TSTP Solution File: GRP130-3.003 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GRP130-3.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n015.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 : Sat Jul 16 10:16:21 EDT 2022
% Result : Unsatisfiable 1.63s 1.90s
% Output : CNFRefutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 41
% Syntax : Number of formulae : 226 ( 128 unt; 10 typ; 0 def)
% Number of atoms : 1381 ( 347 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 2311 ( 352 ~; 471 |; 0 &;1488 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 538 ( 0 ^ 538 !; 0 ?; 538 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cycle,type,
cycle: $i > $i > $o ).
thf(tp_e_0,type,
e_0: $i ).
thf(tp_e_1,type,
e_1: $i ).
thf(tp_e_2,type,
e_2: $i ).
thf(tp_e_3,type,
e_3: $i ).
thf(tp_equalish,type,
equalish: $i > $i > $o ).
thf(tp_greater,type,
greater: $i > $i > $o ).
thf(tp_group_element,type,
group_element: $i > $o ).
thf(tp_next,type,
next: $i > $i > $o ).
thf(tp_product,type,
product: $i > $i > $i > $o ).
thf(1,axiom,
! [W: $i,Y: $i,X: $i,Z: $i] :
( ~ ( product @ W @ Y @ X )
| ~ ( product @ Z @ Y @ X )
| ( equalish @ W @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
thf(2,axiom,
! [X: $i,W: $i,Y: $i,Z: $i] :
( ~ ( product @ X @ W @ Y )
| ~ ( product @ X @ Z @ Y )
| ( equalish @ W @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
thf(3,axiom,
! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( product @ X @ Y @ W )
| ~ ( product @ X @ Y @ Z )
| ( equalish @ W @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function2) ).
thf(4,axiom,
! [X: $i,Y: $i] :
( ~ ( group_element @ X )
| ~ ( group_element @ Y )
| ( product @ X @ Y @ e_1 )
| ( product @ X @ Y @ e_2 )
| ( product @ X @ Y @ e_3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
thf(5,axiom,
~ ( equalish @ e_3 @ e_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
thf(6,axiom,
~ ( equalish @ e_3 @ e_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
thf(7,axiom,
~ ( equalish @ e_2 @ e_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
thf(8,axiom,
~ ( equalish @ e_2 @ e_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
thf(9,axiom,
~ ( equalish @ e_1 @ e_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
thf(10,axiom,
~ ( equalish @ e_1 @ e_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
thf(11,axiom,
group_element @ e_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
thf(12,axiom,
group_element @ e_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
thf(13,axiom,
group_element @ e_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
thf(14,axiom,
! [X: $i,Y: $i,Z: $i,X1: $i] :
( ~ ( cycle @ X @ Y )
| ~ ( product @ X @ e_1 @ Z )
| ~ ( greater @ Y @ e_0 )
| ~ ( next @ X @ X1 )
| ( equalish @ Z @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cycle7) ).
thf(15,axiom,
! [X: $i,Y: $i] :
( ~ ( cycle @ X @ e_0 )
| ~ ( product @ X @ e_1 @ Y )
| ~ ( greater @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cycle6) ).
thf(16,axiom,
! [X: $i,Z1: $i,Y: $i,W: $i,Z2: $i] :
( ~ ( cycle @ X @ Z1 )
| ~ ( cycle @ Y @ e_0 )
| ~ ( cycle @ W @ Z2 )
| ~ ( next @ Y @ W )
| ~ ( greater @ Y @ X )
| ~ ( greater @ Z1 @ Z2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cycle5) ).
thf(17,axiom,
! [X: $i,Y: $i,W: $i,Z: $i,Z1: $i] :
( ~ ( cycle @ X @ Y )
| ~ ( cycle @ W @ Z )
| ~ ( next @ X @ W )
| ~ ( greater @ Y @ e_0 )
| ~ ( next @ Z @ Z1 )
| ( equalish @ Y @ Z1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cycle4) ).
thf(18,axiom,
cycle @ e_3 @ e_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cycle3) ).
thf(19,axiom,
! [X: $i] :
( ~ ( group_element @ X )
| ( cycle @ X @ e_0 )
| ( cycle @ X @ e_1 )
| ( cycle @ X @ e_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cycle2) ).
thf(20,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( cycle @ X @ Y )
| ~ ( cycle @ X @ Z )
| ( equalish @ Y @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cycle1) ).
thf(21,axiom,
greater @ e_3 @ e_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_greater_e_2) ).
thf(22,axiom,
greater @ e_3 @ e_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_greater_e_1) ).
thf(23,axiom,
greater @ e_2 @ e_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_greater_e_1) ).
thf(24,axiom,
greater @ e_3 @ e_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_greater_e_0) ).
thf(25,axiom,
greater @ e_2 @ e_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_greater_e_0) ).
thf(26,axiom,
greater @ e_1 @ e_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_greater_e_0) ).
thf(27,axiom,
next @ e_2 @ e_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_then_e_3) ).
thf(28,axiom,
next @ e_1 @ e_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_then_e_2) ).
thf(29,axiom,
next @ e_0 @ e_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_0_then_e_1) ).
thf(30,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(31,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[30]) ).
thf(32,negated_conjecture,
! [X: $i,Y: $i,Z1: $i,Z2: $i] :
( ~ ( product @ X @ Y @ Z1 )
| ~ ( product @ X @ Z1 @ Z2 )
| ( product @ Z2 @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).
thf(33,plain,
$false = $false,
inference(unfold_def,[status(thm)],[31]) ).
thf(34,plain,
( ( ! [W: $i,Y: $i,X: $i,Z: $i] :
( ~ ( product @ W @ Y @ X )
| ~ ( product @ Z @ Y @ X )
| ( equalish @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(35,plain,
( ( ! [X: $i,W: $i,Y: $i,Z: $i] :
( ~ ( product @ X @ W @ Y )
| ~ ( product @ X @ Z @ Y )
| ( equalish @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(36,plain,
( ( ! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( product @ X @ Y @ W )
| ~ ( product @ X @ Y @ Z )
| ( equalish @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(37,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( group_element @ X )
| ~ ( group_element @ Y )
| ( product @ X @ Y @ e_1 )
| ( product @ X @ Y @ e_2 )
| ( product @ X @ Y @ e_3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(38,plain,
( ( ~ ( equalish @ e_3 @ e_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(39,plain,
( ( ~ ( equalish @ e_3 @ e_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(40,plain,
( ( ~ ( equalish @ e_2 @ e_3 ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(41,plain,
( ( ~ ( equalish @ e_2 @ e_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(42,plain,
( ( ~ ( equalish @ e_1 @ e_3 ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(43,plain,
( ( ~ ( equalish @ e_1 @ e_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(44,plain,
( ( group_element @ e_3 )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(45,plain,
( ( group_element @ e_2 )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(46,plain,
( ( group_element @ e_1 )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(47,plain,
( ( ! [X: $i,Y: $i,Z: $i,X1: $i] :
( ~ ( cycle @ X @ Y )
| ~ ( product @ X @ e_1 @ Z )
| ~ ( greater @ Y @ e_0 )
| ~ ( next @ X @ X1 )
| ( equalish @ Z @ X1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(48,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( cycle @ X @ e_0 )
| ~ ( product @ X @ e_1 @ Y )
| ~ ( greater @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(49,plain,
( ( ! [X: $i,Z1: $i,Y: $i,W: $i,Z2: $i] :
( ~ ( cycle @ X @ Z1 )
| ~ ( cycle @ Y @ e_0 )
| ~ ( cycle @ W @ Z2 )
| ~ ( next @ Y @ W )
| ~ ( greater @ Y @ X )
| ~ ( greater @ Z1 @ Z2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(50,plain,
( ( ! [X: $i,Y: $i,W: $i,Z: $i,Z1: $i] :
( ~ ( cycle @ X @ Y )
| ~ ( cycle @ W @ Z )
| ~ ( next @ X @ W )
| ~ ( greater @ Y @ e_0 )
| ~ ( next @ Z @ Z1 )
| ( equalish @ Y @ Z1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(51,plain,
( ( cycle @ e_3 @ e_0 )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(52,plain,
( ( ! [X: $i] :
( ~ ( group_element @ X )
| ( cycle @ X @ e_0 )
| ( cycle @ X @ e_1 )
| ( cycle @ X @ e_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(53,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( cycle @ X @ Y )
| ~ ( cycle @ X @ Z )
| ( equalish @ Y @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(54,plain,
( ( greater @ e_3 @ e_2 )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(55,plain,
( ( greater @ e_3 @ e_1 )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(56,plain,
( ( greater @ e_2 @ e_1 )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(57,plain,
( ( greater @ e_3 @ e_0 )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(58,plain,
( ( greater @ e_2 @ e_0 )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(59,plain,
( ( greater @ e_1 @ e_0 )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(60,plain,
( ( next @ e_2 @ e_3 )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(61,plain,
( ( next @ e_1 @ e_2 )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(62,plain,
( ( next @ e_0 @ e_1 )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(63,plain,
( ( ! [X: $i,Y: $i,Z1: $i,Z2: $i] :
( ~ ( product @ X @ Y @ Z1 )
| ~ ( product @ X @ Z1 @ Z2 )
| ( product @ Z2 @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(64,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[33]) ).
thf(65,plain,
( ( ! [W: $i,Y: $i,X: $i] :
( ~ ( product @ W @ Y @ X )
| ! [Z: $i] :
( ~ ( product @ Z @ Y @ X )
| ( equalish @ W @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[34]) ).
thf(66,plain,
( ( ! [X: $i,W: $i,Y: $i] :
( ~ ( product @ X @ W @ Y )
| ! [Z: $i] :
( ~ ( product @ X @ Z @ Y )
| ( equalish @ W @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[35]) ).
thf(67,plain,
( ( ! [X: $i,Y: $i,W: $i] :
( ~ ( product @ X @ Y @ W )
| ! [Z: $i] :
( ~ ( product @ X @ Y @ Z )
| ( equalish @ W @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[36]) ).
thf(68,plain,
( ( ! [X: $i] :
( ~ ( group_element @ X )
| ! [Y: $i] :
( ~ ( group_element @ Y )
| ( product @ X @ Y @ e_1 )
| ( product @ X @ Y @ e_2 )
| ( product @ X @ Y @ e_3 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[37]) ).
thf(69,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( cycle @ X @ Y )
| ! [Z: $i] :
( ~ ( product @ X @ e_1 @ Z )
| ~ ( greater @ Y @ e_0 )
| ! [X1: $i] :
( ~ ( next @ X @ X1 )
| ( equalish @ Z @ X1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[47]) ).
thf(70,plain,
( ( ! [X: $i] :
( ~ ( cycle @ X @ e_0 )
| ! [Y: $i] :
( ~ ( product @ X @ e_1 @ Y )
| ~ ( greater @ Y @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[48]) ).
thf(71,plain,
( ( ! [X: $i,Z1: $i,Y: $i] :
( ~ ( cycle @ X @ Z1 )
| ~ ( cycle @ Y @ e_0 )
| ! [W: $i,Z2: $i] :
( ~ ( cycle @ W @ Z2 )
| ~ ( next @ Y @ W )
| ~ ( greater @ Y @ X )
| ~ ( greater @ Z1 @ Z2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[49]) ).
thf(72,plain,
( ( ! [X: $i,Y: $i,W: $i] :
( ~ ( cycle @ X @ Y )
| ! [Z: $i] :
( ~ ( cycle @ W @ Z )
| ~ ( next @ X @ W )
| ~ ( greater @ Y @ e_0 )
| ! [Z1: $i] :
( ~ ( next @ Z @ Z1 )
| ( equalish @ Y @ Z1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[50]) ).
thf(73,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( cycle @ X @ Y )
| ! [Z: $i] :
( ~ ( cycle @ X @ Z )
| ( equalish @ Y @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[53]) ).
thf(74,plain,
( ( ! [X: $i,Y: $i,Z1: $i] :
( ~ ( product @ X @ Y @ Z1 )
| ! [Z2: $i] :
( ~ ( product @ X @ Z1 @ Z2 )
| ( product @ Z2 @ Y @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[63]) ).
thf(75,plain,
( ( ! [X: $i,Y: $i,Z1: $i] :
( ~ ( product @ X @ Y @ Z1 )
| ! [Z2: $i] :
( ~ ( product @ X @ Z1 @ Z2 )
| ( product @ Z2 @ Y @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(76,plain,
( ( next @ e_0 @ e_1 )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(77,plain,
( ( next @ e_1 @ e_2 )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(78,plain,
( ( next @ e_2 @ e_3 )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(79,plain,
( ( greater @ e_1 @ e_0 )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(80,plain,
( ( greater @ e_2 @ e_0 )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(81,plain,
( ( greater @ e_3 @ e_0 )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(82,plain,
( ( greater @ e_2 @ e_1 )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(83,plain,
( ( greater @ e_3 @ e_1 )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(84,plain,
( ( greater @ e_3 @ e_2 )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(85,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( cycle @ X @ Y )
| ! [Z: $i] :
( ~ ( cycle @ X @ Z )
| ( equalish @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(86,plain,
( ( ! [X: $i] :
( ~ ( group_element @ X )
| ( cycle @ X @ e_0 )
| ( cycle @ X @ e_1 )
| ( cycle @ X @ e_2 ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(87,plain,
( ( cycle @ e_3 @ e_0 )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(88,plain,
( ( ! [X: $i,Y: $i,W: $i] :
( ~ ( cycle @ X @ Y )
| ! [Z: $i] :
( ~ ( cycle @ W @ Z )
| ~ ( next @ X @ W )
| ~ ( greater @ Y @ e_0 )
| ! [Z1: $i] :
( ~ ( next @ Z @ Z1 )
| ( equalish @ Y @ Z1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(89,plain,
( ( ! [X: $i,Z1: $i,Y: $i] :
( ~ ( cycle @ X @ Z1 )
| ~ ( cycle @ Y @ e_0 )
| ! [W: $i,Z2: $i] :
( ~ ( cycle @ W @ Z2 )
| ~ ( next @ Y @ W )
| ~ ( greater @ Y @ X )
| ~ ( greater @ Z1 @ Z2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(90,plain,
( ( ! [X: $i] :
( ~ ( cycle @ X @ e_0 )
| ! [Y: $i] :
( ~ ( product @ X @ e_1 @ Y )
| ~ ( greater @ Y @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(91,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( cycle @ X @ Y )
| ! [Z: $i] :
( ~ ( product @ X @ e_1 @ Z )
| ~ ( greater @ Y @ e_0 )
| ! [X1: $i] :
( ~ ( next @ X @ X1 )
| ( equalish @ Z @ X1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(92,plain,
( ( group_element @ e_1 )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(93,plain,
( ( group_element @ e_2 )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(94,plain,
( ( group_element @ e_3 )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(95,plain,
( ( ~ ( equalish @ e_1 @ e_2 ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(96,plain,
( ( ~ ( equalish @ e_1 @ e_3 ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(97,plain,
( ( ~ ( equalish @ e_2 @ e_1 ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(98,plain,
( ( ~ ( equalish @ e_2 @ e_3 ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(99,plain,
( ( ~ ( equalish @ e_3 @ e_1 ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(100,plain,
( ( ~ ( equalish @ e_3 @ e_2 ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(101,plain,
( ( ! [X: $i] :
( ~ ( group_element @ X )
| ! [Y: $i] :
( ~ ( group_element @ Y )
| ( product @ X @ Y @ e_1 )
| ( product @ X @ Y @ e_2 )
| ( product @ X @ Y @ e_3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(102,plain,
( ( ! [X: $i,Y: $i,W: $i] :
( ~ ( product @ X @ Y @ W )
| ! [Z: $i] :
( ~ ( product @ X @ Y @ Z )
| ( equalish @ W @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(103,plain,
( ( ! [X: $i,W: $i,Y: $i] :
( ~ ( product @ X @ W @ Y )
| ! [Z: $i] :
( ~ ( product @ X @ Z @ Y )
| ( equalish @ W @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(104,plain,
( ( ! [W: $i,Y: $i,X: $i] :
( ~ ( product @ W @ Y @ X )
| ! [Z: $i] :
( ~ ( product @ Z @ Y @ X )
| ( equalish @ W @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(105,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(106,plain,
! [SV1: $i] :
( ( ! [SY38: $i,SY39: $i] :
( ~ ( product @ SV1 @ SY38 @ SY39 )
| ! [SY40: $i] :
( ~ ( product @ SV1 @ SY39 @ SY40 )
| ( product @ SY40 @ SY38 @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(107,plain,
! [SV2: $i] :
( ( ! [SY41: $i] :
( ~ ( cycle @ SV2 @ SY41 )
| ! [SY42: $i] :
( ~ ( cycle @ SV2 @ SY42 )
| ( equalish @ SY41 @ SY42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(108,plain,
! [SV3: $i] :
( ( ~ ( group_element @ SV3 )
| ( cycle @ SV3 @ e_0 )
| ( cycle @ SV3 @ e_1 )
| ( cycle @ SV3 @ e_2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(109,plain,
! [SV4: $i] :
( ( ! [SY43: $i,SY44: $i] :
( ~ ( cycle @ SV4 @ SY43 )
| ! [SY45: $i] :
( ~ ( cycle @ SY44 @ SY45 )
| ~ ( next @ SV4 @ SY44 )
| ~ ( greater @ SY43 @ e_0 )
| ! [Z1: $i] :
( ~ ( next @ SY45 @ Z1 )
| ( equalish @ SY43 @ Z1 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(110,plain,
! [SV5: $i] :
( ( ! [SY47: $i,SY48: $i] :
( ~ ( cycle @ SV5 @ SY47 )
| ~ ( cycle @ SY48 @ e_0 )
| ! [SY49: $i,SY50: $i] :
( ~ ( cycle @ SY49 @ SY50 )
| ~ ( next @ SY48 @ SY49 )
| ~ ( greater @ SY48 @ SV5 )
| ~ ( greater @ SY47 @ SY50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(111,plain,
! [SV6: $i] :
( ( ~ ( cycle @ SV6 @ e_0 )
| ! [SY51: $i] :
( ~ ( product @ SV6 @ e_1 @ SY51 )
| ~ ( greater @ SY51 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(112,plain,
! [SV7: $i] :
( ( ! [SY52: $i] :
( ~ ( cycle @ SV7 @ SY52 )
| ! [SY53: $i] :
( ~ ( product @ SV7 @ e_1 @ SY53 )
| ~ ( greater @ SY52 @ e_0 )
| ! [SY54: $i] :
( ~ ( next @ SV7 @ SY54 )
| ( equalish @ SY53 @ SY54 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(113,plain,
( ( equalish @ e_1 @ e_2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(114,plain,
( ( equalish @ e_1 @ e_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(115,plain,
( ( equalish @ e_2 @ e_1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(116,plain,
( ( equalish @ e_2 @ e_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(117,plain,
( ( equalish @ e_3 @ e_1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(118,plain,
( ( equalish @ e_3 @ e_2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(119,plain,
! [SV8: $i] :
( ( ~ ( group_element @ SV8 )
| ! [SY55: $i] :
( ~ ( group_element @ SY55 )
| ( product @ SV8 @ SY55 @ e_1 )
| ( product @ SV8 @ SY55 @ e_2 )
| ( product @ SV8 @ SY55 @ e_3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(120,plain,
! [SV9: $i] :
( ( ! [SY56: $i,SY57: $i] :
( ~ ( product @ SV9 @ SY56 @ SY57 )
| ! [SY58: $i] :
( ~ ( product @ SV9 @ SY56 @ SY58 )
| ( equalish @ SY57 @ SY58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(121,plain,
! [SV10: $i] :
( ( ! [SY59: $i,SY60: $i] :
( ~ ( product @ SV10 @ SY59 @ SY60 )
| ! [SY61: $i] :
( ~ ( product @ SV10 @ SY61 @ SY60 )
| ( equalish @ SY59 @ SY61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(122,plain,
! [SV11: $i] :
( ( ! [SY62: $i,SY63: $i] :
( ~ ( product @ SV11 @ SY62 @ SY63 )
| ! [SY64: $i] :
( ~ ( product @ SY64 @ SY62 @ SY63 )
| ( equalish @ SV11 @ SY64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(123,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(124,plain,
! [SV12: $i,SV1: $i] :
( ( ! [SY65: $i] :
( ~ ( product @ SV1 @ SV12 @ SY65 )
| ! [SY66: $i] :
( ~ ( product @ SV1 @ SY65 @ SY66 )
| ( product @ SY66 @ SV12 @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(125,plain,
! [SV13: $i,SV2: $i] :
( ( ~ ( cycle @ SV2 @ SV13 )
| ! [SY67: $i] :
( ~ ( cycle @ SV2 @ SY67 )
| ( equalish @ SV13 @ SY67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(126,plain,
! [SV3: $i] :
( ( ( ~ ( group_element @ SV3 ) )
= $true )
| ( ( ( cycle @ SV3 @ e_0 )
| ( cycle @ SV3 @ e_1 )
| ( cycle @ SV3 @ e_2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(127,plain,
! [SV14: $i,SV4: $i] :
( ( ! [SY68: $i] :
( ~ ( cycle @ SV4 @ SV14 )
| ! [SY69: $i] :
( ~ ( cycle @ SY68 @ SY69 )
| ~ ( next @ SV4 @ SY68 )
| ~ ( greater @ SV14 @ e_0 )
| ! [SY70: $i] :
( ~ ( next @ SY69 @ SY70 )
| ( equalish @ SV14 @ SY70 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(128,plain,
! [SV15: $i,SV5: $i] :
( ( ! [SY71: $i] :
( ~ ( cycle @ SV5 @ SV15 )
| ~ ( cycle @ SY71 @ e_0 )
| ! [SY72: $i,SY73: $i] :
( ~ ( cycle @ SY72 @ SY73 )
| ~ ( next @ SY71 @ SY72 )
| ~ ( greater @ SY71 @ SV5 )
| ~ ( greater @ SV15 @ SY73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(129,plain,
! [SV6: $i] :
( ( ( ~ ( cycle @ SV6 @ e_0 ) )
= $true )
| ( ( ! [SY51: $i] :
( ~ ( product @ SV6 @ e_1 @ SY51 )
| ~ ( greater @ SY51 @ SV6 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(130,plain,
! [SV16: $i,SV7: $i] :
( ( ~ ( cycle @ SV7 @ SV16 )
| ! [SY74: $i] :
( ~ ( product @ SV7 @ e_1 @ SY74 )
| ~ ( greater @ SV16 @ e_0 )
| ! [SY54: $i] :
( ~ ( next @ SV7 @ SY54 )
| ( equalish @ SY74 @ SY54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(131,plain,
! [SV8: $i] :
( ( ( ~ ( group_element @ SV8 ) )
= $true )
| ( ( ! [SY55: $i] :
( ~ ( group_element @ SY55 )
| ( product @ SV8 @ SY55 @ e_1 )
| ( product @ SV8 @ SY55 @ e_2 )
| ( product @ SV8 @ SY55 @ e_3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(132,plain,
! [SV17: $i,SV9: $i] :
( ( ! [SY76: $i] :
( ~ ( product @ SV9 @ SV17 @ SY76 )
| ! [SY77: $i] :
( ~ ( product @ SV9 @ SV17 @ SY77 )
| ( equalish @ SY76 @ SY77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(133,plain,
! [SV18: $i,SV10: $i] :
( ( ! [SY78: $i] :
( ~ ( product @ SV10 @ SV18 @ SY78 )
| ! [SY79: $i] :
( ~ ( product @ SV10 @ SY79 @ SY78 )
| ( equalish @ SV18 @ SY79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(134,plain,
! [SV19: $i,SV11: $i] :
( ( ! [SY80: $i] :
( ~ ( product @ SV11 @ SV19 @ SY80 )
| ! [SY81: $i] :
( ~ ( product @ SY81 @ SV19 @ SY80 )
| ( equalish @ SV11 @ SY81 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(135,plain,
! [SV20: $i,SV12: $i,SV1: $i] :
( ( ~ ( product @ SV1 @ SV12 @ SV20 )
| ! [SY82: $i] :
( ~ ( product @ SV1 @ SV20 @ SY82 )
| ( product @ SY82 @ SV12 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(136,plain,
! [SV13: $i,SV2: $i] :
( ( ( ~ ( cycle @ SV2 @ SV13 ) )
= $true )
| ( ( ! [SY67: $i] :
( ~ ( cycle @ SV2 @ SY67 )
| ( equalish @ SV13 @ SY67 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(137,plain,
! [SV3: $i] :
( ( ( group_element @ SV3 )
= $false )
| ( ( ( cycle @ SV3 @ e_0 )
| ( cycle @ SV3 @ e_1 )
| ( cycle @ SV3 @ e_2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(138,plain,
! [SV21: $i,SV14: $i,SV4: $i] :
( ( ~ ( cycle @ SV4 @ SV14 )
| ! [SY83: $i] :
( ~ ( cycle @ SV21 @ SY83 )
| ~ ( next @ SV4 @ SV21 )
| ~ ( greater @ SV14 @ e_0 )
| ! [SY70: $i] :
( ~ ( next @ SY83 @ SY70 )
| ( equalish @ SV14 @ SY70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(139,plain,
! [SV22: $i,SV15: $i,SV5: $i] :
( ( ~ ( cycle @ SV5 @ SV15 )
| ~ ( cycle @ SV22 @ e_0 )
| ! [SY85: $i,SY86: $i] :
( ~ ( cycle @ SY85 @ SY86 )
| ~ ( next @ SV22 @ SY85 )
| ~ ( greater @ SV22 @ SV5 )
| ~ ( greater @ SV15 @ SY86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(140,plain,
! [SV6: $i] :
( ( ( cycle @ SV6 @ e_0 )
= $false )
| ( ( ! [SY51: $i] :
( ~ ( product @ SV6 @ e_1 @ SY51 )
| ~ ( greater @ SY51 @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(141,plain,
! [SV16: $i,SV7: $i] :
( ( ( ~ ( cycle @ SV7 @ SV16 ) )
= $true )
| ( ( ! [SY74: $i] :
( ~ ( product @ SV7 @ e_1 @ SY74 )
| ~ ( greater @ SV16 @ e_0 )
| ! [SY54: $i] :
( ~ ( next @ SV7 @ SY54 )
| ( equalish @ SY74 @ SY54 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(142,plain,
! [SV8: $i] :
( ( ( group_element @ SV8 )
= $false )
| ( ( ! [SY55: $i] :
( ~ ( group_element @ SY55 )
| ( product @ SV8 @ SY55 @ e_1 )
| ( product @ SV8 @ SY55 @ e_2 )
| ( product @ SV8 @ SY55 @ e_3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(143,plain,
! [SV23: $i,SV17: $i,SV9: $i] :
( ( ~ ( product @ SV9 @ SV17 @ SV23 )
| ! [SY87: $i] :
( ~ ( product @ SV9 @ SV17 @ SY87 )
| ( equalish @ SV23 @ SY87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(144,plain,
! [SV24: $i,SV18: $i,SV10: $i] :
( ( ~ ( product @ SV10 @ SV18 @ SV24 )
| ! [SY88: $i] :
( ~ ( product @ SV10 @ SY88 @ SV24 )
| ( equalish @ SV18 @ SY88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(145,plain,
! [SV25: $i,SV19: $i,SV11: $i] :
( ( ~ ( product @ SV11 @ SV19 @ SV25 )
| ! [SY89: $i] :
( ~ ( product @ SY89 @ SV19 @ SV25 )
| ( equalish @ SV11 @ SY89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(146,plain,
! [SV20: $i,SV12: $i,SV1: $i] :
( ( ( ~ ( product @ SV1 @ SV12 @ SV20 ) )
= $true )
| ( ( ! [SY82: $i] :
( ~ ( product @ SV1 @ SV20 @ SY82 )
| ( product @ SY82 @ SV12 @ SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(147,plain,
! [SV13: $i,SV2: $i] :
( ( ( cycle @ SV2 @ SV13 )
= $false )
| ( ( ! [SY67: $i] :
( ~ ( cycle @ SV2 @ SY67 )
| ( equalish @ SV13 @ SY67 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(148,plain,
! [SV3: $i] :
( ( ( cycle @ SV3 @ e_0 )
= $true )
| ( ( ( cycle @ SV3 @ e_1 )
| ( cycle @ SV3 @ e_2 ) )
= $true )
| ( ( group_element @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(149,plain,
! [SV21: $i,SV14: $i,SV4: $i] :
( ( ( ~ ( cycle @ SV4 @ SV14 ) )
= $true )
| ( ( ! [SY83: $i] :
( ~ ( cycle @ SV21 @ SY83 )
| ~ ( next @ SV4 @ SV21 )
| ~ ( greater @ SV14 @ e_0 )
| ! [SY70: $i] :
( ~ ( next @ SY83 @ SY70 )
| ( equalish @ SV14 @ SY70 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(150,plain,
! [SV22: $i,SV15: $i,SV5: $i] :
( ( ( ~ ( cycle @ SV5 @ SV15 ) )
= $true )
| ( ( ~ ( cycle @ SV22 @ e_0 )
| ! [SY85: $i,SY86: $i] :
( ~ ( cycle @ SY85 @ SY86 )
| ~ ( next @ SV22 @ SY85 )
| ~ ( greater @ SV22 @ SV5 )
| ~ ( greater @ SV15 @ SY86 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(151,plain,
! [SV26: $i,SV6: $i] :
( ( ( ~ ( product @ SV6 @ e_1 @ SV26 )
| ~ ( greater @ SV26 @ SV6 ) )
= $true )
| ( ( cycle @ SV6 @ e_0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(152,plain,
! [SV16: $i,SV7: $i] :
( ( ( cycle @ SV7 @ SV16 )
= $false )
| ( ( ! [SY74: $i] :
( ~ ( product @ SV7 @ e_1 @ SY74 )
| ~ ( greater @ SV16 @ e_0 )
| ! [SY54: $i] :
( ~ ( next @ SV7 @ SY54 )
| ( equalish @ SY74 @ SY54 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(153,plain,
! [SV8: $i,SV27: $i] :
( ( ( ~ ( group_element @ SV27 )
| ( product @ SV8 @ SV27 @ e_1 )
| ( product @ SV8 @ SV27 @ e_2 )
| ( product @ SV8 @ SV27 @ e_3 ) )
= $true )
| ( ( group_element @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(154,plain,
! [SV23: $i,SV17: $i,SV9: $i] :
( ( ( ~ ( product @ SV9 @ SV17 @ SV23 ) )
= $true )
| ( ( ! [SY87: $i] :
( ~ ( product @ SV9 @ SV17 @ SY87 )
| ( equalish @ SV23 @ SY87 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(155,plain,
! [SV24: $i,SV18: $i,SV10: $i] :
( ( ( ~ ( product @ SV10 @ SV18 @ SV24 ) )
= $true )
| ( ( ! [SY88: $i] :
( ~ ( product @ SV10 @ SY88 @ SV24 )
| ( equalish @ SV18 @ SY88 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(156,plain,
! [SV25: $i,SV19: $i,SV11: $i] :
( ( ( ~ ( product @ SV11 @ SV19 @ SV25 ) )
= $true )
| ( ( ! [SY89: $i] :
( ~ ( product @ SY89 @ SV19 @ SV25 )
| ( equalish @ SV11 @ SY89 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(157,plain,
! [SV20: $i,SV12: $i,SV1: $i] :
( ( ( product @ SV1 @ SV12 @ SV20 )
= $false )
| ( ( ! [SY82: $i] :
( ~ ( product @ SV1 @ SV20 @ SY82 )
| ( product @ SY82 @ SV12 @ SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(158,plain,
! [SV13: $i,SV28: $i,SV2: $i] :
( ( ( ~ ( cycle @ SV2 @ SV28 )
| ( equalish @ SV13 @ SV28 ) )
= $true )
| ( ( cycle @ SV2 @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(159,plain,
! [SV3: $i] :
( ( ( cycle @ SV3 @ e_1 )
= $true )
| ( ( cycle @ SV3 @ e_2 )
= $true )
| ( ( cycle @ SV3 @ e_0 )
= $true )
| ( ( group_element @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(160,plain,
! [SV21: $i,SV14: $i,SV4: $i] :
( ( ( cycle @ SV4 @ SV14 )
= $false )
| ( ( ! [SY83: $i] :
( ~ ( cycle @ SV21 @ SY83 )
| ~ ( next @ SV4 @ SV21 )
| ~ ( greater @ SV14 @ e_0 )
| ! [SY70: $i] :
( ~ ( next @ SY83 @ SY70 )
| ( equalish @ SV14 @ SY70 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(161,plain,
! [SV22: $i,SV15: $i,SV5: $i] :
( ( ( cycle @ SV5 @ SV15 )
= $false )
| ( ( ~ ( cycle @ SV22 @ e_0 )
| ! [SY85: $i,SY86: $i] :
( ~ ( cycle @ SY85 @ SY86 )
| ~ ( next @ SV22 @ SY85 )
| ~ ( greater @ SV22 @ SV5 )
| ~ ( greater @ SV15 @ SY86 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(162,plain,
! [SV26: $i,SV6: $i] :
( ( ( ~ ( product @ SV6 @ e_1 @ SV26 ) )
= $true )
| ( ( ~ ( greater @ SV26 @ SV6 ) )
= $true )
| ( ( cycle @ SV6 @ e_0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(163,plain,
! [SV16: $i,SV29: $i,SV7: $i] :
( ( ( ~ ( product @ SV7 @ e_1 @ SV29 )
| ~ ( greater @ SV16 @ e_0 )
| ! [SY90: $i] :
( ~ ( next @ SV7 @ SY90 )
| ( equalish @ SV29 @ SY90 ) ) )
= $true )
| ( ( cycle @ SV7 @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(164,plain,
! [SV8: $i,SV27: $i] :
( ( ( ~ ( group_element @ SV27 ) )
= $true )
| ( ( ( product @ SV8 @ SV27 @ e_1 )
| ( product @ SV8 @ SV27 @ e_2 )
| ( product @ SV8 @ SV27 @ e_3 ) )
= $true )
| ( ( group_element @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(165,plain,
! [SV23: $i,SV17: $i,SV9: $i] :
( ( ( product @ SV9 @ SV17 @ SV23 )
= $false )
| ( ( ! [SY87: $i] :
( ~ ( product @ SV9 @ SV17 @ SY87 )
| ( equalish @ SV23 @ SY87 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(166,plain,
! [SV24: $i,SV18: $i,SV10: $i] :
( ( ( product @ SV10 @ SV18 @ SV24 )
= $false )
| ( ( ! [SY88: $i] :
( ~ ( product @ SV10 @ SY88 @ SV24 )
| ( equalish @ SV18 @ SY88 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(167,plain,
! [SV25: $i,SV19: $i,SV11: $i] :
( ( ( product @ SV11 @ SV19 @ SV25 )
= $false )
| ( ( ! [SY89: $i] :
( ~ ( product @ SY89 @ SV19 @ SV25 )
| ( equalish @ SV11 @ SY89 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(168,plain,
! [SV12: $i,SV30: $i,SV20: $i,SV1: $i] :
( ( ( ~ ( product @ SV1 @ SV20 @ SV30 )
| ( product @ SV30 @ SV12 @ SV1 ) )
= $true )
| ( ( product @ SV1 @ SV12 @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(169,plain,
! [SV13: $i,SV28: $i,SV2: $i] :
( ( ( ~ ( cycle @ SV2 @ SV28 ) )
= $true )
| ( ( equalish @ SV13 @ SV28 )
= $true )
| ( ( cycle @ SV2 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(170,plain,
! [SV14: $i,SV4: $i,SV31: $i,SV21: $i] :
( ( ( ~ ( cycle @ SV21 @ SV31 )
| ~ ( next @ SV4 @ SV21 )
| ~ ( greater @ SV14 @ e_0 )
| ! [SY91: $i] :
( ~ ( next @ SV31 @ SY91 )
| ( equalish @ SV14 @ SY91 ) ) )
= $true )
| ( ( cycle @ SV4 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(171,plain,
! [SV15: $i,SV5: $i,SV22: $i] :
( ( ( ~ ( cycle @ SV22 @ e_0 ) )
= $true )
| ( ( ! [SY85: $i,SY86: $i] :
( ~ ( cycle @ SY85 @ SY86 )
| ~ ( next @ SV22 @ SY85 )
| ~ ( greater @ SV22 @ SV5 )
| ~ ( greater @ SV15 @ SY86 ) ) )
= $true )
| ( ( cycle @ SV5 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(172,plain,
! [SV26: $i,SV6: $i] :
( ( ( product @ SV6 @ e_1 @ SV26 )
= $false )
| ( ( ~ ( greater @ SV26 @ SV6 ) )
= $true )
| ( ( cycle @ SV6 @ e_0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(173,plain,
! [SV16: $i,SV29: $i,SV7: $i] :
( ( ( ~ ( product @ SV7 @ e_1 @ SV29 ) )
= $true )
| ( ( ~ ( greater @ SV16 @ e_0 )
| ! [SY90: $i] :
( ~ ( next @ SV7 @ SY90 )
| ( equalish @ SV29 @ SY90 ) ) )
= $true )
| ( ( cycle @ SV7 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(174,plain,
! [SV8: $i,SV27: $i] :
( ( ( group_element @ SV27 )
= $false )
| ( ( ( product @ SV8 @ SV27 @ e_1 )
| ( product @ SV8 @ SV27 @ e_2 )
| ( product @ SV8 @ SV27 @ e_3 ) )
= $true )
| ( ( group_element @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(175,plain,
! [SV23: $i,SV32: $i,SV17: $i,SV9: $i] :
( ( ( ~ ( product @ SV9 @ SV17 @ SV32 )
| ( equalish @ SV23 @ SV32 ) )
= $true )
| ( ( product @ SV9 @ SV17 @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(176,plain,
! [SV18: $i,SV24: $i,SV33: $i,SV10: $i] :
( ( ( ~ ( product @ SV10 @ SV33 @ SV24 )
| ( equalish @ SV18 @ SV33 ) )
= $true )
| ( ( product @ SV10 @ SV18 @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(177,plain,
! [SV11: $i,SV25: $i,SV19: $i,SV34: $i] :
( ( ( ~ ( product @ SV34 @ SV19 @ SV25 )
| ( equalish @ SV11 @ SV34 ) )
= $true )
| ( ( product @ SV11 @ SV19 @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(178,plain,
! [SV12: $i,SV30: $i,SV20: $i,SV1: $i] :
( ( ( ~ ( product @ SV1 @ SV20 @ SV30 ) )
= $true )
| ( ( product @ SV30 @ SV12 @ SV1 )
= $true )
| ( ( product @ SV1 @ SV12 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(179,plain,
! [SV13: $i,SV28: $i,SV2: $i] :
( ( ( cycle @ SV2 @ SV28 )
= $false )
| ( ( equalish @ SV13 @ SV28 )
= $true )
| ( ( cycle @ SV2 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(180,plain,
! [SV14: $i,SV4: $i,SV31: $i,SV21: $i] :
( ( ( ~ ( cycle @ SV21 @ SV31 ) )
= $true )
| ( ( ~ ( next @ SV4 @ SV21 )
| ~ ( greater @ SV14 @ e_0 )
| ! [SY91: $i] :
( ~ ( next @ SV31 @ SY91 )
| ( equalish @ SV14 @ SY91 ) ) )
= $true )
| ( ( cycle @ SV4 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(181,plain,
! [SV15: $i,SV5: $i,SV22: $i] :
( ( ( cycle @ SV22 @ e_0 )
= $false )
| ( ( ! [SY85: $i,SY86: $i] :
( ~ ( cycle @ SY85 @ SY86 )
| ~ ( next @ SV22 @ SY85 )
| ~ ( greater @ SV22 @ SV5 )
| ~ ( greater @ SV15 @ SY86 ) ) )
= $true )
| ( ( cycle @ SV5 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(182,plain,
! [SV6: $i,SV26: $i] :
( ( ( greater @ SV26 @ SV6 )
= $false )
| ( ( product @ SV6 @ e_1 @ SV26 )
= $false )
| ( ( cycle @ SV6 @ e_0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(183,plain,
! [SV16: $i,SV29: $i,SV7: $i] :
( ( ( product @ SV7 @ e_1 @ SV29 )
= $false )
| ( ( ~ ( greater @ SV16 @ e_0 )
| ! [SY90: $i] :
( ~ ( next @ SV7 @ SY90 )
| ( equalish @ SV29 @ SY90 ) ) )
= $true )
| ( ( cycle @ SV7 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(184,plain,
! [SV27: $i,SV8: $i] :
( ( ( product @ SV8 @ SV27 @ e_1 )
= $true )
| ( ( ( product @ SV8 @ SV27 @ e_2 )
| ( product @ SV8 @ SV27 @ e_3 ) )
= $true )
| ( ( group_element @ SV27 )
= $false )
| ( ( group_element @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(185,plain,
! [SV23: $i,SV32: $i,SV17: $i,SV9: $i] :
( ( ( ~ ( product @ SV9 @ SV17 @ SV32 ) )
= $true )
| ( ( equalish @ SV23 @ SV32 )
= $true )
| ( ( product @ SV9 @ SV17 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(186,plain,
! [SV18: $i,SV24: $i,SV33: $i,SV10: $i] :
( ( ( ~ ( product @ SV10 @ SV33 @ SV24 ) )
= $true )
| ( ( equalish @ SV18 @ SV33 )
= $true )
| ( ( product @ SV10 @ SV18 @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(187,plain,
! [SV11: $i,SV25: $i,SV19: $i,SV34: $i] :
( ( ( ~ ( product @ SV34 @ SV19 @ SV25 ) )
= $true )
| ( ( equalish @ SV11 @ SV34 )
= $true )
| ( ( product @ SV11 @ SV19 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(188,plain,
! [SV12: $i,SV30: $i,SV20: $i,SV1: $i] :
( ( ( product @ SV1 @ SV20 @ SV30 )
= $false )
| ( ( product @ SV30 @ SV12 @ SV1 )
= $true )
| ( ( product @ SV1 @ SV12 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(189,plain,
! [SV14: $i,SV4: $i,SV31: $i,SV21: $i] :
( ( ( cycle @ SV21 @ SV31 )
= $false )
| ( ( ~ ( next @ SV4 @ SV21 )
| ~ ( greater @ SV14 @ e_0 )
| ! [SY91: $i] :
( ~ ( next @ SV31 @ SY91 )
| ( equalish @ SV14 @ SY91 ) ) )
= $true )
| ( ( cycle @ SV4 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(190,plain,
! [SV15: $i,SV5: $i,SV22: $i,SV35: $i] :
( ( ( ! [SY92: $i] :
( ~ ( cycle @ SV35 @ SY92 )
| ~ ( next @ SV22 @ SV35 )
| ~ ( greater @ SV22 @ SV5 )
| ~ ( greater @ SV15 @ SY92 ) ) )
= $true )
| ( ( cycle @ SV22 @ e_0 )
= $false )
| ( ( cycle @ SV5 @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(191,plain,
! [SV29: $i,SV7: $i,SV16: $i] :
( ( ( ~ ( greater @ SV16 @ e_0 ) )
= $true )
| ( ( ! [SY90: $i] :
( ~ ( next @ SV7 @ SY90 )
| ( equalish @ SV29 @ SY90 ) ) )
= $true )
| ( ( product @ SV7 @ e_1 @ SV29 )
= $false )
| ( ( cycle @ SV7 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(192,plain,
! [SV27: $i,SV8: $i] :
( ( ( product @ SV8 @ SV27 @ e_2 )
= $true )
| ( ( product @ SV8 @ SV27 @ e_3 )
= $true )
| ( ( product @ SV8 @ SV27 @ e_1 )
= $true )
| ( ( group_element @ SV27 )
= $false )
| ( ( group_element @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(193,plain,
! [SV23: $i,SV32: $i,SV17: $i,SV9: $i] :
( ( ( product @ SV9 @ SV17 @ SV32 )
= $false )
| ( ( equalish @ SV23 @ SV32 )
= $true )
| ( ( product @ SV9 @ SV17 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(194,plain,
! [SV18: $i,SV24: $i,SV33: $i,SV10: $i] :
( ( ( product @ SV10 @ SV33 @ SV24 )
= $false )
| ( ( equalish @ SV18 @ SV33 )
= $true )
| ( ( product @ SV10 @ SV18 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(195,plain,
! [SV11: $i,SV25: $i,SV19: $i,SV34: $i] :
( ( ( product @ SV34 @ SV19 @ SV25 )
= $false )
| ( ( equalish @ SV11 @ SV34 )
= $true )
| ( ( product @ SV11 @ SV19 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(196,plain,
! [SV31: $i,SV14: $i,SV21: $i,SV4: $i] :
( ( ( ~ ( next @ SV4 @ SV21 ) )
= $true )
| ( ( ~ ( greater @ SV14 @ e_0 )
| ! [SY91: $i] :
( ~ ( next @ SV31 @ SY91 )
| ( equalish @ SV14 @ SY91 ) ) )
= $true )
| ( ( cycle @ SV21 @ SV31 )
= $false )
| ( ( cycle @ SV4 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(197,plain,
! [SV15: $i,SV5: $i,SV22: $i,SV36: $i,SV35: $i] :
( ( ( ~ ( cycle @ SV35 @ SV36 )
| ~ ( next @ SV22 @ SV35 )
| ~ ( greater @ SV22 @ SV5 )
| ~ ( greater @ SV15 @ SV36 ) )
= $true )
| ( ( cycle @ SV22 @ e_0 )
= $false )
| ( ( cycle @ SV5 @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(198,plain,
! [SV29: $i,SV7: $i,SV16: $i] :
( ( ( greater @ SV16 @ e_0 )
= $false )
| ( ( ! [SY90: $i] :
( ~ ( next @ SV7 @ SY90 )
| ( equalish @ SV29 @ SY90 ) ) )
= $true )
| ( ( product @ SV7 @ e_1 @ SV29 )
= $false )
| ( ( cycle @ SV7 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(199,plain,
! [SV31: $i,SV14: $i,SV21: $i,SV4: $i] :
( ( ( next @ SV4 @ SV21 )
= $false )
| ( ( ~ ( greater @ SV14 @ e_0 )
| ! [SY91: $i] :
( ~ ( next @ SV31 @ SY91 )
| ( equalish @ SV14 @ SY91 ) ) )
= $true )
| ( ( cycle @ SV21 @ SV31 )
= $false )
| ( ( cycle @ SV4 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(200,plain,
! [SV15: $i,SV5: $i,SV22: $i,SV36: $i,SV35: $i] :
( ( ( ~ ( cycle @ SV35 @ SV36 ) )
= $true )
| ( ( ~ ( next @ SV22 @ SV35 )
| ~ ( greater @ SV22 @ SV5 )
| ~ ( greater @ SV15 @ SV36 ) )
= $true )
| ( ( cycle @ SV22 @ e_0 )
= $false )
| ( ( cycle @ SV5 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(201,plain,
! [SV16: $i,SV29: $i,SV37: $i,SV7: $i] :
( ( ( ~ ( next @ SV7 @ SV37 )
| ( equalish @ SV29 @ SV37 ) )
= $true )
| ( ( greater @ SV16 @ e_0 )
= $false )
| ( ( product @ SV7 @ e_1 @ SV29 )
= $false )
| ( ( cycle @ SV7 @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(202,plain,
! [SV21: $i,SV4: $i,SV31: $i,SV14: $i] :
( ( ( ~ ( greater @ SV14 @ e_0 ) )
= $true )
| ( ( ! [SY91: $i] :
( ~ ( next @ SV31 @ SY91 )
| ( equalish @ SV14 @ SY91 ) ) )
= $true )
| ( ( next @ SV4 @ SV21 )
= $false )
| ( ( cycle @ SV21 @ SV31 )
= $false )
| ( ( cycle @ SV4 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(203,plain,
! [SV15: $i,SV5: $i,SV22: $i,SV36: $i,SV35: $i] :
( ( ( cycle @ SV35 @ SV36 )
= $false )
| ( ( ~ ( next @ SV22 @ SV35 )
| ~ ( greater @ SV22 @ SV5 )
| ~ ( greater @ SV15 @ SV36 ) )
= $true )
| ( ( cycle @ SV22 @ e_0 )
= $false )
| ( ( cycle @ SV5 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(204,plain,
! [SV16: $i,SV29: $i,SV37: $i,SV7: $i] :
( ( ( ~ ( next @ SV7 @ SV37 ) )
= $true )
| ( ( equalish @ SV29 @ SV37 )
= $true )
| ( ( greater @ SV16 @ e_0 )
= $false )
| ( ( product @ SV7 @ e_1 @ SV29 )
= $false )
| ( ( cycle @ SV7 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(205,plain,
! [SV21: $i,SV4: $i,SV31: $i,SV14: $i] :
( ( ( greater @ SV14 @ e_0 )
= $false )
| ( ( ! [SY91: $i] :
( ~ ( next @ SV31 @ SY91 )
| ( equalish @ SV14 @ SY91 ) ) )
= $true )
| ( ( next @ SV4 @ SV21 )
= $false )
| ( ( cycle @ SV21 @ SV31 )
= $false )
| ( ( cycle @ SV4 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(206,plain,
! [SV36: $i,SV15: $i,SV5: $i,SV35: $i,SV22: $i] :
( ( ( ~ ( next @ SV22 @ SV35 ) )
= $true )
| ( ( ~ ( greater @ SV22 @ SV5 )
| ~ ( greater @ SV15 @ SV36 ) )
= $true )
| ( ( cycle @ SV35 @ SV36 )
= $false )
| ( ( cycle @ SV22 @ e_0 )
= $false )
| ( ( cycle @ SV5 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(207,plain,
! [SV16: $i,SV29: $i,SV37: $i,SV7: $i] :
( ( ( next @ SV7 @ SV37 )
= $false )
| ( ( equalish @ SV29 @ SV37 )
= $true )
| ( ( greater @ SV16 @ e_0 )
= $false )
| ( ( product @ SV7 @ e_1 @ SV29 )
= $false )
| ( ( cycle @ SV7 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(208,plain,
! [SV21: $i,SV4: $i,SV14: $i,SV38: $i,SV31: $i] :
( ( ( ~ ( next @ SV31 @ SV38 )
| ( equalish @ SV14 @ SV38 ) )
= $true )
| ( ( greater @ SV14 @ e_0 )
= $false )
| ( ( next @ SV4 @ SV21 )
= $false )
| ( ( cycle @ SV21 @ SV31 )
= $false )
| ( ( cycle @ SV4 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(209,plain,
! [SV36: $i,SV15: $i,SV5: $i,SV35: $i,SV22: $i] :
( ( ( next @ SV22 @ SV35 )
= $false )
| ( ( ~ ( greater @ SV22 @ SV5 )
| ~ ( greater @ SV15 @ SV36 ) )
= $true )
| ( ( cycle @ SV35 @ SV36 )
= $false )
| ( ( cycle @ SV22 @ e_0 )
= $false )
| ( ( cycle @ SV5 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(210,plain,
! [SV21: $i,SV4: $i,SV14: $i,SV38: $i,SV31: $i] :
( ( ( ~ ( next @ SV31 @ SV38 ) )
= $true )
| ( ( equalish @ SV14 @ SV38 )
= $true )
| ( ( greater @ SV14 @ e_0 )
= $false )
| ( ( next @ SV4 @ SV21 )
= $false )
| ( ( cycle @ SV21 @ SV31 )
= $false )
| ( ( cycle @ SV4 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(211,plain,
! [SV35: $i,SV36: $i,SV15: $i,SV5: $i,SV22: $i] :
( ( ( ~ ( greater @ SV22 @ SV5 ) )
= $true )
| ( ( ~ ( greater @ SV15 @ SV36 ) )
= $true )
| ( ( next @ SV22 @ SV35 )
= $false )
| ( ( cycle @ SV35 @ SV36 )
= $false )
| ( ( cycle @ SV22 @ e_0 )
= $false )
| ( ( cycle @ SV5 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(212,plain,
! [SV21: $i,SV4: $i,SV14: $i,SV38: $i,SV31: $i] :
( ( ( next @ SV31 @ SV38 )
= $false )
| ( ( equalish @ SV14 @ SV38 )
= $true )
| ( ( greater @ SV14 @ e_0 )
= $false )
| ( ( next @ SV4 @ SV21 )
= $false )
| ( ( cycle @ SV21 @ SV31 )
= $false )
| ( ( cycle @ SV4 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(213,plain,
! [SV35: $i,SV36: $i,SV15: $i,SV5: $i,SV22: $i] :
( ( ( greater @ SV22 @ SV5 )
= $false )
| ( ( ~ ( greater @ SV15 @ SV36 ) )
= $true )
| ( ( next @ SV22 @ SV35 )
= $false )
| ( ( cycle @ SV35 @ SV36 )
= $false )
| ( ( cycle @ SV22 @ e_0 )
= $false )
| ( ( cycle @ SV5 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(214,plain,
! [SV35: $i,SV5: $i,SV22: $i,SV36: $i,SV15: $i] :
( ( ( greater @ SV15 @ SV36 )
= $false )
| ( ( greater @ SV22 @ SV5 )
= $false )
| ( ( next @ SV22 @ SV35 )
= $false )
| ( ( cycle @ SV35 @ SV36 )
= $false )
| ( ( cycle @ SV22 @ e_0 )
= $false )
| ( ( cycle @ SV5 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(215,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[76,214,212,207,195,194,193,192,188,182,179,159,123,118,117,116,115,114,113,94,93,92,87,84,83,82,81,80,79,78,77]) ).
thf(216,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.07 % Problem : GRP130-3.003 : TPTP v8.1.0. Released v1.2.0.
% 0.01/0.07 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.07/0.26 % Computer : n015.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 600
% 0.07/0.26 % DateTime : Mon Jun 13 18:21:38 EDT 2022
% 0.07/0.26 % CPUTime :
% 0.11/0.27
% 0.11/0.27 No.of.Axioms: 30
% 0.11/0.27
% 0.11/0.27 Length.of.Defs: 0
% 0.11/0.27
% 0.11/0.27 Contains.Choice.Funs: false
% 0.11/0.28 (rf:0,axioms:30,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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:32,loop_count:0,foatp_calls:0,translation:fof_full)..........
% 1.63/1.90
% 1.63/1.90 ********************************
% 1.63/1.90 * All subproblems solved! *
% 1.63/1.90 ********************************
% 1.63/1.90 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:30,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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:215,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.74/1.91
% 1.74/1.91 %**** Beginning of derivation protocol ****
% 1.74/1.91 % SZS output start CNFRefutation
% See solution above
% 1.74/1.91
% 1.74/1.91 %**** End of derivation protocol ****
% 1.74/1.91 %**** no. of clauses in derivation: 216 ****
% 1.74/1.91 %**** clause counter: 215 ****
% 1.74/1.91
% 1.74/1.91 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:30,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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:215,loop_count:0,foatp_calls:1,translation:fof_full)
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