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
%------------------------------------------------------------------------------