).

tff(319,plain,
    ( ( p_0
      | ~ p_1 )
  <=> p_0 ),
    inference(transitivity,[status(thm)],[318,317]) ).

tff(320,plain,
    ( ( p_0
      | ~ p_1
      | $false )
  <=> ( p_0
      | ~ p_1 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(321,plain,
    ( ( p_0
      | ~ p_1
      | ~ p_2 )
  <=> ( p_0
      | ~ p_1
      | $false ) ),
    inference(monotonicity,[status(thm)],[228]) ).

tff(322,plain,
    ( ( p_0
      | ~ p_1
      | ~ p_2 )
  <=> ( p_0
      | ~ p_1 ) ),
    inference(transitivity,[status(thm)],[321,320]) ).

tff(323,plain,
    ( ( p_0
      | ~ p_1
      | ~ p_2 )
  <=> ( p_0
      | ~ p_1
      | ~ p_2 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(324,axiom,
    ( p_0
    | ~ p_1
    | ~ p_2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_type11_1) ).

tff(325,plain,
    ( p_0
    | ~ p_1
    | ~ p_2 ),
    inference(modus_ponens,[status(thm)],[324,323]) ).

tff(326,plain,
    ( p_0
    | ~ p_1 ),
    inference(modus_ponens,[status(thm)],[325,322]) ).

tff(327,plain,
    p_0,
    inference(modus_ponens,[status(thm)],[326,319]) ).

tff(328,plain,
    ( p_0
  <=> $true ),
    inference(modus_ponens,[status(thm)],[327,316]) ).

tff(329,plain,
    ( ~ p_0
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[328]) ).

tff(330,plain,
    ( ~ p_0
  <=> $false ),
    inference(transitivity,[status(thm)],[329,2]) ).

tff(331,plain,
    ( ( ~ p_0
      | ~ q_0 )
  <=> ( $false
      | $false ) ),
    inference(monotonicity,[status(thm)],[330,314]) ).

tff(332,plain,
    ( ( ~ p_0
      | ~ q_0 )
  <=> $false ),
    inference(transitivity,[status(thm)],[331,1]) ).

tff(333,axiom,
    ( ~ p_0
    | ~ q_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_goal_1) ).

tff(334,plain,
    $false,
    inference(modus_ponens,[status(thm)],[333,332]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : SYN090-1.008 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.00/0.11  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.31  % Computer : n013.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Mon Sep  5 01:40:17 EDT 2022
% 0.10/0.31  % CPUTime  : 
% 0.10/0.31  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.31  Usage: tptp [options] [-file:]file
% 0.10/0.31    -h, -?       prints this message.
% 0.10/0.31    -smt2        print SMT-LIB2 benchmark.
% 0.10/0.31    -m, -model   generate model.
% 0.10/0.31    -p, -proof   generate proof.
% 0.10/0.31    -c, -core    generate unsat core of named formulas.
% 0.10/0.31    -st, -statistics display statistics.
% 0.10/0.31    -t:timeout   set timeout (in second).
% 0.10/0.31    -smt2status  display status in smt2 format instead of SZS.
% 0.10/0.31    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.31    -<param>:<value> configuration parameter and value.
% 0.10/0.31    -o:<output-file> file to place output in.
% 0.16/0.35  % SZS status Unsatisfiable
% 0.16/0.35  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------