TSTP Solution File: SYO499^1 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYO499^1 : 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 : n027.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 17:35:00 EDT 2022
% Result : Theorem 0.21s 0.46s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 10
% Syntax : Number of formulae : 156 ( 45 unt; 9 typ; 0 def)
% Number of atoms : 1714 ( 650 equ; 0 cnn)
% Maximal formula atoms : 6 ( 11 avg)
% Number of connectives : 1019 ( 180 ~; 257 |; 10 &; 572 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 ^ 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $o ).
thf(tp_b,type,
b: $o ).
thf(tp_c,type,
c: $o ).
thf(tp_f,type,
f: $o > $i ).
thf(tp_f1,type,
f1: $o > $i ).
thf(tp_f2,type,
f2: $o > $i ).
thf(tp_g,type,
g: $o > $i ).
thf(tp_g1,type,
g1: $o > $i ).
thf(tp_g2,type,
g2: $o > $i ).
thf(1,conjecture,
( ( ( f @ a )
= ( g @ b ) )
| ( ( f @ b )
!= ( g @ a ) )
| ( ( f1 @ a )
= ( g1 @ c ) )
| ( ( f1 @ c )
!= ( g1 @ a ) )
| ( ( f2 @ b )
= ( g2 @ c ) )
| ( ( f2 @ c )
!= ( g2 @ b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
( ( ( ( f @ a )
= ( g @ b ) )
| ( ( f @ b )
!= ( g @ a ) )
| ( ( f1 @ a )
= ( g1 @ c ) )
| ( ( f1 @ c )
!= ( g1 @ a ) )
| ( ( f2 @ b )
= ( g2 @ c ) )
| ( ( f2 @ c )
!= ( g2 @ b ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ( f @ a )
= ( g @ b ) )
| ( ( f @ b )
!= ( g @ a ) )
| ( ( f1 @ a )
= ( g1 @ c ) )
| ( ( f1 @ c )
!= ( g1 @ a ) )
| ( ( f2 @ b )
= ( g2 @ c ) )
| ( ( f2 @ c )
!= ( g2 @ b ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ~ ( ( ( f @ a )
= ( g @ b ) )
| ( ( f @ b )
!= ( g @ a ) )
| ( ( f1 @ a )
= ( g1 @ c ) )
| ( ( f1 @ c )
!= ( g1 @ a ) )
| ( ( f2 @ b )
= ( g2 @ c ) )
| ( ( f2 @ c )
!= ( g2 @ b ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ( ( f2 @ c )
= ( g2 @ b ) )
& ( ( f2 @ b )
!= ( g2 @ c ) )
& ( ( f1 @ c )
= ( g1 @ a ) )
& ( ( f1 @ a )
!= ( g1 @ c ) )
& ( ( f @ b )
= ( g @ a ) )
& ( ( f @ a )
!= ( g @ b ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(6,plain,
( ( ( ( f2 @ c )
= ( g2 @ b ) )
& ( ( f2 @ b )
!= ( g2 @ c ) )
& ( ( f1 @ c )
= ( g1 @ a ) )
& ( ( f1 @ a )
!= ( g1 @ c ) )
& ( ( f @ b )
= ( g @ a ) )
& ( ( f @ a )
!= ( g @ b ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(7,plain,
( ( ~ ( ( ( f2 @ c )
!= ( g2 @ b ) )
| ~ ~ ( ~ ( ( ( f2 @ b )
!= ( g2 @ c ) ) )
| ~ ~ ( ( ( f1 @ c )
!= ( g1 @ a ) )
| ~ ~ ( ~ ( ( ( f1 @ a )
!= ( g1 @ c ) ) )
| ~ ~ ( ( ( f @ b )
!= ( g @ a ) )
| ~ ( ( ( f @ a )
!= ( g @ b ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(8,plain,
( ( ( ( f2 @ c )
!= ( g2 @ b ) )
| ~ ~ ( ~ ( ( ( f2 @ b )
!= ( g2 @ c ) ) )
| ~ ~ ( ( ( f1 @ c )
!= ( g1 @ a ) )
| ~ ~ ( ~ ( ( ( f1 @ a )
!= ( g1 @ c ) ) )
| ~ ~ ( ( ( f @ b )
!= ( g @ a ) )
| ~ ( ( ( f @ a )
!= ( g @ b ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7]) ).
thf(9,plain,
( ( ( ( f2 @ c )
!= ( g2 @ b ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[8]) ).
thf(10,plain,
( ( ~ ~ ( ~ ( ( ( f2 @ b )
!= ( g2 @ c ) ) )
| ~ ~ ( ( ( f1 @ c )
!= ( g1 @ a ) )
| ~ ~ ( ~ ( ( ( f1 @ a )
!= ( g1 @ c ) ) )
| ~ ~ ( ( ( f @ b )
!= ( g @ a ) )
| ~ ( ( ( f @ a )
!= ( g @ b ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[8]) ).
thf(11,plain,
( ( ( f2 @ c )
= ( g2 @ b ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[9]) ).
thf(12,plain,
( ( ~ ( ~ ( ( ( f2 @ b )
!= ( g2 @ c ) ) )
| ~ ~ ( ( ( f1 @ c )
!= ( g1 @ a ) )
| ~ ~ ( ~ ( ( ( f1 @ a )
!= ( g1 @ c ) ) )
| ~ ~ ( ( ( f @ b )
!= ( g @ a ) )
| ~ ( ( ( f @ a )
!= ( g @ b ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[10]) ).
thf(13,plain,
( ( ~ ( ( ( f2 @ b )
!= ( g2 @ c ) ) )
| ~ ~ ( ( ( f1 @ c )
!= ( g1 @ a ) )
| ~ ~ ( ~ ( ( ( f1 @ a )
!= ( g1 @ c ) ) )
| ~ ~ ( ( ( f @ b )
!= ( g @ a ) )
| ~ ( ( ( f @ a )
!= ( g @ b ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(14,plain,
( ( ~ ( ( ( f2 @ b )
!= ( g2 @ c ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(15,plain,
( ( ~ ~ ( ( ( f1 @ c )
!= ( g1 @ a ) )
| ~ ~ ( ~ ( ( ( f1 @ a )
!= ( g1 @ c ) ) )
| ~ ~ ( ( ( f @ b )
!= ( g @ a ) )
| ~ ( ( ( f @ a )
!= ( g @ b ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ( ( f2 @ b )
!= ( g2 @ c ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ( ( ( f1 @ c )
!= ( g1 @ a ) )
| ~ ~ ( ~ ( ( ( f1 @ a )
!= ( g1 @ c ) ) )
| ~ ~ ( ( ( f @ b )
!= ( g @ a ) )
| ~ ( ( ( f @ a )
!= ( g @ b ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(18,plain,
( ( ( f2 @ b )
= ( g2 @ c ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(19,plain,
( ( ( ( f1 @ c )
!= ( g1 @ a ) )
| ~ ~ ( ~ ( ( ( f1 @ a )
!= ( g1 @ c ) ) )
| ~ ~ ( ( ( f @ b )
!= ( g @ a ) )
| ~ ( ( ( f @ a )
!= ( g @ b ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(20,plain,
( ( ( ( f1 @ c )
!= ( g1 @ a ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[19]) ).
thf(21,plain,
( ( ~ ~ ( ~ ( ( ( f1 @ a )
!= ( g1 @ c ) ) )
| ~ ~ ( ( ( f @ b )
!= ( g @ a ) )
| ~ ( ( ( f @ a )
!= ( g @ b ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[19]) ).
thf(22,plain,
( ( ( f1 @ c )
= ( g1 @ a ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(23,plain,
( ( ~ ( ~ ( ( ( f1 @ a )
!= ( g1 @ c ) ) )
| ~ ~ ( ( ( f @ b )
!= ( g @ a ) )
| ~ ( ( ( f @ a )
!= ( g @ b ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(24,plain,
( ( ~ ( ( ( f1 @ a )
!= ( g1 @ c ) ) )
| ~ ~ ( ( ( f @ b )
!= ( g @ a ) )
| ~ ( ( ( f @ a )
!= ( g @ b ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(25,plain,
( ( ~ ( ( ( f1 @ a )
!= ( g1 @ c ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(26,plain,
( ( ~ ~ ( ( ( f @ b )
!= ( g @ a ) )
| ~ ( ( ( f @ a )
!= ( g @ b ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(27,plain,
( ( ( ( f1 @ a )
!= ( g1 @ c ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(28,plain,
( ( ~ ( ( ( f @ b )
!= ( g @ a ) )
| ~ ( ( ( f @ a )
!= ( g @ b ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(29,plain,
( ( ( f1 @ a )
= ( g1 @ c ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(30,plain,
( ( ( ( f @ b )
!= ( g @ a ) )
| ~ ( ( ( f @ a )
!= ( g @ b ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(31,plain,
( ( ( ( f @ b )
!= ( g @ a ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(32,plain,
( ( ~ ( ( ( f @ a )
!= ( g @ b ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(33,plain,
( ( ( f @ b )
= ( g @ a ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(34,plain,
( ( ( ( f @ a )
!= ( g @ b ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(35,plain,
( ( ( f @ a )
= ( g @ b ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(36,plain,
( ( ( ( f2 @ b )
= ( g2 @ c ) )
= ( ( f2 @ c )
= ( g2 @ b ) ) )
= $false ),
inference(res,[status(thm)],[18,11]) ).
thf(37,plain,
( ( ( ( f2 @ b )
= ( g2 @ b ) )
= $false )
| ( ( ( g2 @ c )
= ( f2 @ c ) )
= $false ) ),
inference(extuni,[status(esa)],[36]) ).
thf(38,plain,
( ( c = $true )
| ( b = $true )
| ( b = $true )
| ( c = $true ) ),
inference(extuni,[status(esa)],[36]) ).
thf(40,plain,
( ( ( ( g2 @ c )
= ( g2 @ b ) )
= $false )
| ( b = $true )
| ( c = $true ) ),
inference(extuni,[status(esa)],[36]) ).
thf(42,plain,
( ( c = $false )
| ( b = $false )
| ( b = $false )
| ( c = $false ) ),
inference(extuni,[status(esa)],[36]) ).
thf(43,plain,
( ( ( ( g2 @ c )
= ( g2 @ b ) )
= $false )
| ( b = $false )
| ( c = $false ) ),
inference(extuni,[status(esa)],[36]) ).
thf(44,plain,
( ( c = $true )
| ( b = $true )
| ( ( ( f2 @ b )
= ( f2 @ c ) )
= $false ) ),
inference(extuni,[status(esa)],[36]) ).
thf(45,plain,
( ( c = $false )
| ( b = $false )
| ( ( ( f2 @ b )
= ( f2 @ c ) )
= $false ) ),
inference(extuni,[status(esa)],[36]) ).
thf(46,plain,
( ( ( ( g2 @ c )
= ( g2 @ b ) )
= $false )
| ( ( ( f2 @ b )
= ( f2 @ c ) )
= $false ) ),
inference(extuni,[status(esa)],[36]) ).
thf(47,plain,
( ( c = $false )
| ( b = $false ) ),
inference(sim,[status(thm)],[42]) ).
thf(48,plain,
( ( c = $true )
| ( b = $true ) ),
inference(sim,[status(thm)],[38]) ).
thf(49,plain,
( ( ( ( f1 @ c )
= ( g1 @ a ) )
= ( ( f2 @ b )
= ( g2 @ c ) ) )
= $false ),
inference(res,[status(thm)],[22,18]) ).
thf(50,plain,
( ( ( ( f1 @ c )
= ( g2 @ c ) )
= $false )
| ( ( ( g1 @ a )
= ( f2 @ b ) )
= $false ) ),
inference(extuni,[status(esa)],[49]) ).
thf(51,plain,
( ( ( ( g1 @ a )
= ( g2 @ c ) )
= $false )
| ( ( ( f1 @ c )
= ( f2 @ b ) )
= $false ) ),
inference(extuni,[status(esa)],[49]) ).
thf(52,plain,
( ( ( ( f1 @ a )
= ( g1 @ c ) )
= ( ( f1 @ c )
= ( g1 @ a ) ) )
= $false ),
inference(res,[status(thm)],[29,22]) ).
thf(53,plain,
( ( ( ( f1 @ a )
= ( g1 @ c ) )
= ( ( f2 @ c )
= ( g2 @ b ) ) )
= $false ),
inference(res,[status(thm)],[29,11]) ).
thf(54,plain,
( ( ( ( f1 @ a )
= ( g2 @ b ) )
= $false )
| ( ( ( g1 @ c )
= ( f2 @ c ) )
= $false ) ),
inference(extuni,[status(esa)],[53]) ).
thf(55,plain,
( ( ( ( g1 @ c )
= ( g2 @ b ) )
= $false )
| ( ( ( f1 @ a )
= ( f2 @ c ) )
= $false ) ),
inference(extuni,[status(esa)],[53]) ).
thf(56,plain,
( ( ( ( f1 @ a )
= ( g1 @ a ) )
= $false )
| ( ( ( g1 @ c )
= ( f1 @ c ) )
= $false ) ),
inference(extuni,[status(esa)],[52]) ).
thf(57,plain,
( ( c = $true )
| ( a = $true )
| ( a = $true )
| ( c = $true ) ),
inference(extuni,[status(esa)],[52]) ).
thf(59,plain,
( ( ( ( g1 @ c )
= ( g1 @ a ) )
= $false )
| ( a = $true )
| ( c = $true ) ),
inference(extuni,[status(esa)],[52]) ).
thf(61,plain,
( ( c = $false )
| ( a = $false )
| ( a = $false )
| ( c = $false ) ),
inference(extuni,[status(esa)],[52]) ).
thf(62,plain,
( ( ( ( g1 @ c )
= ( g1 @ a ) )
= $false )
| ( a = $false )
| ( c = $false ) ),
inference(extuni,[status(esa)],[52]) ).
thf(63,plain,
( ( c = $true )
| ( a = $true )
| ( ( ( f1 @ a )
= ( f1 @ c ) )
= $false ) ),
inference(extuni,[status(esa)],[52]) ).
thf(64,plain,
( ( c = $false )
| ( a = $false )
| ( ( ( f1 @ a )
= ( f1 @ c ) )
= $false ) ),
inference(extuni,[status(esa)],[52]) ).
thf(65,plain,
( ( ( ( g1 @ c )
= ( g1 @ a ) )
= $false )
| ( ( ( f1 @ a )
= ( f1 @ c ) )
= $false ) ),
inference(extuni,[status(esa)],[52]) ).
thf(66,plain,
( ( c = $false )
| ( a = $false ) ),
inference(sim,[status(thm)],[61]) ).
thf(67,plain,
( ( c = $true )
| ( a = $true ) ),
inference(sim,[status(thm)],[57]) ).
thf(68,plain,
( ( ( ( f @ b )
= ( g @ a ) )
= ( ( f1 @ a )
= ( g1 @ c ) ) )
= $false ),
inference(res,[status(thm)],[33,29]) ).
thf(69,plain,
( ( ( ( f @ b )
= ( g @ a ) )
= ( ( f2 @ b )
= ( g2 @ c ) ) )
= $false ),
inference(res,[status(thm)],[33,18]) ).
thf(70,plain,
( ( ( ( f @ b )
= ( g2 @ c ) )
= $false )
| ( ( ( g @ a )
= ( f2 @ b ) )
= $false ) ),
inference(extuni,[status(esa)],[69]) ).
thf(71,plain,
( ( ( ( g @ a )
= ( g2 @ c ) )
= $false )
| ( ( ( f @ b )
= ( f2 @ b ) )
= $false ) ),
inference(extuni,[status(esa)],[69]) ).
thf(72,plain,
( ( ( ( f @ b )
= ( g1 @ c ) )
= $false )
| ( ( ( g @ a )
= ( f1 @ a ) )
= $false ) ),
inference(extuni,[status(esa)],[68]) ).
thf(73,plain,
( ( ( ( g @ a )
= ( g1 @ c ) )
= $false )
| ( ( ( f @ b )
= ( f1 @ a ) )
= $false ) ),
inference(extuni,[status(esa)],[68]) ).
thf(74,plain,
( ( ( ( f @ a )
= ( g @ b ) )
= ( ( f @ b )
= ( g @ a ) ) )
= $false ),
inference(res,[status(thm)],[35,33]) ).
thf(75,plain,
( ( ( ( f @ a )
= ( g @ b ) )
= ( ( f1 @ c )
= ( g1 @ a ) ) )
= $false ),
inference(res,[status(thm)],[35,22]) ).
thf(76,plain,
( ( ( ( f @ a )
= ( g @ b ) )
= ( ( f2 @ c )
= ( g2 @ b ) ) )
= $false ),
inference(res,[status(thm)],[35,11]) ).
thf(77,plain,
( ( ( ( f @ a )
= ( g2 @ b ) )
= $false )
| ( ( ( g @ b )
= ( f2 @ c ) )
= $false ) ),
inference(extuni,[status(esa)],[76]) ).
thf(78,plain,
( ( ( ( g @ b )
= ( g2 @ b ) )
= $false )
| ( ( ( f @ a )
= ( f2 @ c ) )
= $false ) ),
inference(extuni,[status(esa)],[76]) ).
thf(79,plain,
( ( ( ( f @ a )
= ( g1 @ a ) )
= $false )
| ( ( ( g @ b )
= ( f1 @ c ) )
= $false ) ),
inference(extuni,[status(esa)],[75]) ).
thf(80,plain,
( ( ( ( g @ b )
= ( g1 @ a ) )
= $false )
| ( ( ( f @ a )
= ( f1 @ c ) )
= $false ) ),
inference(extuni,[status(esa)],[75]) ).
thf(81,plain,
( ( ( ( f @ a )
= ( g @ a ) )
= $false )
| ( ( ( g @ b )
= ( f @ b ) )
= $false ) ),
inference(extuni,[status(esa)],[74]) ).
thf(82,plain,
( ( b = $true )
| ( a = $true )
| ( a = $true )
| ( b = $true ) ),
inference(extuni,[status(esa)],[74]) ).
thf(84,plain,
( ( ( ( g @ b )
= ( g @ a ) )
= $false )
| ( a = $true )
| ( b = $true ) ),
inference(extuni,[status(esa)],[74]) ).
thf(86,plain,
( ( b = $false )
| ( a = $false )
| ( a = $false )
| ( b = $false ) ),
inference(extuni,[status(esa)],[74]) ).
thf(87,plain,
( ( ( ( g @ b )
= ( g @ a ) )
= $false )
| ( a = $false )
| ( b = $false ) ),
inference(extuni,[status(esa)],[74]) ).
thf(88,plain,
( ( b = $true )
| ( a = $true )
| ( ( ( f @ a )
= ( f @ b ) )
= $false ) ),
inference(extuni,[status(esa)],[74]) ).
thf(89,plain,
( ( b = $false )
| ( a = $false )
| ( ( ( f @ a )
= ( f @ b ) )
= $false ) ),
inference(extuni,[status(esa)],[74]) ).
thf(90,plain,
( ( ( ( g @ b )
= ( g @ a ) )
= $false )
| ( ( ( f @ a )
= ( f @ b ) )
= $false ) ),
inference(extuni,[status(esa)],[74]) ).
thf(91,plain,
( ( b = $false )
| ( a = $false ) ),
inference(sim,[status(thm)],[86]) ).
thf(92,plain,
( ( b = $true )
| ( a = $true ) ),
inference(sim,[status(thm)],[82]) ).
thf(93,plain,
( ( ( ( ( g2 @ c )
= ( f2 @ c ) )
= ( ( f @ b )
= ( g @ a ) ) )
= $false )
| ( ( ( f2 @ b )
= ( g2 @ b ) )
= $false ) ),
inference(res,[status(thm)],[37,33]) ).
thf(94,plain,
( ( ( ( ( f2 @ b )
= ( g2 @ b ) )
= ( ( f @ b )
= ( g @ a ) ) )
= $false )
| ( ( ( g2 @ c )
= ( f2 @ c ) )
= $false ) ),
inference(res,[status(thm)],[37,33]) ).
thf(95,plain,
( ( ( ( ( g2 @ c )
= ( f2 @ c ) )
= ( ( f1 @ c )
= ( g1 @ a ) ) )
= $false )
| ( ( ( f2 @ b )
= ( g2 @ b ) )
= $false ) ),
inference(res,[status(thm)],[37,22]) ).
thf(96,plain,
( ( ( ( ( f2 @ b )
= ( g2 @ b ) )
= ( ( f1 @ c )
= ( g1 @ a ) ) )
= $false )
| ( ( ( g2 @ c )
= ( f2 @ c ) )
= $false ) ),
inference(res,[status(thm)],[37,22]) ).
thf(97,plain,
( ( ( ( ( g2 @ c )
= ( f2 @ c ) )
= ( ( f2 @ c )
= ( g2 @ b ) ) )
= $false )
| ( ( ( f2 @ b )
= ( g2 @ b ) )
= $false ) ),
inference(res,[status(thm)],[37,11]) ).
thf(98,plain,
( ( ( ( ( f2 @ b )
= ( g2 @ b ) )
= ( ( f2 @ c )
= ( g2 @ b ) ) )
= $false )
| ( ( ( g2 @ c )
= ( f2 @ c ) )
= $false ) ),
inference(res,[status(thm)],[37,11]) ).
thf(99,plain,
( ( ( ( g2 @ c )
= ( f2 @ c ) )
= $false )
| ( ( ( ( f2 @ b )
= ( g2 @ b ) )
= ( ( g2 @ c )
= ( f2 @ c ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[37]) ).
thf(100,plain,
( ( ( ( g2 @ c )
= ( f2 @ c ) )
= $false )
| ( ( ( f2 @ b )
= ( g2 @ b ) )
= $false )
| ( ( ( g2 @ b )
= ( f2 @ c ) )
= $false ) ),
inference(extuni,[status(esa)],[98]) ).
thf(101,plain,
( ( ( ( g2 @ c )
= ( f2 @ c ) )
= $false )
| ( b = $true )
| ( c = $true ) ),
inference(extuni,[status(esa)],[98]) ).
thf(102,plain,
( ( ( ( g2 @ c )
= ( f2 @ c ) )
= $false )
| ( b = $false )
| ( c = $false ) ),
inference(extuni,[status(esa)],[98]) ).
thf(103,plain,
( ( ( ( g2 @ c )
= ( f2 @ c ) )
= $false )
| ( ( ( f2 @ b )
= ( f2 @ c ) )
= $false ) ),
inference(extuni,[status(esa)],[98]) ).
thf(104,plain,
( ( ( ( f2 @ b )
= ( g2 @ b ) )
= $false )
| ( c = $true )
| ( b = $true ) ),
inference(extuni,[status(esa)],[97]) ).
thf(105,plain,
( ( ( ( f2 @ b )
= ( g2 @ b ) )
= $false )
| ( c = $false )
| ( b = $false ) ),
inference(extuni,[status(esa)],[97]) ).
thf(106,plain,
( ( ( ( f2 @ b )
= ( g2 @ b ) )
= $false )
| ( ( ( g2 @ c )
= ( g2 @ b ) )
= $false ) ),
inference(extuni,[status(esa)],[97]) ).
thf(107,plain,
( ( ( ( f2 @ b )
= ( g2 @ b ) )
= $false )
| ( ( ( f2 @ c )
= ( g2 @ b ) )
= $false )
| ( ( ( g2 @ c )
= ( f2 @ c ) )
= $false ) ),
inference(extuni,[status(esa)],[97]) ).
thf(108,plain,
( ( ( ( g2 @ c )
= ( f2 @ c ) )
= $false )
| ( ( ( f2 @ b )
= ( g1 @ a ) )
= $false )
| ( ( ( g2 @ b )
= ( f1 @ c ) )
= $false ) ),
inference(extuni,[status(esa)],[96]) ).
thf(109,plain,
( ( ( ( g2 @ c )
= ( f2 @ c ) )
= $false )
| ( ( ( g2 @ b )
= ( g1 @ a ) )
= $false )
| ( ( ( f2 @ b )
= ( f1 @ c ) )
= $false ) ),
inference(extuni,[status(esa)],[96]) ).
thf(110,plain,
( ( ( ( f2 @ b )
= ( g2 @ b ) )
= $false )
| ( ( ( g2 @ c )
= ( g1 @ a ) )
= $false )
| ( ( ( f2 @ c )
= ( f1 @ c ) )
= $false ) ),
inference(extuni,[status(esa)],[95]) ).
thf(111,plain,
( ( ( ( f2 @ b )
= ( g2 @ b ) )
= $false )
| ( ( ( f2 @ c )
= ( g1 @ a ) )
= $false )
| ( ( ( g2 @ c )
= ( f1 @ c ) )
= $false ) ),
inference(extuni,[status(esa)],[95]) ).
thf(112,plain,
( ( ( ( g2 @ c )
= ( f2 @ c ) )
= $false )
| ( ( ( f2 @ b )
= ( g @ a ) )
= $false )
| ( ( ( g2 @ b )
= ( f @ b ) )
= $false ) ),
inference(extuni,[status(esa)],[94]) ).
thf(113,plain,
( ( ( ( g2 @ c )
= ( f2 @ c ) )
= $false )
| ( ( ( g2 @ b )
= ( g @ a ) )
= $false )
| ( ( ( f2 @ b )
= ( f @ b ) )
= $false ) ),
inference(extuni,[status(esa)],[94]) ).
thf(114,plain,
( ( ( ( f2 @ b )
= ( g2 @ b ) )
= $false )
| ( ( ( g2 @ c )
= ( g @ a ) )
= $false )
| ( ( ( f2 @ c )
= ( f @ b ) )
= $false ) ),
inference(extuni,[status(esa)],[93]) ).
thf(115,plain,
( ( ( ( f2 @ b )
= ( g2 @ b ) )
= $false )
| ( ( ( f2 @ c )
= ( g @ a ) )
= $false )
| ( ( ( g2 @ c )
= ( f @ b ) )
= $false ) ),
inference(extuni,[status(esa)],[93]) ).
thf(116,plain,
( ( b = $true )
| ( c = $true )
| ( b = $true )
| ( c = $true )
| ( ( ( g2 @ c )
= ( f2 @ c ) )
= $false ) ),
inference(extuni,[status(esa)],[99]) ).
thf(118,plain,
( ( ( ( f2 @ b )
= ( f2 @ c ) )
= $false )
| ( b = $true )
| ( c = $true )
| ( ( ( g2 @ c )
= ( f2 @ c ) )
= $false ) ),
inference(extuni,[status(esa)],[99]) ).
thf(120,plain,
( ( b = $false )
| ( c = $false )
| ( b = $false )
| ( c = $false )
| ( ( ( g2 @ c )
= ( f2 @ c ) )
= $false ) ),
inference(extuni,[status(esa)],[99]) ).
thf(121,plain,
( ( ( ( f2 @ b )
= ( f2 @ c ) )
= $false )
| ( b = $false )
| ( c = $false )
| ( ( ( g2 @ c )
= ( f2 @ c ) )
= $false ) ),
inference(extuni,[status(esa)],[99]) ).
thf(122,plain,
( ( b = $true )
| ( c = $true )
| ( ( ( g2 @ b )
= ( g2 @ c ) )
= $false )
| ( ( ( g2 @ c )
= ( f2 @ c ) )
= $false ) ),
inference(extuni,[status(esa)],[99]) ).
thf(123,plain,
( ( b = $false )
| ( c = $false )
| ( ( ( g2 @ b )
= ( g2 @ c ) )
= $false )
| ( ( ( g2 @ c )
= ( f2 @ c ) )
= $false ) ),
inference(extuni,[status(esa)],[99]) ).
thf(124,plain,
( ( ( ( f2 @ b )
= ( f2 @ c ) )
= $false )
| ( ( ( g2 @ b )
= ( g2 @ c ) )
= $false )
| ( ( ( g2 @ c )
= ( f2 @ c ) )
= $false ) ),
inference(extuni,[status(esa)],[99]) ).
thf(125,plain,
( ( ( ( g2 @ b )
= ( f2 @ c ) )
= $false )
| ( ( ( f2 @ b )
= ( g2 @ c ) )
= $false )
| ( ( ( g2 @ c )
= ( f2 @ c ) )
= $false ) ),
inference(extuni,[status(esa)],[99]) ).
thf(126,plain,
( ( b = $false )
| ( c = $false )
| ( ( ( g2 @ c )
= ( f2 @ c ) )
= $false ) ),
inference(sim,[status(thm)],[120]) ).
thf(127,plain,
( ( b = $true )
| ( c = $true )
| ( ( ( g2 @ c )
= ( f2 @ c ) )
= $false ) ),
inference(sim,[status(thm)],[116]) ).
thf(138,plain,
( ( ( ( ( g2 @ c )
= ( g2 @ b ) )
= ( ( f @ b )
= ( g @ a ) ) )
= $false )
| ( b = $true )
| ( c = $true ) ),
inference(res,[status(thm)],[40,33]) ).
thf(141,plain,
( ( ( ( ( g2 @ c )
= ( g2 @ b ) )
= ( ( f1 @ c )
= ( g1 @ a ) ) )
= $false )
| ( b = $true )
| ( c = $true ) ),
inference(res,[status(thm)],[40,22]) ).
thf(144,plain,
( ( ( ( ( g2 @ c )
= ( g2 @ b ) )
= ( ( f2 @ c )
= ( g2 @ b ) ) )
= $false )
| ( b = $true )
| ( c = $true ) ),
inference(res,[status(thm)],[40,11]) ).
thf(145,plain,
( ( c = $true )
| ( b = $true )
| ( c = $true )
| ( b = $true )
| ( ( ( g2 @ b )
= ( f2 @ c ) )
= $false ) ),
inference(extuni,[status(esa)],[144]) ).
thf(147,plain,
( ( c = $true )
| ( b = $true )
| ( ( ( g2 @ c )
= ( g2 @ b ) )
= $false )
| ( ( ( g2 @ b )
= ( f2 @ c ) )
= $false ) ),
inference(extuni,[status(esa)],[144]) ).
thf(148,plain,
( ( c = $true )
| ( b = $true )
| ( ( ( g2 @ c )
= ( f2 @ c ) )
= $false ) ),
inference(extuni,[status(esa)],[144]) ).
thf(149,plain,
( ( c = $true )
| ( b = $true )
| ( ( ( g2 @ c )
= ( g1 @ a ) )
= $false )
| ( ( ( g2 @ b )
= ( f1 @ c ) )
= $false ) ),
inference(extuni,[status(esa)],[141]) ).
thf(150,plain,
( ( c = $true )
| ( b = $true )
| ( ( ( g2 @ b )
= ( g1 @ a ) )
= $false )
| ( ( ( g2 @ c )
= ( f1 @ c ) )
= $false ) ),
inference(extuni,[status(esa)],[141]) ).
thf(151,plain,
( ( c = $true )
| ( b = $true )
| ( ( ( g2 @ c )
= ( g @ a ) )
= $false )
| ( ( ( g2 @ b )
= ( f @ b ) )
= $false ) ),
inference(extuni,[status(esa)],[138]) ).
thf(152,plain,
( ( c = $true )
| ( b = $true )
| ( ( ( g2 @ b )
= ( g @ a ) )
= $false )
| ( ( ( g2 @ c )
= ( f @ b ) )
= $false ) ),
inference(extuni,[status(esa)],[138]) ).
thf(153,plain,
( ( c = $true )
| ( b = $true )
| ( c = $true )
| ( b = $true ) ),
inference(extuni,[status(esa)],[40]) ).
thf(155,plain,
( ( c = $true )
| ( b = $true )
| ( ( ( g2 @ b )
= ( f2 @ c ) )
= $false ) ),
inference(sim,[status(thm)],[145]) ).
thf(156,plain,
( ( c = $true )
| ( b = $true ) ),
inference(sim,[status(thm)],[153]) ).
thf(165,plain,
( ( ( ( ( g2 @ c )
= ( g2 @ b ) )
= ( ( f @ b )
= ( g @ a ) ) )
= $false )
| ( b = $false )
| ( c = $false ) ),
inference(res,[status(thm)],[43,33]) ).
thf(168,plain,
( ( ( ( ( g2 @ c )
= ( g2 @ b ) )
= ( ( f1 @ c )
= ( g1 @ a ) ) )
= $false )
| ( b = $false )
| ( c = $false ) ),
inference(res,[status(thm)],[43,22]) ).
thf(171,plain,
( ( ( ( ( g2 @ c )
= ( g2 @ b ) )
= ( ( f2 @ c )
= ( g2 @ b ) ) )
= $false )
| ( b = $false )
| ( c = $false ) ),
inference(res,[status(thm)],[43,11]) ).
thf(173,plain,
( ( c = $false )
| ( b = $false )
| ( c = $false )
| ( b = $false )
| ( ( ( g2 @ b )
= ( f2 @ c ) )
= $false ) ),
inference(extuni,[status(esa)],[171]) ).
thf(174,plain,
( ( c = $false )
| ( b = $false )
| ( ( ( g2 @ c )
= ( g2 @ b ) )
= $false )
| ( ( ( g2 @ b )
= ( f2 @ c ) )
= $false ) ),
inference(extuni,[status(esa)],[171]) ).
thf(175,plain,
( ( c = $false )
| ( b = $false )
| ( ( ( g2 @ c )
= ( f2 @ c ) )
= $false ) ),
inference(extuni,[status(esa)],[171]) ).
thf(176,plain,
( ( c = $false )
| ( b = $false )
| ( ( ( g2 @ c )
= ( g1 @ a ) )
= $false )
| ( ( ( g2 @ b )
= ( f1 @ c ) )
= $false ) ),
inference(extuni,[status(esa)],[168]) ).
thf(177,plain,
( ( c = $false )
| ( b = $false )
| ( ( ( g2 @ b )
= ( g1 @ a ) )
= $false )
| ( ( ( g2 @ c )
= ( f1 @ c ) )
= $false ) ),
inference(extuni,[status(esa)],[168]) ).
thf(178,plain,
( ( c = $false )
| ( b = $false )
| ( ( ( g2 @ c )
= ( g @ a ) )
= $false )
| ( ( ( g2 @ b )
= ( f @ b ) )
= $false ) ),
inference(extuni,[status(esa)],[165]) ).
thf(179,plain,
( ( c = $false )
| ( b = $false )
| ( ( ( g2 @ b )
= ( g @ a ) )
= $false )
| ( ( ( g2 @ c )
= ( f @ b ) )
= $false ) ),
inference(extuni,[status(esa)],[165]) ).
thf(199,plain,
( ( c = $false )
| ( b = $false )
| ( c = $false )
| ( b = $false ) ),
inference(extuni,[status(esa)],[43]) ).
thf(200,plain,
( ( c = $false )
| ( b = $false )
| ( ( ( g2 @ b )
= ( f2 @ c ) )
= $false ) ),
inference(sim,[status(thm)],[173]) ).
thf(201,plain,
( ( c = $false )
| ( b = $false ) ),
inference(sim,[status(thm)],[199]) ).
thf(202,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[11,201,200,179,178,177,176,175,174,156,155,152,151,150,149,148,147,127,126,125,124,123,122,121,118,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,92,91,90,89,88,87,84,81,80,79,78,77,73,72,71,70,67,66,65,64,63,62,59,56,55,54,51,50,48,47,46,45,44,43,40,37,35,33,29,22,18]) ).
thf(203,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[202]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SYO499^1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sat Jul 9 08:51:01 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35
% 0.14/0.35 No.of.Axioms: 0
% 0.14/0.35
% 0.14/0.35 Length.of.Defs: 0
% 0.14/0.35
% 0.14/0.35 Contains.Choice.Funs: false
% 0.14/0.35 (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)....
% 0.21/0.46
% 0.21/0.46 ********************************
% 0.21/0.46 * All subproblems solved! *
% 0.21/0.46 ********************************
% 0.21/0.46 % 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:202,loop_count:10,foatp_calls:2,translation:fof_full)
% 0.21/0.51
% 0.21/0.51 %**** Beginning of derivation protocol ****
% 0.21/0.51 % SZS output start CNFRefutation
% See solution above
% 0.21/0.51
% 0.21/0.51 %**** End of derivation protocol ****
% 0.21/0.51 %**** no. of clauses in derivation: 147 ****
% 0.21/0.51 %**** clause counter: 202 ****
% 0.21/0.51
% 0.21/0.51 % 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:202,loop_count:10,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------