TSTP Solution File: SYO500^1 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYO500^1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n020.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 : 600s
% DateTime : Thu Jul 21 17:35:10 EDT 2022
% Result : Theorem 0.20s 0.46s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 3
% Syntax : Number of formulae : 127 ( 14 unt; 2 typ; 0 def)
% Number of atoms : 1992 ( 444 equ; 0 cnn)
% Maximal formula atoms : 6 ( 15 avg)
% Number of connectives : 1011 ( 32 ~; 300 |; 0 &; 679 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 2 usr; 3 con; 0-2 aty)
% Number of variables : 0 ( 0 ^ 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_f,type,
f: $o > $o ).
thf(tp_x,type,
x: $o ).
thf(1,conjecture,
( ( f @ ( f @ ( f @ x ) ) )
= ( f @ x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
( ( ( f @ ( f @ ( f @ x ) ) )
= ( f @ x ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= ( f @ x ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ( ( f @ ( f @ ( f @ x ) ) )
!= ( f @ x ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ( ( f @ ( f @ ( f @ x ) ) )
!= ( f @ x ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(6,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= ( f @ x ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5]) ).
thf(7,plain,
( ( ~ ( ( f @ ( f @ ( f @ x ) ) )
| ( f @ x ) )
| ~ ( ~ ( f @ ( f @ ( f @ x ) ) )
| ~ ( f @ x ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[6]) ).
thf(8,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= ( f @ x ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ( ( f @ ( f @ ( f @ x ) ) )
| ( f @ x ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7]) ).
thf(10,plain,
( ( ~ ( ~ ( f @ ( f @ ( f @ x ) ) )
| ~ ( f @ x ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7]) ).
thf(11,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
| ( f @ x ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[9]) ).
thf(12,plain,
( ( ~ ( f @ ( f @ ( f @ x ) ) )
| ~ ( f @ x ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[10]) ).
thf(13,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $true )
| ( ( f @ x )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[11]) ).
thf(14,plain,
( ( ( ~ ( f @ ( f @ ( f @ x ) ) ) )
= $true )
| ( ( ~ ( f @ x ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( ( ~ ( f @ x ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(16,plain,
( ( ( f @ x )
= $false )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(17,plain,
( ( ( f @ x )
= $true )
| ( ( ( f @ ( f @ ( f @ x ) ) )
= ( f @ x ) )
= $false ) ),
inference(fac_restr,[status(thm)],[13]) ).
thf(18,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( ( ( f @ x )
= ( f @ ( f @ ( f @ x ) ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[16]) ).
thf(19,plain,
( ( ( ~ ( ( f @ ( f @ ( f @ x ) ) )
| ( f @ x ) )
| ~ ( ~ ( f @ ( f @ ( f @ x ) ) )
| ~ ( f @ x ) ) )
= $false )
| ( ( f @ x )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[17]) ).
thf(20,plain,
( ( ( ( f @ ( f @ ( f @ x ) ) )
= ( f @ x ) )
= $false )
| ( ( f @ x )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[17]) ).
thf(21,plain,
( ( ( ~ ( ( f @ x )
| ( f @ ( f @ ( f @ x ) ) ) )
| ~ ( ~ ( f @ x )
| ~ ( f @ ( f @ ( f @ x ) ) ) ) )
= $false )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[18]) ).
thf(22,plain,
( ( ( ( f @ x )
= ( f @ ( f @ ( f @ x ) ) ) )
= $false )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[18]) ).
thf(23,plain,
( ( ( ~ ( ( f @ ( f @ ( f @ x ) ) )
| ( f @ x ) ) )
= $false )
| ( ( f @ x )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[19]) ).
thf(26,plain,
( ( ( ~ ( ~ ( f @ x )
| ~ ( f @ ( f @ ( f @ x ) ) ) ) )
= $false )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(27,plain,
( ( ( ( f @ ( f @ ( f @ x ) ) )
| ( f @ x ) )
= $true )
| ( ( f @ x )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[23]) ).
thf(30,plain,
( ( ( ~ ( f @ x )
| ~ ( f @ ( f @ ( f @ x ) ) ) )
= $true )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(31,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $true )
| ( ( f @ x )
= $true )
| ( ( f @ x )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(34,plain,
( ( ( ~ ( f @ x ) )
= $true )
| ( ( ~ ( f @ ( f @ ( f @ x ) ) ) )
= $true )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(36,plain,
( ( ( f @ x )
= $false )
| ( ( ~ ( f @ ( f @ ( f @ x ) ) ) )
= $true )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(38,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( ( f @ x )
= $false )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(39,plain,
( ( ( f @ x )
= $true )
| ( ( f @ ( f @ x ) )
= $true )
| ( x = $true ) ),
inference(extuni,[status(esa)],[20]) ).
thf(40,plain,
( ( ( f @ x )
= $true )
| ( ( f @ ( f @ x ) )
= $false )
| ( x = $false ) ),
inference(extuni,[status(esa)],[20]) ).
thf(41,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( x = $true )
| ( ( f @ ( f @ x ) )
= $true ) ),
inference(extuni,[status(esa)],[22]) ).
thf(42,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( x = $false )
| ( ( f @ ( f @ x ) )
= $false ) ),
inference(extuni,[status(esa)],[22]) ).
thf(43,plain,
( ( ( f @ ( f @ x ) )
= $true )
| ( x = $true ) ),
inference(extuni,[status(esa)],[8]) ).
thf(44,plain,
( ( ( f @ ( f @ x ) )
= $false )
| ( x = $false ) ),
inference(extuni,[status(esa)],[8]) ).
thf(45,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $true )
| ( ( f @ x )
= $true ) ),
inference(sim,[status(thm)],[31]) ).
thf(46,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( ( f @ x )
= $false ) ),
inference(sim,[status(thm)],[38]) ).
thf(47,plain,
( ( ( f @ ( f @ x ) )
= $true )
| ( x = $true ) ),
inference(extuni,[status(esa)],[8]) ).
thf(48,plain,
( ( ( f @ ( f @ x ) )
= $false )
| ( x = $false ) ),
inference(extuni,[status(esa)],[8]) ).
thf(51,plain,
( ( ( f @ x )
= $true )
| ( ( ( f @ ( f @ ( f @ x ) ) )
= ( f @ x ) )
= $false ) ),
inference(fac_restr,[status(thm)],[13]) ).
thf(52,plain,
( ( ( f @ ( f @ x ) )
= $true )
| ( x = $true )
| ( ( f @ x )
= $true ) ),
inference(extuni,[status(esa)],[51]) ).
thf(53,plain,
( ( ( f @ ( f @ x ) )
= $false )
| ( x = $false )
| ( ( f @ x )
= $true ) ),
inference(extuni,[status(esa)],[51]) ).
thf(54,plain,
( ( ( ( f @ ( f @ ( f @ x ) ) )
= ( f @ x ) )
= $false )
| ( ( f @ x )
= $false )
| ( ( f @ ( f @ ( f @ x ) ) )
= $true ) ),
inference(res,[status(thm)],[16,13]) ).
thf(57,plain,
( ( ( ( f @ x )
= ( f @ ( f @ ( f @ x ) ) ) )
= $false )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( ( f @ x )
= $true ) ),
inference(res,[status(thm)],[16,13]) ).
thf(58,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( ( ( f @ x )
= ( f @ ( f @ ( f @ x ) ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[16]) ).
thf(59,plain,
( ( ( f @ x )
= $true )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( x = $true )
| ( ( f @ ( f @ x ) )
= $true ) ),
inference(extuni,[status(esa)],[57]) ).
thf(60,plain,
( ( ( f @ x )
= $true )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( x = $false )
| ( ( f @ ( f @ x ) )
= $false ) ),
inference(extuni,[status(esa)],[57]) ).
thf(63,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $true )
| ( ( f @ x )
= $false )
| ( ( f @ ( f @ x ) )
= $true )
| ( x = $true ) ),
inference(extuni,[status(esa)],[54]) ).
thf(64,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $true )
| ( ( f @ x )
= $false )
| ( ( f @ ( f @ x ) )
= $false )
| ( x = $false ) ),
inference(extuni,[status(esa)],[54]) ).
thf(65,plain,
( ( x = $true )
| ( ( f @ ( f @ x ) )
= $true )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false ) ),
inference(extuni,[status(esa)],[58]) ).
thf(66,plain,
( ( x = $false )
| ( ( f @ ( f @ x ) )
= $false )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false ) ),
inference(extuni,[status(esa)],[58]) ).
thf(69,plain,
( ( ( ( f @ x )
= ( f @ ( f @ ( f @ x ) ) ) )
= $false )
| ( ( f @ ( f @ x ) )
= $true )
| ( x = $true )
| ( ( f @ x )
= $false ) ),
inference(res,[status(thm)],[39,16]) ).
thf(71,plain,
( ( ( ( f @ ( f @ x ) )
= ( f @ x ) )
= $false )
| ( ( f @ x )
= $true )
| ( x = $true )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false ) ),
inference(res,[status(thm)],[39,16]) ).
thf(72,plain,
( ( ( ( f @ x )
= ( f @ x ) )
= $false )
| ( ( f @ ( f @ x ) )
= $true )
| ( x = $true )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false ) ),
inference(res,[status(thm)],[39,16]) ).
thf(76,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( x = $true )
| ( ( f @ ( f @ x ) )
= $true ) ),
inference(extuni,[status(esa)],[72]) ).
thf(77,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( x = $true )
| ( ( f @ x )
= $true )
| ( ( f @ x )
= $true )
| ( x = $true ) ),
inference(extuni,[status(esa)],[71]) ).
thf(79,plain,
( ( ( f @ x )
= $false )
| ( x = $true )
| ( ( f @ ( f @ x ) )
= $true )
| ( x = $true )
| ( ( f @ ( f @ x ) )
= $true ) ),
inference(extuni,[status(esa)],[69]) ).
thf(85,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( x = $true )
| ( ( f @ x )
= $true ) ),
inference(sim,[status(thm)],[77]) ).
thf(86,plain,
( ( ( f @ x )
= $false )
| ( x = $true )
| ( ( f @ ( f @ x ) )
= $true ) ),
inference(sim,[status(thm)],[79]) ).
thf(97,plain,
( ( ( ( f @ x )
= ( f @ ( f @ ( f @ x ) ) ) )
= $false )
| ( ( f @ ( f @ x ) )
= $false )
| ( x = $false )
| ( ( f @ x )
= $false ) ),
inference(res,[status(thm)],[40,16]) ).
thf(98,plain,
( ( ( ( f @ x )
= ( f @ x ) )
= $false )
| ( ( f @ ( f @ x ) )
= $false )
| ( x = $false )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false ) ),
inference(res,[status(thm)],[40,16]) ).
thf(102,plain,
( ( ( ( f @ ( f @ x ) )
= ( f @ ( f @ ( f @ x ) ) ) )
= $false )
| ( ( f @ x )
= $true )
| ( x = $false )
| ( ( f @ x )
= $true ) ),
inference(res,[status(thm)],[40,13]) ).
thf(106,plain,
( ( ( f @ x )
= $true )
| ( x = $false )
| ( ( f @ x )
= $true )
| ( ( f @ x )
= $true )
| ( ( f @ ( f @ x ) )
= $true ) ),
inference(extuni,[status(esa)],[102]) ).
thf(110,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( x = $false )
| ( ( f @ ( f @ x ) )
= $false ) ),
inference(extuni,[status(esa)],[98]) ).
thf(112,plain,
( ( ( f @ x )
= $false )
| ( x = $false )
| ( ( f @ ( f @ x ) )
= $false )
| ( x = $false )
| ( ( f @ ( f @ x ) )
= $false ) ),
inference(extuni,[status(esa)],[97]) ).
thf(121,plain,
( ( ( f @ x )
= $true )
| ( x = $false )
| ( ( f @ ( f @ x ) )
= $true ) ),
inference(sim,[status(thm)],[106]) ).
thf(122,plain,
( ( ( f @ x )
= $false )
| ( x = $false )
| ( ( f @ ( f @ x ) )
= $false ) ),
inference(sim,[status(thm)],[112]) ).
thf(123,plain,
( ( ( ( f @ ( f @ ( f @ x ) ) )
= ( f @ ( f @ x ) ) )
= $false )
| ( x = $true )
| ( ( f @ ( f @ x ) )
= $true )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( x = $true ) ),
inference(res,[status(thm)],[41,41]) ).
thf(125,plain,
( ( ( ( f @ ( f @ x ) )
= ( f @ ( f @ ( f @ x ) ) ) )
= $false )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( x = $true )
| ( x = $true )
| ( ( f @ ( f @ x ) )
= $true ) ),
inference(res,[status(thm)],[41,41]) ).
thf(133,plain,
( ( ( ( f @ ( f @ ( f @ x ) ) )
= ( f @ ( f @ x ) ) )
= $false )
| ( x = $true )
| ( ( f @ ( f @ x ) )
= $true )
| ( ( f @ x )
= $true )
| ( x = $true ) ),
inference(res,[status(thm)],[41,39]) ).
thf(134,plain,
( ( ( ( f @ ( f @ ( f @ x ) ) )
= ( f @ x ) )
= $false )
| ( x = $true )
| ( ( f @ ( f @ x ) )
= $true )
| ( ( f @ ( f @ x ) )
= $true )
| ( x = $true ) ),
inference(res,[status(thm)],[41,39]) ).
thf(135,plain,
( ( ( ( f @ ( f @ x ) )
= ( f @ ( f @ ( f @ x ) ) ) )
= $false )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( x = $true )
| ( ( f @ x )
= $false ) ),
inference(res,[status(thm)],[41,16]) ).
thf(137,plain,
( ( ( ( f @ ( f @ x ) )
= ( f @ x ) )
= $false )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( x = $true )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false ) ),
inference(res,[status(thm)],[41,16]) ).
thf(139,plain,
( ( ( ( f @ ( f @ ( f @ x ) ) )
= ( f @ x ) )
= $false )
| ( x = $true )
| ( ( f @ ( f @ x ) )
= $true )
| ( ( f @ ( f @ ( f @ x ) ) )
= $true ) ),
inference(res,[status(thm)],[41,13]) ).
thf(140,plain,
( ( ( ( f @ ( f @ ( f @ x ) ) )
= ( f @ ( f @ ( f @ x ) ) ) )
= $false )
| ( x = $true )
| ( ( f @ ( f @ x ) )
= $true )
| ( ( f @ x )
= $true ) ),
inference(res,[status(thm)],[41,13]) ).
thf(143,plain,
( ( ( f @ x )
= $true )
| ( ( f @ ( f @ x ) )
= $true )
| ( x = $true ) ),
inference(extuni,[status(esa)],[140]) ).
thf(144,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $true )
| ( ( f @ ( f @ x ) )
= $true )
| ( x = $true )
| ( ( f @ ( f @ x ) )
= $true )
| ( x = $true ) ),
inference(extuni,[status(esa)],[139]) ).
thf(146,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( x = $true )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( ( f @ x )
= $true )
| ( x = $true ) ),
inference(extuni,[status(esa)],[137]) ).
thf(151,plain,
( ( ( f @ x )
= $false )
| ( x = $true )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( ( f @ x )
= $false )
| ( ( f @ ( f @ x ) )
= $false ) ),
inference(extuni,[status(esa)],[135]) ).
thf(152,plain,
( ( x = $true )
| ( ( f @ ( f @ x ) )
= $true )
| ( ( f @ ( f @ x ) )
= $true )
| ( x = $true )
| ( ( f @ ( f @ x ) )
= $true )
| ( x = $true ) ),
inference(extuni,[status(esa)],[134]) ).
thf(154,plain,
( ( x = $true )
| ( ( f @ x )
= $true )
| ( ( f @ ( f @ x ) )
= $true )
| ( x = $true )
| ( ( f @ x )
= $true )
| ( x = $true ) ),
inference(extuni,[status(esa)],[133]) ).
thf(156,plain,
( ( x = $true )
| ( ( f @ x )
= $true )
| ( ( f @ ( f @ x ) )
= $true )
| ( x = $true )
| ( ( f @ ( f @ x ) )
= $true )
| ( ( f @ x )
= $true ) ),
inference(extuni,[status(esa)],[133]) ).
thf(162,plain,
( ( ( f @ ( f @ x ) )
= $true )
| ( x = $true )
| ( x = $true )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( x = $true )
| ( ( f @ x )
= $true ) ),
inference(extuni,[status(esa)],[125]) ).
thf(164,plain,
( ( ( f @ ( f @ x ) )
= $true )
| ( x = $true )
| ( x = $true )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( ( f @ x )
= $true )
| ( ( f @ ( f @ x ) )
= $true ) ),
inference(extuni,[status(esa)],[125]) ).
thf(166,plain,
( ( x = $true )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( ( f @ ( f @ x ) )
= $true )
| ( x = $true )
| ( ( f @ x )
= $true )
| ( x = $true ) ),
inference(extuni,[status(esa)],[123]) ).
thf(168,plain,
( ( x = $true )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( ( f @ ( f @ x ) )
= $true )
| ( x = $true )
| ( ( f @ ( f @ x ) )
= $true )
| ( ( f @ x )
= $true ) ),
inference(extuni,[status(esa)],[123]) ).
thf(170,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $true )
| ( ( f @ ( f @ x ) )
= $true )
| ( x = $true ) ),
inference(sim,[status(thm)],[144]) ).
thf(171,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( x = $true )
| ( ( f @ x )
= $true ) ),
inference(sim,[status(thm)],[146]) ).
thf(172,plain,
( ( ( f @ x )
= $false )
| ( x = $true )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( ( f @ ( f @ x ) )
= $false ) ),
inference(sim,[status(thm)],[151]) ).
thf(173,plain,
( ( x = $true )
| ( ( f @ ( f @ x ) )
= $true ) ),
inference(sim,[status(thm)],[152]) ).
thf(174,plain,
( ( x = $true )
| ( ( f @ x )
= $true )
| ( ( f @ ( f @ x ) )
= $true ) ),
inference(sim,[status(thm)],[156]) ).
thf(175,plain,
( ( x = $true )
| ( ( f @ x )
= $true )
| ( ( f @ ( f @ x ) )
= $true ) ),
inference(sim,[status(thm)],[154]) ).
thf(176,plain,
( ( ( f @ ( f @ x ) )
= $true )
| ( x = $true )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( ( f @ x )
= $true ) ),
inference(sim,[status(thm)],[164]) ).
thf(177,plain,
( ( ( f @ ( f @ x ) )
= $true )
| ( x = $true )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( ( f @ x )
= $true ) ),
inference(sim,[status(thm)],[162]) ).
thf(178,plain,
( ( x = $true )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( ( f @ ( f @ x ) )
= $true )
| ( ( f @ x )
= $true ) ),
inference(sim,[status(thm)],[168]) ).
thf(179,plain,
( ( x = $true )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( ( f @ ( f @ x ) )
= $true )
| ( ( f @ x )
= $true ) ),
inference(sim,[status(thm)],[166]) ).
thf(186,plain,
( ( ( ( f @ ( f @ x ) )
= ( f @ x ) )
= $false )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( x = $false )
| ( ( f @ ( f @ x ) )
= $false )
| ( x = $false ) ),
inference(res,[status(thm)],[42,40]) ).
thf(188,plain,
( ( ( ( f @ ( f @ ( f @ x ) ) )
= ( f @ x ) )
= $false )
| ( x = $false )
| ( ( f @ ( f @ x ) )
= $false )
| ( ( f @ ( f @ x ) )
= $false )
| ( x = $false ) ),
inference(res,[status(thm)],[42,40]) ).
thf(200,plain,
( ( ( ( f @ ( f @ ( f @ x ) ) )
= ( f @ x ) )
= $false )
| ( x = $false )
| ( ( f @ ( f @ x ) )
= $false )
| ( ( f @ ( f @ ( f @ x ) ) )
= $true ) ),
inference(res,[status(thm)],[42,13]) ).
thf(201,plain,
( ( ( ( f @ ( f @ x ) )
= ( f @ ( f @ ( f @ x ) ) ) )
= $false )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( x = $false )
| ( ( f @ x )
= $true ) ),
inference(res,[status(thm)],[42,13]) ).
thf(203,plain,
( ( ( ( f @ ( f @ ( f @ x ) ) )
= ( f @ ( f @ ( f @ x ) ) ) )
= $false )
| ( x = $false )
| ( ( f @ ( f @ x ) )
= $false )
| ( ( f @ x )
= $true ) ),
inference(res,[status(thm)],[42,13]) ).
thf(204,plain,
( ( ( f @ x )
= $true )
| ( ( f @ ( f @ x ) )
= $false )
| ( x = $false ) ),
inference(extuni,[status(esa)],[203]) ).
thf(207,plain,
( ( ( f @ x )
= $true )
| ( x = $false )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( ( f @ x )
= $true )
| ( ( f @ ( f @ x ) )
= $true ) ),
inference(extuni,[status(esa)],[201]) ).
thf(210,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $true )
| ( ( f @ ( f @ x ) )
= $false )
| ( x = $false )
| ( ( f @ ( f @ x ) )
= $false )
| ( x = $false ) ),
inference(extuni,[status(esa)],[200]) ).
thf(224,plain,
( ( x = $false )
| ( ( f @ ( f @ x ) )
= $false )
| ( ( f @ ( f @ x ) )
= $false )
| ( x = $false )
| ( ( f @ ( f @ x ) )
= $false )
| ( x = $false ) ),
inference(extuni,[status(esa)],[188]) ).
thf(226,plain,
( ( x = $false )
| ( ( f @ ( f @ x ) )
= $false )
| ( x = $false )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( ( f @ x )
= $false )
| ( x = $false ) ),
inference(extuni,[status(esa)],[186]) ).
thf(233,plain,
( ( ( f @ x )
= $true )
| ( x = $false )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( ( f @ ( f @ x ) )
= $true ) ),
inference(sim,[status(thm)],[207]) ).
thf(234,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $true )
| ( ( f @ ( f @ x ) )
= $false )
| ( x = $false ) ),
inference(sim,[status(thm)],[210]) ).
thf(235,plain,
( ( x = $false )
| ( ( f @ ( f @ x ) )
= $false ) ),
inference(sim,[status(thm)],[224]) ).
thf(236,plain,
( ( x = $false )
| ( ( f @ ( f @ x ) )
= $false )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( ( f @ x )
= $false ) ),
inference(sim,[status(thm)],[226]) ).
thf(248,plain,
( ( ( ( f @ ( f @ x ) )
= ( f @ ( f @ ( f @ x ) ) ) )
= $false )
| ( x = $true )
| ( ( f @ x )
= $false ) ),
inference(res,[status(thm)],[43,16]) ).
thf(250,plain,
( ( ( ( f @ ( f @ x ) )
= ( f @ x ) )
= $false )
| ( x = $true )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false ) ),
inference(res,[status(thm)],[43,16]) ).
thf(254,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( x = $true )
| ( ( f @ x )
= $true )
| ( x = $true ) ),
inference(extuni,[status(esa)],[250]) ).
thf(259,plain,
( ( ( f @ x )
= $false )
| ( x = $true )
| ( ( f @ x )
= $false )
| ( ( f @ ( f @ x ) )
= $false ) ),
inference(extuni,[status(esa)],[248]) ).
thf(268,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( x = $true )
| ( ( f @ x )
= $true ) ),
inference(sim,[status(thm)],[254]) ).
thf(269,plain,
( ( ( f @ x )
= $false )
| ( x = $true )
| ( ( f @ ( f @ x ) )
= $false ) ),
inference(sim,[status(thm)],[259]) ).
thf(275,plain,
( ( ( ( f @ ( f @ x ) )
= ( f @ x ) )
= $false )
| ( x = $false )
| ( ( f @ ( f @ ( f @ x ) ) )
= $true ) ),
inference(res,[status(thm)],[44,13]) ).
thf(277,plain,
( ( ( ( f @ ( f @ x ) )
= ( f @ ( f @ ( f @ x ) ) ) )
= $false )
| ( x = $false )
| ( ( f @ x )
= $true ) ),
inference(res,[status(thm)],[44,13]) ).
thf(281,plain,
( ( ( f @ x )
= $true )
| ( x = $false )
| ( ( f @ x )
= $true )
| ( ( f @ ( f @ x ) )
= $true ) ),
inference(extuni,[status(esa)],[277]) ).
thf(284,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $true )
| ( x = $false )
| ( ( f @ x )
= $false )
| ( x = $false ) ),
inference(extuni,[status(esa)],[275]) ).
thf(287,plain,
( ( ( f @ x )
= $true )
| ( x = $false )
| ( ( f @ ( f @ x ) )
= $true ) ),
inference(sim,[status(thm)],[281]) ).
thf(288,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $true )
| ( x = $false )
| ( ( f @ x )
= $false ) ),
inference(sim,[status(thm)],[284]) ).
thf(289,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[8,288,287,269,268,236,235,234,233,204,179,178,177,176,175,174,173,172,171,170,143,122,121,110,86,85,76,66,65,64,63,60,59,53,52,48,47,46,45,44,43,16,13]) ).
thf(290,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[289]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYO500^1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jul 8 23:10:28 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 0
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 0
% 0.12/0.34
% 0.12/0.34 Contains.Choice.Funs: false
% 0.12/0.34 (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full).....
% 0.20/0.46
% 0.20/0.46 ********************************
% 0.20/0.46 * All subproblems solved! *
% 0.20/0.46 ********************************
% 0.20/0.46 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:289,loop_count:10,foatp_calls:3,translation:fof_full)
% 0.20/0.47
% 0.20/0.47 %**** Beginning of derivation protocol ****
% 0.20/0.47 % SZS output start CNFRefutation
% See solution above
% 0.20/0.47
% 0.20/0.47 %**** End of derivation protocol ****
% 0.20/0.47 %**** no. of clauses in derivation: 125 ****
% 0.20/0.47 %**** clause counter: 289 ****
% 0.20/0.47
% 0.20/0.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:289,loop_count:10,foatp_calls:3,translation:fof_full)
%------------------------------------------------------------------------------