TSTP Solution File: SYN010-1.005.005 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN010-1.005.005 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 23:53:10 EDT 2022
% Result : Unsatisfiable 0.13s 0.35s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 160
% Syntax : Number of formulae : 449 ( 27 unt; 26 typ; 0 def)
% Number of atoms : 3030 ( 0 equ)
% Maximal formula atoms : 12 ( 7 avg)
% Number of connectives : 4735 (2128 ~;2254 |; 0 &)
% ( 353 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 6 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 : 28 ( 26 usr; 28 prp; 0-0 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(p_1_5_type,type,
p_1_5: $o ).
tff(p_1_4_type,type,
p_1_4: $o ).
tff(p_1_3_type,type,
p_1_3: $o ).
tff(p_1_2_type,type,
p_1_2: $o ).
tff(p_1_1_type,type,
p_1_1: $o ).
tff(p_2_5_type,type,
p_2_5: $o ).
tff(p_2_4_type,type,
p_2_4: $o ).
tff(p_2_3_type,type,
p_2_3: $o ).
tff(p_2_2_type,type,
p_2_2: $o ).
tff(p_2_1_type,type,
p_2_1: $o ).
tff(p_3_5_type,type,
p_3_5: $o ).
tff(p_3_4_type,type,
p_3_4: $o ).
tff(p_3_3_type,type,
p_3_3: $o ).
tff(p_3_2_type,type,
p_3_2: $o ).
tff(p_3_1_type,type,
p_3_1: $o ).
tff(p_4_5_type,type,
p_4_5: $o ).
tff(p_4_4_type,type,
p_4_4: $o ).
tff(p_4_3_type,type,
p_4_3: $o ).
tff(p_4_2_type,type,
p_4_2: $o ).
tff(p_4_1_type,type,
p_4_1: $o ).
tff(p_5_5_type,type,
p_5_5: $o ).
tff(p_5_4_type,type,
p_5_4: $o ).
tff(p_5_3_type,type,
p_5_3: $o ).
tff(p_5_2_type,type,
p_5_2: $o ).
tff(p_5_1_type,type,
p_5_1: $o ).
tff(p_0_type,type,
p_0: $o ).
tff(1,plain,
( ( $false
| $false
| $false
| $false
| $false )
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( ( p_1_5
| $false
| $false
| $false
| $false
| $false )
<=> p_1_5 ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
( ( p_2_5
| $false
| $false
| $false
| $false
| $false )
<=> p_2_5 ),
inference(rewrite,[status(thm)],]) ).
tff(5,plain,
( ( p_3_5
| $false
| $false
| $false
| $false
| $false )
<=> p_3_5 ),
inference(rewrite,[status(thm)],]) ).
tff(6,plain,
( ( p_4_5
| $false
| $false
| $false
| $false
| $false )
<=> p_4_5 ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
p_5_5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_27) ).
tff(8,plain,
( p_5_5
<=> $true ),
inference(iff_true,[status(thm)],[7]) ).
tff(9,plain,
( ~ p_5_5
<=> ~ $true ),
inference(monotonicity,[status(thm)],[8]) ).
tff(10,plain,
( ~ p_5_5
<=> $false ),
inference(transitivity,[status(thm)],[9,2]) ).
tff(11,axiom,
p_5_4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_26) ).
tff(12,plain,
( p_5_4
<=> $true ),
inference(iff_true,[status(thm)],[11]) ).
tff(13,plain,
( ~ p_5_4
<=> ~ $true ),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
( ~ p_5_4
<=> $false ),
inference(transitivity,[status(thm)],[13,2]) ).
tff(15,axiom,
p_5_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_25) ).
tff(16,plain,
( p_5_3
<=> $true ),
inference(iff_true,[status(thm)],[15]) ).
tff(17,plain,
( ~ p_5_3
<=> ~ $true ),
inference(monotonicity,[status(thm)],[16]) ).
tff(18,plain,
( ~ p_5_3
<=> $false ),
inference(transitivity,[status(thm)],[17,2]) ).
tff(19,axiom,
p_5_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_24) ).
tff(20,plain,
( p_5_2
<=> $true ),
inference(iff_true,[status(thm)],[19]) ).
tff(21,plain,
( ~ p_5_2
<=> ~ $true ),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
( ~ p_5_2
<=> $false ),
inference(transitivity,[status(thm)],[21,2]) ).
tff(23,axiom,
p_5_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_23) ).
tff(24,plain,
( p_5_1
<=> $true ),
inference(iff_true,[status(thm)],[23]) ).
tff(25,plain,
( ~ p_5_1
<=> ~ $true ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ~ p_5_1
<=> $false ),
inference(transitivity,[status(thm)],[25,2]) ).
tff(27,plain,
( ( p_4_5
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 )
<=> ( p_4_5
| $false
| $false
| $false
| $false
| $false ) ),
inference(monotonicity,[status(thm)],[26,22,18,14,10]) ).
tff(28,plain,
( ( p_4_5
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 )
<=> p_4_5 ),
inference(transitivity,[status(thm)],[27,6]) ).
tff(29,plain,
( ( p_4_5
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 )
<=> ( p_4_5
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( p_4_5
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4 )
<=> ( p_4_5
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4 ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( ( p_4_5
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3 )
<=> ( p_4_5
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
( ( p_4_5
| ~ p_5_1
| ~ p_5_2 )
<=> ( p_4_5
| ~ p_5_1
| ~ p_5_2 ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
( ( p_4_5
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3 )
<=> ( p_4_5
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3 ) ),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
( ( p_4_5
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3 )
<=> ( p_4_5
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3 ) ),
inference(transitivity,[status(thm)],[33,31]) ).
tff(35,plain,
( ( p_4_5
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4 )
<=> ( p_4_5
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4 ) ),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
( ( p_4_5
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4 )
<=> ( p_4_5
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4 ) ),
inference(transitivity,[status(thm)],[35,30]) ).
tff(37,plain,
( ( p_4_5
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 )
<=> ( p_4_5
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 ) ),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
( ( p_4_5
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 )
<=> ( p_4_5
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 ) ),
inference(transitivity,[status(thm)],[37,29]) ).
tff(39,axiom,
( p_4_5
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_22) ).
tff(40,plain,
( p_4_5
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
p_4_5,
inference(modus_ponens,[status(thm)],[40,28]) ).
tff(42,plain,
( p_4_5
<=> $true ),
inference(iff_true,[status(thm)],[41]) ).
tff(43,plain,
( ~ p_4_5
<=> ~ $true ),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
( ~ p_4_5
<=> $false ),
inference(transitivity,[status(thm)],[43,2]) ).
tff(45,plain,
( ( p_4_4
| $false
| $false
| $false
| $false
| $false )
<=> p_4_4 ),
inference(rewrite,[status(thm)],]) ).
tff(46,plain,
( ( p_4_4
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 )
<=> ( p_4_4
| $false
| $false
| $false
| $false
| $false ) ),
inference(monotonicity,[status(thm)],[26,22,18,14,10]) ).
tff(47,plain,
( ( p_4_4
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 )
<=> p_4_4 ),
inference(transitivity,[status(thm)],[46,45]) ).
tff(48,plain,
( ( p_4_4
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 )
<=> ( p_4_4
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,plain,
( ( p_4_4
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4 )
<=> ( p_4_4
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4 ) ),
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
( ( p_4_4
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3 )
<=> ( p_4_4
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
( ( p_4_4
| ~ p_5_1
| ~ p_5_2 )
<=> ( p_4_4
| ~ p_5_1
| ~ p_5_2 ) ),
inference(rewrite,[status(thm)],]) ).
tff(52,plain,
( ( p_4_4
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3 )
<=> ( p_4_4
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3 ) ),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
( ( p_4_4
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3 )
<=> ( p_4_4
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3 ) ),
inference(transitivity,[status(thm)],[52,50]) ).
tff(54,plain,
( ( p_4_4
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4 )
<=> ( p_4_4
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4 ) ),
inference(monotonicity,[status(thm)],[53]) ).
tff(55,plain,
( ( p_4_4
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4 )
<=> ( p_4_4
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4 ) ),
inference(transitivity,[status(thm)],[54,49]) ).
tff(56,plain,
( ( p_4_4
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 )
<=> ( p_4_4
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 ) ),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
( ( p_4_4
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 )
<=> ( p_4_4
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 ) ),
inference(transitivity,[status(thm)],[56,48]) ).
tff(58,axiom,
( p_4_4
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_21) ).
tff(59,plain,
( p_4_4
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
p_4_4,
inference(modus_ponens,[status(thm)],[59,47]) ).
tff(61,plain,
( p_4_4
<=> $true ),
inference(iff_true,[status(thm)],[60]) ).
tff(62,plain,
( ~ p_4_4
<=> ~ $true ),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
( ~ p_4_4
<=> $false ),
inference(transitivity,[status(thm)],[62,2]) ).
tff(64,plain,
( ( p_4_3
| $false
| $false
| $false
| $false
| $false )
<=> p_4_3 ),
inference(rewrite,[status(thm)],]) ).
tff(65,plain,
( ( p_4_3
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 )
<=> ( p_4_3
| $false
| $false
| $false
| $false
| $false ) ),
inference(monotonicity,[status(thm)],[26,22,18,14,10]) ).
tff(66,plain,
( ( p_4_3
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 )
<=> p_4_3 ),
inference(transitivity,[status(thm)],[65,64]) ).
tff(67,plain,
( ( p_4_3
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 )
<=> ( p_4_3
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,plain,
( ( p_4_3
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4 )
<=> ( p_4_3
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4 ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
( ( p_4_3
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3 )
<=> ( p_4_3
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(70,plain,
( ( p_4_3
| ~ p_5_1
| ~ p_5_2 )
<=> ( p_4_3
| ~ p_5_1
| ~ p_5_2 ) ),
inference(rewrite,[status(thm)],]) ).
tff(71,plain,
( ( p_4_3
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3 )
<=> ( p_4_3
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3 ) ),
inference(monotonicity,[status(thm)],[70]) ).
tff(72,plain,
( ( p_4_3
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3 )
<=> ( p_4_3
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3 ) ),
inference(transitivity,[status(thm)],[71,69]) ).
tff(73,plain,
( ( p_4_3
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4 )
<=> ( p_4_3
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4 ) ),
inference(monotonicity,[status(thm)],[72]) ).
tff(74,plain,
( ( p_4_3
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4 )
<=> ( p_4_3
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4 ) ),
inference(transitivity,[status(thm)],[73,68]) ).
tff(75,plain,
( ( p_4_3
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 )
<=> ( p_4_3
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 ) ),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,plain,
( ( p_4_3
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 )
<=> ( p_4_3
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 ) ),
inference(transitivity,[status(thm)],[75,67]) ).
tff(77,axiom,
( p_4_3
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_20) ).
tff(78,plain,
( p_4_3
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
p_4_3,
inference(modus_ponens,[status(thm)],[78,66]) ).
tff(80,plain,
( p_4_3
<=> $true ),
inference(iff_true,[status(thm)],[79]) ).
tff(81,plain,
( ~ p_4_3
<=> ~ $true ),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
( ~ p_4_3
<=> $false ),
inference(transitivity,[status(thm)],[81,2]) ).
tff(83,plain,
( ( p_4_2
| $false
| $false
| $false
| $false
| $false )
<=> p_4_2 ),
inference(rewrite,[status(thm)],]) ).
tff(84,plain,
( ( p_4_2
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 )
<=> ( p_4_2
| $false
| $false
| $false
| $false
| $false ) ),
inference(monotonicity,[status(thm)],[26,22,18,14,10]) ).
tff(85,plain,
( ( p_4_2
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 )
<=> p_4_2 ),
inference(transitivity,[status(thm)],[84,83]) ).
tff(86,plain,
( ( p_4_2
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 )
<=> ( p_4_2
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 ) ),
inference(rewrite,[status(thm)],]) ).
tff(87,plain,
( ( p_4_2
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4 )
<=> ( p_4_2
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4 ) ),
inference(rewrite,[status(thm)],]) ).
tff(88,plain,
( ( p_4_2
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3 )
<=> ( p_4_2
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(89,plain,
( ( p_4_2
| ~ p_5_1
| ~ p_5_2 )
<=> ( p_4_2
| ~ p_5_1
| ~ p_5_2 ) ),
inference(rewrite,[status(thm)],]) ).
tff(90,plain,
( ( p_4_2
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3 )
<=> ( p_4_2
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3 ) ),
inference(monotonicity,[status(thm)],[89]) ).
tff(91,plain,
( ( p_4_2
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3 )
<=> ( p_4_2
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3 ) ),
inference(transitivity,[status(thm)],[90,88]) ).
tff(92,plain,
( ( p_4_2
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4 )
<=> ( p_4_2
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4 ) ),
inference(monotonicity,[status(thm)],[91]) ).
tff(93,plain,
( ( p_4_2
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4 )
<=> ( p_4_2
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4 ) ),
inference(transitivity,[status(thm)],[92,87]) ).
tff(94,plain,
( ( p_4_2
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 )
<=> ( p_4_2
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 ) ),
inference(monotonicity,[status(thm)],[93]) ).
tff(95,plain,
( ( p_4_2
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 )
<=> ( p_4_2
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 ) ),
inference(transitivity,[status(thm)],[94,86]) ).
tff(96,axiom,
( p_4_2
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_19) ).
tff(97,plain,
( p_4_2
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 ),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
p_4_2,
inference(modus_ponens,[status(thm)],[97,85]) ).
tff(99,plain,
( p_4_2
<=> $true ),
inference(iff_true,[status(thm)],[98]) ).
tff(100,plain,
( ~ p_4_2
<=> ~ $true ),
inference(monotonicity,[status(thm)],[99]) ).
tff(101,plain,
( ~ p_4_2
<=> $false ),
inference(transitivity,[status(thm)],[100,2]) ).
tff(102,plain,
( ( p_4_1
| $false
| $false
| $false
| $false
| $false )
<=> p_4_1 ),
inference(rewrite,[status(thm)],]) ).
tff(103,plain,
( ( p_4_1
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 )
<=> ( p_4_1
| $false
| $false
| $false
| $false
| $false ) ),
inference(monotonicity,[status(thm)],[26,22,18,14,10]) ).
tff(104,plain,
( ( p_4_1
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 )
<=> p_4_1 ),
inference(transitivity,[status(thm)],[103,102]) ).
tff(105,plain,
( ( p_4_1
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 )
<=> ( p_4_1
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 ) ),
inference(rewrite,[status(thm)],]) ).
tff(106,plain,
( ( p_4_1
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4 )
<=> ( p_4_1
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4 ) ),
inference(rewrite,[status(thm)],]) ).
tff(107,plain,
( ( p_4_1
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3 )
<=> ( p_4_1
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(108,plain,
( ( p_4_1
| ~ p_5_1
| ~ p_5_2 )
<=> ( p_4_1
| ~ p_5_1
| ~ p_5_2 ) ),
inference(rewrite,[status(thm)],]) ).
tff(109,plain,
( ( p_4_1
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3 )
<=> ( p_4_1
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3 ) ),
inference(monotonicity,[status(thm)],[108]) ).
tff(110,plain,
( ( p_4_1
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3 )
<=> ( p_4_1
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3 ) ),
inference(transitivity,[status(thm)],[109,107]) ).
tff(111,plain,
( ( p_4_1
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4 )
<=> ( p_4_1
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4 ) ),
inference(monotonicity,[status(thm)],[110]) ).
tff(112,plain,
( ( p_4_1
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4 )
<=> ( p_4_1
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4 ) ),
inference(transitivity,[status(thm)],[111,106]) ).
tff(113,plain,
( ( p_4_1
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 )
<=> ( p_4_1
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 ) ),
inference(monotonicity,[status(thm)],[112]) ).
tff(114,plain,
( ( p_4_1
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 )
<=> ( p_4_1
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 ) ),
inference(transitivity,[status(thm)],[113,105]) ).
tff(115,axiom,
( p_4_1
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_18) ).
tff(116,plain,
( p_4_1
| ~ p_5_1
| ~ p_5_2
| ~ p_5_3
| ~ p_5_4
| ~ p_5_5 ),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
p_4_1,
inference(modus_ponens,[status(thm)],[116,104]) ).
tff(118,plain,
( p_4_1
<=> $true ),
inference(iff_true,[status(thm)],[117]) ).
tff(119,plain,
( ~ p_4_1
<=> ~ $true ),
inference(monotonicity,[status(thm)],[118]) ).
tff(120,plain,
( ~ p_4_1
<=> $false ),
inference(transitivity,[status(thm)],[119,2]) ).
tff(121,plain,
( ( p_3_5
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 )
<=> ( p_3_5
| $false
| $false
| $false
| $false
| $false ) ),
inference(monotonicity,[status(thm)],[120,101,82,63,44]) ).
tff(122,plain,
( ( p_3_5
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 )
<=> p_3_5 ),
inference(transitivity,[status(thm)],[121,5]) ).
tff(123,plain,
( ( p_3_5
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 )
<=> ( p_3_5
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 ) ),
inference(rewrite,[status(thm)],]) ).
tff(124,plain,
( ( p_3_5
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4 )
<=> ( p_3_5
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4 ) ),
inference(rewrite,[status(thm)],]) ).
tff(125,plain,
( ( p_3_5
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3 )
<=> ( p_3_5
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(126,plain,
( ( p_3_5
| ~ p_4_1
| ~ p_4_2 )
<=> ( p_3_5
| ~ p_4_1
| ~ p_4_2 ) ),
inference(rewrite,[status(thm)],]) ).
tff(127,plain,
( ( p_3_5
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3 )
<=> ( p_3_5
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3 ) ),
inference(monotonicity,[status(thm)],[126]) ).
tff(128,plain,
( ( p_3_5
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3 )
<=> ( p_3_5
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3 ) ),
inference(transitivity,[status(thm)],[127,125]) ).
tff(129,plain,
( ( p_3_5
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4 )
<=> ( p_3_5
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4 ) ),
inference(monotonicity,[status(thm)],[128]) ).
tff(130,plain,
( ( p_3_5
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4 )
<=> ( p_3_5
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4 ) ),
inference(transitivity,[status(thm)],[129,124]) ).
tff(131,plain,
( ( p_3_5
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 )
<=> ( p_3_5
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 ) ),
inference(monotonicity,[status(thm)],[130]) ).
tff(132,plain,
( ( p_3_5
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 )
<=> ( p_3_5
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 ) ),
inference(transitivity,[status(thm)],[131,123]) ).
tff(133,axiom,
( p_3_5
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_17) ).
tff(134,plain,
( p_3_5
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 ),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
p_3_5,
inference(modus_ponens,[status(thm)],[134,122]) ).
tff(136,plain,
( p_3_5
<=> $true ),
inference(iff_true,[status(thm)],[135]) ).
tff(137,plain,
( ~ p_3_5
<=> ~ $true ),
inference(monotonicity,[status(thm)],[136]) ).
tff(138,plain,
( ~ p_3_5
<=> $false ),
inference(transitivity,[status(thm)],[137,2]) ).
tff(139,plain,
( ( p_3_4
| $false
| $false
| $false
| $false
| $false )
<=> p_3_4 ),
inference(rewrite,[status(thm)],]) ).
tff(140,plain,
( ( p_3_4
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 )
<=> ( p_3_4
| $false
| $false
| $false
| $false
| $false ) ),
inference(monotonicity,[status(thm)],[120,101,82,63,44]) ).
tff(141,plain,
( ( p_3_4
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 )
<=> p_3_4 ),
inference(transitivity,[status(thm)],[140,139]) ).
tff(142,plain,
( ( p_3_4
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 )
<=> ( p_3_4
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 ) ),
inference(rewrite,[status(thm)],]) ).
tff(143,plain,
( ( p_3_4
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4 )
<=> ( p_3_4
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4 ) ),
inference(rewrite,[status(thm)],]) ).
tff(144,plain,
( ( p_3_4
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3 )
<=> ( p_3_4
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(145,plain,
( ( p_3_4
| ~ p_4_1
| ~ p_4_2 )
<=> ( p_3_4
| ~ p_4_1
| ~ p_4_2 ) ),
inference(rewrite,[status(thm)],]) ).
tff(146,plain,
( ( p_3_4
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3 )
<=> ( p_3_4
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3 ) ),
inference(monotonicity,[status(thm)],[145]) ).
tff(147,plain,
( ( p_3_4
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3 )
<=> ( p_3_4
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3 ) ),
inference(transitivity,[status(thm)],[146,144]) ).
tff(148,plain,
( ( p_3_4
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4 )
<=> ( p_3_4
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4 ) ),
inference(monotonicity,[status(thm)],[147]) ).
tff(149,plain,
( ( p_3_4
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4 )
<=> ( p_3_4
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4 ) ),
inference(transitivity,[status(thm)],[148,143]) ).
tff(150,plain,
( ( p_3_4
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 )
<=> ( p_3_4
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 ) ),
inference(monotonicity,[status(thm)],[149]) ).
tff(151,plain,
( ( p_3_4
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 )
<=> ( p_3_4
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 ) ),
inference(transitivity,[status(thm)],[150,142]) ).
tff(152,axiom,
( p_3_4
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_16) ).
tff(153,plain,
( p_3_4
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 ),
inference(modus_ponens,[status(thm)],[152,151]) ).
tff(154,plain,
p_3_4,
inference(modus_ponens,[status(thm)],[153,141]) ).
tff(155,plain,
( p_3_4
<=> $true ),
inference(iff_true,[status(thm)],[154]) ).
tff(156,plain,
( ~ p_3_4
<=> ~ $true ),
inference(monotonicity,[status(thm)],[155]) ).
tff(157,plain,
( ~ p_3_4
<=> $false ),
inference(transitivity,[status(thm)],[156,2]) ).
tff(158,plain,
( ( p_3_3
| $false
| $false
| $false
| $false
| $false )
<=> p_3_3 ),
inference(rewrite,[status(thm)],]) ).
tff(159,plain,
( ( p_3_3
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 )
<=> ( p_3_3
| $false
| $false
| $false
| $false
| $false ) ),
inference(monotonicity,[status(thm)],[120,101,82,63,44]) ).
tff(160,plain,
( ( p_3_3
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 )
<=> p_3_3 ),
inference(transitivity,[status(thm)],[159,158]) ).
tff(161,plain,
( ( p_3_3
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 )
<=> ( p_3_3
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 ) ),
inference(rewrite,[status(thm)],]) ).
tff(162,plain,
( ( p_3_3
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4 )
<=> ( p_3_3
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4 ) ),
inference(rewrite,[status(thm)],]) ).
tff(163,plain,
( ( p_3_3
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3 )
<=> ( p_3_3
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(164,plain,
( ( p_3_3
| ~ p_4_1
| ~ p_4_2 )
<=> ( p_3_3
| ~ p_4_1
| ~ p_4_2 ) ),
inference(rewrite,[status(thm)],]) ).
tff(165,plain,
( ( p_3_3
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3 )
<=> ( p_3_3
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3 ) ),
inference(monotonicity,[status(thm)],[164]) ).
tff(166,plain,
( ( p_3_3
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3 )
<=> ( p_3_3
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3 ) ),
inference(transitivity,[status(thm)],[165,163]) ).
tff(167,plain,
( ( p_3_3
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4 )
<=> ( p_3_3
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4 ) ),
inference(monotonicity,[status(thm)],[166]) ).
tff(168,plain,
( ( p_3_3
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4 )
<=> ( p_3_3
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4 ) ),
inference(transitivity,[status(thm)],[167,162]) ).
tff(169,plain,
( ( p_3_3
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 )
<=> ( p_3_3
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 ) ),
inference(monotonicity,[status(thm)],[168]) ).
tff(170,plain,
( ( p_3_3
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 )
<=> ( p_3_3
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 ) ),
inference(transitivity,[status(thm)],[169,161]) ).
tff(171,axiom,
( p_3_3
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_15) ).
tff(172,plain,
( p_3_3
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 ),
inference(modus_ponens,[status(thm)],[171,170]) ).
tff(173,plain,
p_3_3,
inference(modus_ponens,[status(thm)],[172,160]) ).
tff(174,plain,
( p_3_3
<=> $true ),
inference(iff_true,[status(thm)],[173]) ).
tff(175,plain,
( ~ p_3_3
<=> ~ $true ),
inference(monotonicity,[status(thm)],[174]) ).
tff(176,plain,
( ~ p_3_3
<=> $false ),
inference(transitivity,[status(thm)],[175,2]) ).
tff(177,plain,
( ( p_3_2
| $false
| $false
| $false
| $false
| $false )
<=> p_3_2 ),
inference(rewrite,[status(thm)],]) ).
tff(178,plain,
( ( p_3_2
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 )
<=> ( p_3_2
| $false
| $false
| $false
| $false
| $false ) ),
inference(monotonicity,[status(thm)],[120,101,82,63,44]) ).
tff(179,plain,
( ( p_3_2
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 )
<=> p_3_2 ),
inference(transitivity,[status(thm)],[178,177]) ).
tff(180,plain,
( ( p_3_2
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 )
<=> ( p_3_2
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 ) ),
inference(rewrite,[status(thm)],]) ).
tff(181,plain,
( ( p_3_2
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4 )
<=> ( p_3_2
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4 ) ),
inference(rewrite,[status(thm)],]) ).
tff(182,plain,
( ( p_3_2
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3 )
<=> ( p_3_2
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(183,plain,
( ( p_3_2
| ~ p_4_1
| ~ p_4_2 )
<=> ( p_3_2
| ~ p_4_1
| ~ p_4_2 ) ),
inference(rewrite,[status(thm)],]) ).
tff(184,plain,
( ( p_3_2
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3 )
<=> ( p_3_2
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3 ) ),
inference(monotonicity,[status(thm)],[183]) ).
tff(185,plain,
( ( p_3_2
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3 )
<=> ( p_3_2
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3 ) ),
inference(transitivity,[status(thm)],[184,182]) ).
tff(186,plain,
( ( p_3_2
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4 )
<=> ( p_3_2
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4 ) ),
inference(monotonicity,[status(thm)],[185]) ).
tff(187,plain,
( ( p_3_2
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4 )
<=> ( p_3_2
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4 ) ),
inference(transitivity,[status(thm)],[186,181]) ).
tff(188,plain,
( ( p_3_2
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 )
<=> ( p_3_2
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 ) ),
inference(monotonicity,[status(thm)],[187]) ).
tff(189,plain,
( ( p_3_2
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 )
<=> ( p_3_2
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 ) ),
inference(transitivity,[status(thm)],[188,180]) ).
tff(190,axiom,
( p_3_2
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_14) ).
tff(191,plain,
( p_3_2
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 ),
inference(modus_ponens,[status(thm)],[190,189]) ).
tff(192,plain,
p_3_2,
inference(modus_ponens,[status(thm)],[191,179]) ).
tff(193,plain,
( p_3_2
<=> $true ),
inference(iff_true,[status(thm)],[192]) ).
tff(194,plain,
( ~ p_3_2
<=> ~ $true ),
inference(monotonicity,[status(thm)],[193]) ).
tff(195,plain,
( ~ p_3_2
<=> $false ),
inference(transitivity,[status(thm)],[194,2]) ).
tff(196,plain,
( ( p_3_1
| $false
| $false
| $false
| $false
| $false )
<=> p_3_1 ),
inference(rewrite,[status(thm)],]) ).
tff(197,plain,
( ( p_3_1
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 )
<=> ( p_3_1
| $false
| $false
| $false
| $false
| $false ) ),
inference(monotonicity,[status(thm)],[120,101,82,63,44]) ).
tff(198,plain,
( ( p_3_1
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 )
<=> p_3_1 ),
inference(transitivity,[status(thm)],[197,196]) ).
tff(199,plain,
( ( p_3_1
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 )
<=> ( p_3_1
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 ) ),
inference(rewrite,[status(thm)],]) ).
tff(200,plain,
( ( p_3_1
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4 )
<=> ( p_3_1
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4 ) ),
inference(rewrite,[status(thm)],]) ).
tff(201,plain,
( ( p_3_1
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3 )
<=> ( p_3_1
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(202,plain,
( ( p_3_1
| ~ p_4_1
| ~ p_4_2 )
<=> ( p_3_1
| ~ p_4_1
| ~ p_4_2 ) ),
inference(rewrite,[status(thm)],]) ).
tff(203,plain,
( ( p_3_1
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3 )
<=> ( p_3_1
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3 ) ),
inference(monotonicity,[status(thm)],[202]) ).
tff(204,plain,
( ( p_3_1
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3 )
<=> ( p_3_1
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3 ) ),
inference(transitivity,[status(thm)],[203,201]) ).
tff(205,plain,
( ( p_3_1
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4 )
<=> ( p_3_1
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4 ) ),
inference(monotonicity,[status(thm)],[204]) ).
tff(206,plain,
( ( p_3_1
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4 )
<=> ( p_3_1
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4 ) ),
inference(transitivity,[status(thm)],[205,200]) ).
tff(207,plain,
( ( p_3_1
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 )
<=> ( p_3_1
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 ) ),
inference(monotonicity,[status(thm)],[206]) ).
tff(208,plain,
( ( p_3_1
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 )
<=> ( p_3_1
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 ) ),
inference(transitivity,[status(thm)],[207,199]) ).
tff(209,axiom,
( p_3_1
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_13) ).
tff(210,plain,
( p_3_1
| ~ p_4_1
| ~ p_4_2
| ~ p_4_3
| ~ p_4_4
| ~ p_4_5 ),
inference(modus_ponens,[status(thm)],[209,208]) ).
tff(211,plain,
p_3_1,
inference(modus_ponens,[status(thm)],[210,198]) ).
tff(212,plain,
( p_3_1
<=> $true ),
inference(iff_true,[status(thm)],[211]) ).
tff(213,plain,
( ~ p_3_1
<=> ~ $true ),
inference(monotonicity,[status(thm)],[212]) ).
tff(214,plain,
( ~ p_3_1
<=> $false ),
inference(transitivity,[status(thm)],[213,2]) ).
tff(215,plain,
( ( p_2_5
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 )
<=> ( p_2_5
| $false
| $false
| $false
| $false
| $false ) ),
inference(monotonicity,[status(thm)],[214,195,176,157,138]) ).
tff(216,plain,
( ( p_2_5
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 )
<=> p_2_5 ),
inference(transitivity,[status(thm)],[215,4]) ).
tff(217,plain,
( ( p_2_5
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 )
<=> ( p_2_5
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 ) ),
inference(rewrite,[status(thm)],]) ).
tff(218,plain,
( ( p_2_5
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4 )
<=> ( p_2_5
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4 ) ),
inference(rewrite,[status(thm)],]) ).
tff(219,plain,
( ( p_2_5
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3 )
<=> ( p_2_5
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(220,plain,
( ( p_2_5
| ~ p_3_1
| ~ p_3_2 )
<=> ( p_2_5
| ~ p_3_1
| ~ p_3_2 ) ),
inference(rewrite,[status(thm)],]) ).
tff(221,plain,
( ( p_2_5
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3 )
<=> ( p_2_5
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3 ) ),
inference(monotonicity,[status(thm)],[220]) ).
tff(222,plain,
( ( p_2_5
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3 )
<=> ( p_2_5
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3 ) ),
inference(transitivity,[status(thm)],[221,219]) ).
tff(223,plain,
( ( p_2_5
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4 )
<=> ( p_2_5
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4 ) ),
inference(monotonicity,[status(thm)],[222]) ).
tff(224,plain,
( ( p_2_5
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4 )
<=> ( p_2_5
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4 ) ),
inference(transitivity,[status(thm)],[223,218]) ).
tff(225,plain,
( ( p_2_5
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 )
<=> ( p_2_5
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 ) ),
inference(monotonicity,[status(thm)],[224]) ).
tff(226,plain,
( ( p_2_5
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 )
<=> ( p_2_5
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 ) ),
inference(transitivity,[status(thm)],[225,217]) ).
tff(227,axiom,
( p_2_5
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_12) ).
tff(228,plain,
( p_2_5
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 ),
inference(modus_ponens,[status(thm)],[227,226]) ).
tff(229,plain,
p_2_5,
inference(modus_ponens,[status(thm)],[228,216]) ).
tff(230,plain,
( p_2_5
<=> $true ),
inference(iff_true,[status(thm)],[229]) ).
tff(231,plain,
( ~ p_2_5
<=> ~ $true ),
inference(monotonicity,[status(thm)],[230]) ).
tff(232,plain,
( ~ p_2_5
<=> $false ),
inference(transitivity,[status(thm)],[231,2]) ).
tff(233,plain,
( ( p_2_4
| $false
| $false
| $false
| $false
| $false )
<=> p_2_4 ),
inference(rewrite,[status(thm)],]) ).
tff(234,plain,
( ( p_2_4
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 )
<=> ( p_2_4
| $false
| $false
| $false
| $false
| $false ) ),
inference(monotonicity,[status(thm)],[214,195,176,157,138]) ).
tff(235,plain,
( ( p_2_4
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 )
<=> p_2_4 ),
inference(transitivity,[status(thm)],[234,233]) ).
tff(236,plain,
( ( p_2_4
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 )
<=> ( p_2_4
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 ) ),
inference(rewrite,[status(thm)],]) ).
tff(237,plain,
( ( p_2_4
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4 )
<=> ( p_2_4
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4 ) ),
inference(rewrite,[status(thm)],]) ).
tff(238,plain,
( ( p_2_4
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3 )
<=> ( p_2_4
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(239,plain,
( ( p_2_4
| ~ p_3_1
| ~ p_3_2 )
<=> ( p_2_4
| ~ p_3_1
| ~ p_3_2 ) ),
inference(rewrite,[status(thm)],]) ).
tff(240,plain,
( ( p_2_4
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3 )
<=> ( p_2_4
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3 ) ),
inference(monotonicity,[status(thm)],[239]) ).
tff(241,plain,
( ( p_2_4
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3 )
<=> ( p_2_4
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3 ) ),
inference(transitivity,[status(thm)],[240,238]) ).
tff(242,plain,
( ( p_2_4
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4 )
<=> ( p_2_4
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4 ) ),
inference(monotonicity,[status(thm)],[241]) ).
tff(243,plain,
( ( p_2_4
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4 )
<=> ( p_2_4
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4 ) ),
inference(transitivity,[status(thm)],[242,237]) ).
tff(244,plain,
( ( p_2_4
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 )
<=> ( p_2_4
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 ) ),
inference(monotonicity,[status(thm)],[243]) ).
tff(245,plain,
( ( p_2_4
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 )
<=> ( p_2_4
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 ) ),
inference(transitivity,[status(thm)],[244,236]) ).
tff(246,axiom,
( p_2_4
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_11) ).
tff(247,plain,
( p_2_4
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 ),
inference(modus_ponens,[status(thm)],[246,245]) ).
tff(248,plain,
p_2_4,
inference(modus_ponens,[status(thm)],[247,235]) ).
tff(249,plain,
( p_2_4
<=> $true ),
inference(iff_true,[status(thm)],[248]) ).
tff(250,plain,
( ~ p_2_4
<=> ~ $true ),
inference(monotonicity,[status(thm)],[249]) ).
tff(251,plain,
( ~ p_2_4
<=> $false ),
inference(transitivity,[status(thm)],[250,2]) ).
tff(252,plain,
( ( p_2_3
| $false
| $false
| $false
| $false
| $false )
<=> p_2_3 ),
inference(rewrite,[status(thm)],]) ).
tff(253,plain,
( ( p_2_3
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 )
<=> ( p_2_3
| $false
| $false
| $false
| $false
| $false ) ),
inference(monotonicity,[status(thm)],[214,195,176,157,138]) ).
tff(254,plain,
( ( p_2_3
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 )
<=> p_2_3 ),
inference(transitivity,[status(thm)],[253,252]) ).
tff(255,plain,
( ( p_2_3
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 )
<=> ( p_2_3
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 ) ),
inference(rewrite,[status(thm)],]) ).
tff(256,plain,
( ( p_2_3
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4 )
<=> ( p_2_3
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4 ) ),
inference(rewrite,[status(thm)],]) ).
tff(257,plain,
( ( p_2_3
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3 )
<=> ( p_2_3
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(258,plain,
( ( p_2_3
| ~ p_3_1
| ~ p_3_2 )
<=> ( p_2_3
| ~ p_3_1
| ~ p_3_2 ) ),
inference(rewrite,[status(thm)],]) ).
tff(259,plain,
( ( p_2_3
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3 )
<=> ( p_2_3
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3 ) ),
inference(monotonicity,[status(thm)],[258]) ).
tff(260,plain,
( ( p_2_3
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3 )
<=> ( p_2_3
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3 ) ),
inference(transitivity,[status(thm)],[259,257]) ).
tff(261,plain,
( ( p_2_3
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4 )
<=> ( p_2_3
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4 ) ),
inference(monotonicity,[status(thm)],[260]) ).
tff(262,plain,
( ( p_2_3
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4 )
<=> ( p_2_3
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4 ) ),
inference(transitivity,[status(thm)],[261,256]) ).
tff(263,plain,
( ( p_2_3
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 )
<=> ( p_2_3
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 ) ),
inference(monotonicity,[status(thm)],[262]) ).
tff(264,plain,
( ( p_2_3
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 )
<=> ( p_2_3
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 ) ),
inference(transitivity,[status(thm)],[263,255]) ).
tff(265,axiom,
( p_2_3
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_10) ).
tff(266,plain,
( p_2_3
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 ),
inference(modus_ponens,[status(thm)],[265,264]) ).
tff(267,plain,
p_2_3,
inference(modus_ponens,[status(thm)],[266,254]) ).
tff(268,plain,
( p_2_3
<=> $true ),
inference(iff_true,[status(thm)],[267]) ).
tff(269,plain,
( ~ p_2_3
<=> ~ $true ),
inference(monotonicity,[status(thm)],[268]) ).
tff(270,plain,
( ~ p_2_3
<=> $false ),
inference(transitivity,[status(thm)],[269,2]) ).
tff(271,plain,
( ( p_2_2
| $false
| $false
| $false
| $false
| $false )
<=> p_2_2 ),
inference(rewrite,[status(thm)],]) ).
tff(272,plain,
( ( p_2_2
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 )
<=> ( p_2_2
| $false
| $false
| $false
| $false
| $false ) ),
inference(monotonicity,[status(thm)],[214,195,176,157,138]) ).
tff(273,plain,
( ( p_2_2
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 )
<=> p_2_2 ),
inference(transitivity,[status(thm)],[272,271]) ).
tff(274,plain,
( ( p_2_2
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 )
<=> ( p_2_2
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 ) ),
inference(rewrite,[status(thm)],]) ).
tff(275,plain,
( ( p_2_2
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4 )
<=> ( p_2_2
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4 ) ),
inference(rewrite,[status(thm)],]) ).
tff(276,plain,
( ( p_2_2
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3 )
<=> ( p_2_2
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(277,plain,
( ( p_2_2
| ~ p_3_1
| ~ p_3_2 )
<=> ( p_2_2
| ~ p_3_1
| ~ p_3_2 ) ),
inference(rewrite,[status(thm)],]) ).
tff(278,plain,
( ( p_2_2
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3 )
<=> ( p_2_2
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3 ) ),
inference(monotonicity,[status(thm)],[277]) ).
tff(279,plain,
( ( p_2_2
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3 )
<=> ( p_2_2
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3 ) ),
inference(transitivity,[status(thm)],[278,276]) ).
tff(280,plain,
( ( p_2_2
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4 )
<=> ( p_2_2
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4 ) ),
inference(monotonicity,[status(thm)],[279]) ).
tff(281,plain,
( ( p_2_2
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4 )
<=> ( p_2_2
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4 ) ),
inference(transitivity,[status(thm)],[280,275]) ).
tff(282,plain,
( ( p_2_2
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 )
<=> ( p_2_2
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 ) ),
inference(monotonicity,[status(thm)],[281]) ).
tff(283,plain,
( ( p_2_2
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 )
<=> ( p_2_2
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 ) ),
inference(transitivity,[status(thm)],[282,274]) ).
tff(284,axiom,
( p_2_2
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_9) ).
tff(285,plain,
( p_2_2
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 ),
inference(modus_ponens,[status(thm)],[284,283]) ).
tff(286,plain,
p_2_2,
inference(modus_ponens,[status(thm)],[285,273]) ).
tff(287,plain,
( p_2_2
<=> $true ),
inference(iff_true,[status(thm)],[286]) ).
tff(288,plain,
( ~ p_2_2
<=> ~ $true ),
inference(monotonicity,[status(thm)],[287]) ).
tff(289,plain,
( ~ p_2_2
<=> $false ),
inference(transitivity,[status(thm)],[288,2]) ).
tff(290,plain,
( ( p_2_1
| $false
| $false
| $false
| $false
| $false )
<=> p_2_1 ),
inference(rewrite,[status(thm)],]) ).
tff(291,plain,
( ( p_2_1
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 )
<=> ( p_2_1
| $false
| $false
| $false
| $false
| $false ) ),
inference(monotonicity,[status(thm)],[214,195,176,157,138]) ).
tff(292,plain,
( ( p_2_1
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 )
<=> p_2_1 ),
inference(transitivity,[status(thm)],[291,290]) ).
tff(293,plain,
( ( p_2_1
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 )
<=> ( p_2_1
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 ) ),
inference(rewrite,[status(thm)],]) ).
tff(294,plain,
( ( p_2_1
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4 )
<=> ( p_2_1
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4 ) ),
inference(rewrite,[status(thm)],]) ).
tff(295,plain,
( ( p_2_1
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3 )
<=> ( p_2_1
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(296,plain,
( ( p_2_1
| ~ p_3_1
| ~ p_3_2 )
<=> ( p_2_1
| ~ p_3_1
| ~ p_3_2 ) ),
inference(rewrite,[status(thm)],]) ).
tff(297,plain,
( ( p_2_1
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3 )
<=> ( p_2_1
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3 ) ),
inference(monotonicity,[status(thm)],[296]) ).
tff(298,plain,
( ( p_2_1
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3 )
<=> ( p_2_1
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3 ) ),
inference(transitivity,[status(thm)],[297,295]) ).
tff(299,plain,
( ( p_2_1
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4 )
<=> ( p_2_1
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4 ) ),
inference(monotonicity,[status(thm)],[298]) ).
tff(300,plain,
( ( p_2_1
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4 )
<=> ( p_2_1
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4 ) ),
inference(transitivity,[status(thm)],[299,294]) ).
tff(301,plain,
( ( p_2_1
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 )
<=> ( p_2_1
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 ) ),
inference(monotonicity,[status(thm)],[300]) ).
tff(302,plain,
( ( p_2_1
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 )
<=> ( p_2_1
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 ) ),
inference(transitivity,[status(thm)],[301,293]) ).
tff(303,axiom,
( p_2_1
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8) ).
tff(304,plain,
( p_2_1
| ~ p_3_1
| ~ p_3_2
| ~ p_3_3
| ~ p_3_4
| ~ p_3_5 ),
inference(modus_ponens,[status(thm)],[303,302]) ).
tff(305,plain,
p_2_1,
inference(modus_ponens,[status(thm)],[304,292]) ).
tff(306,plain,
( p_2_1
<=> $true ),
inference(iff_true,[status(thm)],[305]) ).
tff(307,plain,
( ~ p_2_1
<=> ~ $true ),
inference(monotonicity,[status(thm)],[306]) ).
tff(308,plain,
( ~ p_2_1
<=> $false ),
inference(transitivity,[status(thm)],[307,2]) ).
tff(309,plain,
( ( p_1_5
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 )
<=> ( p_1_5
| $false
| $false
| $false
| $false
| $false ) ),
inference(monotonicity,[status(thm)],[308,289,270,251,232]) ).
tff(310,plain,
( ( p_1_5
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 )
<=> p_1_5 ),
inference(transitivity,[status(thm)],[309,3]) ).
tff(311,plain,
( ( p_1_5
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 )
<=> ( p_1_5
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 ) ),
inference(rewrite,[status(thm)],]) ).
tff(312,plain,
( ( p_1_5
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4 )
<=> ( p_1_5
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4 ) ),
inference(rewrite,[status(thm)],]) ).
tff(313,plain,
( ( p_1_5
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3 )
<=> ( p_1_5
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(314,plain,
( ( p_1_5
| ~ p_2_1
| ~ p_2_2 )
<=> ( p_1_5
| ~ p_2_1
| ~ p_2_2 ) ),
inference(rewrite,[status(thm)],]) ).
tff(315,plain,
( ( p_1_5
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3 )
<=> ( p_1_5
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3 ) ),
inference(monotonicity,[status(thm)],[314]) ).
tff(316,plain,
( ( p_1_5
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3 )
<=> ( p_1_5
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3 ) ),
inference(transitivity,[status(thm)],[315,313]) ).
tff(317,plain,
( ( p_1_5
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4 )
<=> ( p_1_5
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4 ) ),
inference(monotonicity,[status(thm)],[316]) ).
tff(318,plain,
( ( p_1_5
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4 )
<=> ( p_1_5
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4 ) ),
inference(transitivity,[status(thm)],[317,312]) ).
tff(319,plain,
( ( p_1_5
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 )
<=> ( p_1_5
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 ) ),
inference(monotonicity,[status(thm)],[318]) ).
tff(320,plain,
( ( p_1_5
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 )
<=> ( p_1_5
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 ) ),
inference(transitivity,[status(thm)],[319,311]) ).
tff(321,axiom,
( p_1_5
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7) ).
tff(322,plain,
( p_1_5
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 ),
inference(modus_ponens,[status(thm)],[321,320]) ).
tff(323,plain,
p_1_5,
inference(modus_ponens,[status(thm)],[322,310]) ).
tff(324,plain,
( p_1_5
<=> $true ),
inference(iff_true,[status(thm)],[323]) ).
tff(325,plain,
( ~ p_1_5
<=> ~ $true ),
inference(monotonicity,[status(thm)],[324]) ).
tff(326,plain,
( ~ p_1_5
<=> $false ),
inference(transitivity,[status(thm)],[325,2]) ).
tff(327,plain,
( ( p_1_4
| $false
| $false
| $false
| $false
| $false )
<=> p_1_4 ),
inference(rewrite,[status(thm)],]) ).
tff(328,plain,
( ( p_1_4
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 )
<=> ( p_1_4
| $false
| $false
| $false
| $false
| $false ) ),
inference(monotonicity,[status(thm)],[308,289,270,251,232]) ).
tff(329,plain,
( ( p_1_4
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 )
<=> p_1_4 ),
inference(transitivity,[status(thm)],[328,327]) ).
tff(330,plain,
( ( p_1_4
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 )
<=> ( p_1_4
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 ) ),
inference(rewrite,[status(thm)],]) ).
tff(331,plain,
( ( p_1_4
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4 )
<=> ( p_1_4
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4 ) ),
inference(rewrite,[status(thm)],]) ).
tff(332,plain,
( ( p_1_4
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3 )
<=> ( p_1_4
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(333,plain,
( ( p_1_4
| ~ p_2_1
| ~ p_2_2 )
<=> ( p_1_4
| ~ p_2_1
| ~ p_2_2 ) ),
inference(rewrite,[status(thm)],]) ).
tff(334,plain,
( ( p_1_4
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3 )
<=> ( p_1_4
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3 ) ),
inference(monotonicity,[status(thm)],[333]) ).
tff(335,plain,
( ( p_1_4
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3 )
<=> ( p_1_4
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3 ) ),
inference(transitivity,[status(thm)],[334,332]) ).
tff(336,plain,
( ( p_1_4
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4 )
<=> ( p_1_4
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4 ) ),
inference(monotonicity,[status(thm)],[335]) ).
tff(337,plain,
( ( p_1_4
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4 )
<=> ( p_1_4
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4 ) ),
inference(transitivity,[status(thm)],[336,331]) ).
tff(338,plain,
( ( p_1_4
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 )
<=> ( p_1_4
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 ) ),
inference(monotonicity,[status(thm)],[337]) ).
tff(339,plain,
( ( p_1_4
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 )
<=> ( p_1_4
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 ) ),
inference(transitivity,[status(thm)],[338,330]) ).
tff(340,axiom,
( p_1_4
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
tff(341,plain,
( p_1_4
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 ),
inference(modus_ponens,[status(thm)],[340,339]) ).
tff(342,plain,
p_1_4,
inference(modus_ponens,[status(thm)],[341,329]) ).
tff(343,plain,
( p_1_4
<=> $true ),
inference(iff_true,[status(thm)],[342]) ).
tff(344,plain,
( ~ p_1_4
<=> ~ $true ),
inference(monotonicity,[status(thm)],[343]) ).
tff(345,plain,
( ~ p_1_4
<=> $false ),
inference(transitivity,[status(thm)],[344,2]) ).
tff(346,plain,
( ( p_1_3
| $false
| $false
| $false
| $false
| $false )
<=> p_1_3 ),
inference(rewrite,[status(thm)],]) ).
tff(347,plain,
( ( p_1_3
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 )
<=> ( p_1_3
| $false
| $false
| $false
| $false
| $false ) ),
inference(monotonicity,[status(thm)],[308,289,270,251,232]) ).
tff(348,plain,
( ( p_1_3
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 )
<=> p_1_3 ),
inference(transitivity,[status(thm)],[347,346]) ).
tff(349,plain,
( ( p_1_3
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 )
<=> ( p_1_3
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 ) ),
inference(rewrite,[status(thm)],]) ).
tff(350,plain,
( ( p_1_3
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4 )
<=> ( p_1_3
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4 ) ),
inference(rewrite,[status(thm)],]) ).
tff(351,plain,
( ( p_1_3
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3 )
<=> ( p_1_3
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(352,plain,
( ( p_1_3
| ~ p_2_1
| ~ p_2_2 )
<=> ( p_1_3
| ~ p_2_1
| ~ p_2_2 ) ),
inference(rewrite,[status(thm)],]) ).
tff(353,plain,
( ( p_1_3
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3 )
<=> ( p_1_3
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3 ) ),
inference(monotonicity,[status(thm)],[352]) ).
tff(354,plain,
( ( p_1_3
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3 )
<=> ( p_1_3
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3 ) ),
inference(transitivity,[status(thm)],[353,351]) ).
tff(355,plain,
( ( p_1_3
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4 )
<=> ( p_1_3
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4 ) ),
inference(monotonicity,[status(thm)],[354]) ).
tff(356,plain,
( ( p_1_3
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4 )
<=> ( p_1_3
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4 ) ),
inference(transitivity,[status(thm)],[355,350]) ).
tff(357,plain,
( ( p_1_3
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 )
<=> ( p_1_3
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 ) ),
inference(monotonicity,[status(thm)],[356]) ).
tff(358,plain,
( ( p_1_3
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 )
<=> ( p_1_3
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 ) ),
inference(transitivity,[status(thm)],[357,349]) ).
tff(359,axiom,
( p_1_3
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
tff(360,plain,
( p_1_3
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 ),
inference(modus_ponens,[status(thm)],[359,358]) ).
tff(361,plain,
p_1_3,
inference(modus_ponens,[status(thm)],[360,348]) ).
tff(362,plain,
( p_1_3
<=> $true ),
inference(iff_true,[status(thm)],[361]) ).
tff(363,plain,
( ~ p_1_3
<=> ~ $true ),
inference(monotonicity,[status(thm)],[362]) ).
tff(364,plain,
( ~ p_1_3
<=> $false ),
inference(transitivity,[status(thm)],[363,2]) ).
tff(365,plain,
( ( p_1_2
| $false
| $false
| $false
| $false
| $false )
<=> p_1_2 ),
inference(rewrite,[status(thm)],]) ).
tff(366,plain,
( ( p_1_2
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 )
<=> ( p_1_2
| $false
| $false
| $false
| $false
| $false ) ),
inference(monotonicity,[status(thm)],[308,289,270,251,232]) ).
tff(367,plain,
( ( p_1_2
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 )
<=> p_1_2 ),
inference(transitivity,[status(thm)],[366,365]) ).
tff(368,plain,
( ( p_1_2
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 )
<=> ( p_1_2
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 ) ),
inference(rewrite,[status(thm)],]) ).
tff(369,plain,
( ( p_1_2
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4 )
<=> ( p_1_2
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4 ) ),
inference(rewrite,[status(thm)],]) ).
tff(370,plain,
( ( p_1_2
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3 )
<=> ( p_1_2
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(371,plain,
( ( p_1_2
| ~ p_2_1
| ~ p_2_2 )
<=> ( p_1_2
| ~ p_2_1
| ~ p_2_2 ) ),
inference(rewrite,[status(thm)],]) ).
tff(372,plain,
( ( p_1_2
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3 )
<=> ( p_1_2
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3 ) ),
inference(monotonicity,[status(thm)],[371]) ).
tff(373,plain,
( ( p_1_2
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3 )
<=> ( p_1_2
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3 ) ),
inference(transitivity,[status(thm)],[372,370]) ).
tff(374,plain,
( ( p_1_2
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4 )
<=> ( p_1_2
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4 ) ),
inference(monotonicity,[status(thm)],[373]) ).
tff(375,plain,
( ( p_1_2
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4 )
<=> ( p_1_2
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4 ) ),
inference(transitivity,[status(thm)],[374,369]) ).
tff(376,plain,
( ( p_1_2
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 )
<=> ( p_1_2
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 ) ),
inference(monotonicity,[status(thm)],[375]) ).
tff(377,plain,
( ( p_1_2
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 )
<=> ( p_1_2
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 ) ),
inference(transitivity,[status(thm)],[376,368]) ).
tff(378,axiom,
( p_1_2
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
tff(379,plain,
( p_1_2
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 ),
inference(modus_ponens,[status(thm)],[378,377]) ).
tff(380,plain,
p_1_2,
inference(modus_ponens,[status(thm)],[379,367]) ).
tff(381,plain,
( p_1_2
<=> $true ),
inference(iff_true,[status(thm)],[380]) ).
tff(382,plain,
( ~ p_1_2
<=> ~ $true ),
inference(monotonicity,[status(thm)],[381]) ).
tff(383,plain,
( ~ p_1_2
<=> $false ),
inference(transitivity,[status(thm)],[382,2]) ).
tff(384,plain,
( ( p_1_1
| $false
| $false
| $false
| $false
| $false )
<=> p_1_1 ),
inference(rewrite,[status(thm)],]) ).
tff(385,plain,
( ( p_1_1
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 )
<=> ( p_1_1
| $false
| $false
| $false
| $false
| $false ) ),
inference(monotonicity,[status(thm)],[308,289,270,251,232]) ).
tff(386,plain,
( ( p_1_1
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 )
<=> p_1_1 ),
inference(transitivity,[status(thm)],[385,384]) ).
tff(387,plain,
( ( p_1_1
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 )
<=> ( p_1_1
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 ) ),
inference(rewrite,[status(thm)],]) ).
tff(388,plain,
( ( p_1_1
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4 )
<=> ( p_1_1
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4 ) ),
inference(rewrite,[status(thm)],]) ).
tff(389,plain,
( ( p_1_1
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3 )
<=> ( p_1_1
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(390,plain,
( ( p_1_1
| ~ p_2_1
| ~ p_2_2 )
<=> ( p_1_1
| ~ p_2_1
| ~ p_2_2 ) ),
inference(rewrite,[status(thm)],]) ).
tff(391,plain,
( ( p_1_1
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3 )
<=> ( p_1_1
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3 ) ),
inference(monotonicity,[status(thm)],[390]) ).
tff(392,plain,
( ( p_1_1
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3 )
<=> ( p_1_1
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3 ) ),
inference(transitivity,[status(thm)],[391,389]) ).
tff(393,plain,
( ( p_1_1
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4 )
<=> ( p_1_1
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4 ) ),
inference(monotonicity,[status(thm)],[392]) ).
tff(394,plain,
( ( p_1_1
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4 )
<=> ( p_1_1
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4 ) ),
inference(transitivity,[status(thm)],[393,388]) ).
tff(395,plain,
( ( p_1_1
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 )
<=> ( p_1_1
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 ) ),
inference(monotonicity,[status(thm)],[394]) ).
tff(396,plain,
( ( p_1_1
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 )
<=> ( p_1_1
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 ) ),
inference(transitivity,[status(thm)],[395,387]) ).
tff(397,axiom,
( p_1_1
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
tff(398,plain,
( p_1_1
| ~ p_2_1
| ~ p_2_2
| ~ p_2_3
| ~ p_2_4
| ~ p_2_5 ),
inference(modus_ponens,[status(thm)],[397,396]) ).
tff(399,plain,
p_1_1,
inference(modus_ponens,[status(thm)],[398,386]) ).
tff(400,plain,
( p_1_1
<=> $true ),
inference(iff_true,[status(thm)],[399]) ).
tff(401,plain,
( ~ p_1_1
<=> ~ $true ),
inference(monotonicity,[status(thm)],[400]) ).
tff(402,plain,
( ~ p_1_1
<=> $false ),
inference(transitivity,[status(thm)],[401,2]) ).
tff(403,plain,
( ( ~ p_1_1
| ~ p_1_2
| ~ p_1_3
| ~ p_1_4
| ~ p_1_5 )
<=> ( $false
| $false
| $false
| $false
| $false ) ),
inference(monotonicity,[status(thm)],[402,383,364,345,326]) ).
tff(404,plain,
( ( ~ p_1_1
| ~ p_1_2
| ~ p_1_3
| ~ p_1_4
| ~ p_1_5 )
<=> $false ),
inference(transitivity,[status(thm)],[403,1]) ).
tff(405,plain,
( ( $false
| ~ p_1_1
| ~ p_1_2
| ~ p_1_3
| ~ p_1_4
| ~ p_1_5 )
<=> ( ~ p_1_1
| ~ p_1_2
| ~ p_1_3
| ~ p_1_4
| ~ p_1_5 ) ),
inference(rewrite,[status(thm)],]) ).
tff(406,axiom,
~ p_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
tff(407,plain,
( p_0
<=> $false ),
inference(iff_false,[status(thm)],[406]) ).
tff(408,plain,
( ( p_0
| ~ p_1_1
| ~ p_1_2
| ~ p_1_3
| ~ p_1_4
| ~ p_1_5 )
<=> ( $false
| ~ p_1_1
| ~ p_1_2
| ~ p_1_3
| ~ p_1_4
| ~ p_1_5 ) ),
inference(monotonicity,[status(thm)],[407]) ).
tff(409,plain,
( ( p_0
| ~ p_1_1
| ~ p_1_2
| ~ p_1_3
| ~ p_1_4
| ~ p_1_5 )
<=> ( ~ p_1_1
| ~ p_1_2
| ~ p_1_3
| ~ p_1_4
| ~ p_1_5 ) ),
inference(transitivity,[status(thm)],[408,405]) ).
tff(410,plain,
( ( p_0
| ~ p_1_1
| ~ p_1_2
| ~ p_1_3
| ~ p_1_4
| ~ p_1_5 )
<=> ( p_0
| ~ p_1_1
| ~ p_1_2
| ~ p_1_3
| ~ p_1_4
| ~ p_1_5 ) ),
inference(rewrite,[status(thm)],]) ).
tff(411,plain,
( ( p_0
| ~ p_1_1
| ~ p_1_2
| ~ p_1_3
| ~ p_1_4 )
<=> ( p_0
| ~ p_1_1
| ~ p_1_2
| ~ p_1_3
| ~ p_1_4 ) ),
inference(rewrite,[status(thm)],]) ).
tff(412,plain,
( ( p_0
| ~ p_1_1
| ~ p_1_2
| ~ p_1_3 )
<=> ( p_0
| ~ p_1_1
| ~ p_1_2
| ~ p_1_3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(413,plain,
( ( p_0
| ~ p_1_1
| ~ p_1_2 )
<=> ( p_0
| ~ p_1_1
| ~ p_1_2 ) ),
inference(rewrite,[status(thm)],]) ).
tff(414,plain,
( ( p_0
| ~ p_1_1
| ~ p_1_2
| ~ p_1_3 )
<=> ( p_0
| ~ p_1_1
| ~ p_1_2
| ~ p_1_3 ) ),
inference(monotonicity,[status(thm)],[413]) ).
tff(415,plain,
( ( p_0
| ~ p_1_1
| ~ p_1_2
| ~ p_1_3 )
<=> ( p_0
| ~ p_1_1
| ~ p_1_2
| ~ p_1_3 ) ),
inference(transitivity,[status(thm)],[414,412]) ).
tff(416,plain,
( ( p_0
| ~ p_1_1
| ~ p_1_2
| ~ p_1_3
| ~ p_1_4 )
<=> ( p_0
| ~ p_1_1
| ~ p_1_2
| ~ p_1_3
| ~ p_1_4 ) ),
inference(monotonicity,[status(thm)],[415]) ).
tff(417,plain,
( ( p_0
| ~ p_1_1
| ~ p_1_2
| ~ p_1_3
| ~ p_1_4 )
<=> ( p_0
| ~ p_1_1
| ~ p_1_2
| ~ p_1_3
| ~ p_1_4 ) ),
inference(transitivity,[status(thm)],[416,411]) ).
tff(418,plain,
( ( p_0
| ~ p_1_1
| ~ p_1_2
| ~ p_1_3
| ~ p_1_4
| ~ p_1_5 )
<=> ( p_0
| ~ p_1_1
| ~ p_1_2
| ~ p_1_3
| ~ p_1_4
| ~ p_1_5 ) ),
inference(monotonicity,[status(thm)],[417]) ).
tff(419,plain,
( ( p_0
| ~ p_1_1
| ~ p_1_2
| ~ p_1_3
| ~ p_1_4
| ~ p_1_5 )
<=> ( p_0
| ~ p_1_1
| ~ p_1_2
| ~ p_1_3
| ~ p_1_4
| ~ p_1_5 ) ),
inference(transitivity,[status(thm)],[418,410]) ).
tff(420,axiom,
( p_0
| ~ p_1_1
| ~ p_1_2
| ~ p_1_3
| ~ p_1_4
| ~ p_1_5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
tff(421,plain,
( p_0
| ~ p_1_1
| ~ p_1_2
| ~ p_1_3
| ~ p_1_4
| ~ p_1_5 ),
inference(modus_ponens,[status(thm)],[420,419]) ).
tff(422,plain,
( ~ p_1_1
| ~ p_1_2
| ~ p_1_3
| ~ p_1_4
| ~ p_1_5 ),
inference(modus_ponens,[status(thm)],[421,409]) ).
tff(423,plain,
$false,
inference(modus_ponens,[status(thm)],[422,404]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SYN010-1.005.005 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n025.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 : Mon Sep 5 01:10:34 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.33 Usage: tptp [options] [-file:]file
% 0.13/0.33 -h, -? prints this message.
% 0.13/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.33 -m, -model generate model.
% 0.13/0.33 -p, -proof generate proof.
% 0.13/0.33 -c, -core generate unsat core of named formulas.
% 0.13/0.33 -st, -statistics display statistics.
% 0.13/0.33 -t:timeout set timeout (in second).
% 0.13/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.33 -<param>:<value> configuration parameter and value.
% 0.13/0.33 -o:<output-file> file to place output in.
% 0.13/0.35 % SZS status Unsatisfiable
% 0.13/0.35 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------