%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GRP124-8.004 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:20:22 AM UTC 2026
% Result : Unsatisfiable 1.15s 0.42s
% Output : CNFRefutation 1.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 49
% Syntax : Number of formulae : 317 ( 200 unt; 0 typ; 0 def)
% Number of atoms : 1912 ( 479 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 3217 ( 442 ~; 637 |; 0 &;2138 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 7 con; 0-3 aty)
% Number of variables : 719 ( 0 ^; 719 !; 0 ?; 719 :)
% 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_e_4,type,
e_4: $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(tp_product1,type,
product1: $i > $i > $i > $o ).
thf(tp_product2,type,
product2: $i > $i > $i > $o ).
thf(1,axiom,
! [X: $i] : ( product2 @ X @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_idempotence) ).
thf(2,axiom,
! [W: $i,Y: $i,X: $i,Z: $i] :
( ~ ( product2 @ W @ Y @ X )
| ~ ( product2 @ Z @ Y @ X )
| ( equalish @ W @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_left_cancellation) ).
thf(3,axiom,
! [X: $i,W: $i,Y: $i,Z: $i] :
( ~ ( product2 @ X @ W @ Y )
| ~ ( product2 @ X @ Z @ Y )
| ( equalish @ W @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_right_cancellation) ).
thf(4,axiom,
! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( product2 @ X @ Y @ W )
| ~ ( product2 @ X @ Y @ Z )
| ( equalish @ W @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_total_function2) ).
thf(5,axiom,
! [X: $i,Y: $i] :
( ~ ( group_element @ X )
| ~ ( group_element @ Y )
| ( product2 @ X @ Y @ e_1 )
| ( product2 @ X @ Y @ e_2 )
| ( product2 @ X @ Y @ e_3 )
| ( product2 @ X @ Y @ e_4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_total_function1) ).
thf(6,axiom,
! [X: $i] : ( product1 @ X @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_idempotence) ).
thf(7,axiom,
! [W: $i,Y: $i,X: $i,Z: $i] :
( ~ ( product1 @ W @ Y @ X )
| ~ ( product1 @ Z @ Y @ X )
| ( equalish @ W @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_left_cancellation) ).
thf(8,axiom,
! [X: $i,W: $i,Y: $i,Z: $i] :
( ~ ( product1 @ X @ W @ Y )
| ~ ( product1 @ X @ Z @ Y )
| ( equalish @ W @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_right_cancellation) ).
thf(9,axiom,
! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( product1 @ X @ Y @ W )
| ~ ( product1 @ X @ Y @ Z )
| ( equalish @ W @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_total_function2) ).
thf(10,axiom,
! [X: $i,Y: $i] :
( ~ ( group_element @ X )
| ~ ( group_element @ Y )
| ( product1 @ X @ Y @ e_1 )
| ( product1 @ X @ Y @ e_2 )
| ( product1 @ X @ Y @ e_3 )
| ( product1 @ X @ Y @ e_4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_total_function1) ).
thf(11,axiom,
~ ( equalish @ e_4 @ e_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_3) ).
thf(12,axiom,
~ ( equalish @ e_4 @ e_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_2) ).
thf(13,axiom,
~ ( equalish @ e_4 @ e_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_1) ).
thf(14,axiom,
~ ( equalish @ e_3 @ e_4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
thf(15,axiom,
~ ( equalish @ e_3 @ e_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
thf(16,axiom,
~ ( equalish @ e_3 @ e_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
thf(17,axiom,
~ ( equalish @ e_2 @ e_4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_4) ).
thf(18,axiom,
~ ( equalish @ e_2 @ e_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
thf(19,axiom,
~ ( equalish @ e_2 @ e_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
thf(20,axiom,
~ ( equalish @ e_1 @ e_4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_4) ).
thf(21,axiom,
~ ( equalish @ e_1 @ e_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
thf(22,axiom,
~ ( equalish @ e_1 @ e_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
thf(23,axiom,
group_element @ e_4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_4) ).
thf(24,axiom,
group_element @ e_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
thf(25,axiom,
group_element @ e_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
thf(26,axiom,
group_element @ e_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
thf(27,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(28,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(29,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(30,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(31,axiom,
cycle @ e_4 @ e_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cycle3) ).
thf(32,axiom,
! [X: $i] :
( ~ ( group_element @ X )
| ( cycle @ X @ e_0 )
| ( cycle @ X @ e_1 )
| ( cycle @ X @ e_2 )
| ( cycle @ X @ e_3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cycle2) ).
thf(33,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(34,axiom,
greater @ e_4 @ e_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_greater_e_3) ).
thf(35,axiom,
greater @ e_4 @ e_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_greater_e_2) ).
thf(36,axiom,
greater @ e_3 @ e_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_greater_e_2) ).
thf(37,axiom,
greater @ e_4 @ e_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_greater_e_1) ).
thf(38,axiom,
greater @ e_3 @ e_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_greater_e_1) ).
thf(39,axiom,
greater @ e_2 @ e_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_greater_e_1) ).
thf(40,axiom,
greater @ e_4 @ e_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_greater_e_0) ).
thf(41,axiom,
greater @ e_3 @ e_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_greater_e_0) ).
thf(42,axiom,
greater @ e_2 @ e_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_greater_e_0) ).
thf(43,axiom,
greater @ e_1 @ e_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_greater_e_0) ).
thf(44,axiom,
next @ e_3 @ e_4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_then_e_4) ).
thf(45,axiom,
next @ e_2 @ e_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_then_e_3) ).
thf(46,axiom,
next @ e_1 @ e_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_then_e_2) ).
thf(47,axiom,
next @ e_0 @ e_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_0_then_e_1) ).
thf(48,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(49,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[48]) ).
thf(50,negated_conjecture,
! [X: $i,Y: $i,Z1: $i,Z2: $i] :
( ~ ( product1 @ X @ Y @ Z1 )
| ~ ( product1 @ Z1 @ X @ Z2 )
| ( product2 @ Z2 @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg2a) ).
thf(51,plain,
$false = $false,
inference(unfold_def,[status(thm)],[49]) ).
thf(52,plain,
( ( ! [X: $i] : ( product2 @ X @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(53,plain,
( ( ! [W: $i,Y: $i,X: $i,Z: $i] :
( ~ ( product2 @ W @ Y @ X )
| ~ ( product2 @ Z @ Y @ X )
| ( equalish @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(54,plain,
( ( ! [X: $i,W: $i,Y: $i,Z: $i] :
( ~ ( product2 @ X @ W @ Y )
| ~ ( product2 @ X @ Z @ Y )
| ( equalish @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(55,plain,
( ( ! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( product2 @ X @ Y @ W )
| ~ ( product2 @ X @ Y @ Z )
| ( equalish @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(56,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( group_element @ X )
| ~ ( group_element @ Y )
| ( product2 @ X @ Y @ e_1 )
| ( product2 @ X @ Y @ e_2 )
| ( product2 @ X @ Y @ e_3 )
| ( product2 @ X @ Y @ e_4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(57,plain,
( ( ! [X: $i] : ( product1 @ X @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(58,plain,
( ( ! [W: $i,Y: $i,X: $i,Z: $i] :
( ~ ( product1 @ W @ Y @ X )
| ~ ( product1 @ Z @ Y @ X )
| ( equalish @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(59,plain,
( ( ! [X: $i,W: $i,Y: $i,Z: $i] :
( ~ ( product1 @ X @ W @ Y )
| ~ ( product1 @ X @ Z @ Y )
| ( equalish @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(60,plain,
( ( ! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( product1 @ X @ Y @ W )
| ~ ( product1 @ X @ Y @ Z )
| ( equalish @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(61,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( group_element @ X )
| ~ ( group_element @ Y )
| ( product1 @ X @ Y @ e_1 )
| ( product1 @ X @ Y @ e_2 )
| ( product1 @ X @ Y @ e_3 )
| ( product1 @ X @ Y @ e_4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(62,plain,
( ( ~ ( equalish @ e_4 @ e_3 ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(63,plain,
( ( ~ ( equalish @ e_4 @ e_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(64,plain,
( ( ~ ( equalish @ e_4 @ e_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(65,plain,
( ( ~ ( equalish @ e_3 @ e_4 ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(66,plain,
( ( ~ ( equalish @ e_3 @ e_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(67,plain,
( ( ~ ( equalish @ e_3 @ e_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(68,plain,
( ( ~ ( equalish @ e_2 @ e_4 ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(69,plain,
( ( ~ ( equalish @ e_2 @ e_3 ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(70,plain,
( ( ~ ( equalish @ e_2 @ e_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(71,plain,
( ( ~ ( equalish @ e_1 @ e_4 ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(72,plain,
( ( ~ ( equalish @ e_1 @ e_3 ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(73,plain,
( ( ~ ( equalish @ e_1 @ e_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(74,plain,
( ( group_element @ e_4 )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(75,plain,
( ( group_element @ e_3 )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(76,plain,
( ( group_element @ e_2 )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(77,plain,
( ( group_element @ e_1 )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(78,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)],[27]) ).
thf(79,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( cycle @ X @ e_0 )
| ~ ( product @ X @ e_1 @ Y )
| ~ ( greater @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(80,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)],[29]) ).
thf(81,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)],[30]) ).
thf(82,plain,
( ( cycle @ e_4 @ e_0 )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(83,plain,
( ( ! [X: $i] :
( ~ ( group_element @ X )
| ( cycle @ X @ e_0 )
| ( cycle @ X @ e_1 )
| ( cycle @ X @ e_2 )
| ( cycle @ X @ e_3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(84,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( cycle @ X @ Y )
| ~ ( cycle @ X @ Z )
| ( equalish @ Y @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(85,plain,
( ( greater @ e_4 @ e_3 )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(86,plain,
( ( greater @ e_4 @ e_2 )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(87,plain,
( ( greater @ e_3 @ e_2 )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(88,plain,
( ( greater @ e_4 @ e_1 )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(89,plain,
( ( greater @ e_3 @ e_1 )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(90,plain,
( ( greater @ e_2 @ e_1 )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(91,plain,
( ( greater @ e_4 @ e_0 )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(92,plain,
( ( greater @ e_3 @ e_0 )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(93,plain,
( ( greater @ e_2 @ e_0 )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(94,plain,
( ( greater @ e_1 @ e_0 )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(95,plain,
( ( next @ e_3 @ e_4 )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(96,plain,
( ( next @ e_2 @ e_3 )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(97,plain,
( ( next @ e_1 @ e_2 )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(98,plain,
( ( next @ e_0 @ e_1 )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(99,plain,
( ( ! [X: $i,Y: $i,Z1: $i,Z2: $i] :
( ~ ( product1 @ X @ Y @ Z1 )
| ~ ( product1 @ Z1 @ X @ Z2 )
| ( product2 @ Z2 @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(100,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[51]) ).
thf(101,plain,
( ( ! [W: $i,Y: $i,X: $i] :
( ~ ( product2 @ W @ Y @ X )
| ! [Z: $i] :
( ~ ( product2 @ Z @ Y @ X )
| ( equalish @ W @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[53]) ).
thf(102,plain,
( ( ! [X: $i,W: $i,Y: $i] :
( ~ ( product2 @ X @ W @ Y )
| ! [Z: $i] :
( ~ ( product2 @ X @ Z @ Y )
| ( equalish @ W @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[54]) ).
thf(103,plain,
( ( ! [X: $i,Y: $i,W: $i] :
( ~ ( product2 @ X @ Y @ W )
| ! [Z: $i] :
( ~ ( product2 @ X @ Y @ Z )
| ( equalish @ W @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[55]) ).
thf(104,plain,
( ( ! [X: $i] :
( ~ ( group_element @ X )
| ! [Y: $i] :
( ~ ( group_element @ Y )
| ( product2 @ X @ Y @ e_1 )
| ( product2 @ X @ Y @ e_2 )
| ( product2 @ X @ Y @ e_3 )
| ( product2 @ X @ Y @ e_4 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[56]) ).
thf(105,plain,
( ( ! [W: $i,Y: $i,X: $i] :
( ~ ( product1 @ W @ Y @ X )
| ! [Z: $i] :
( ~ ( product1 @ Z @ Y @ X )
| ( equalish @ W @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[58]) ).
thf(106,plain,
( ( ! [X: $i,W: $i,Y: $i] :
( ~ ( product1 @ X @ W @ Y )
| ! [Z: $i] :
( ~ ( product1 @ X @ Z @ Y )
| ( equalish @ W @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[59]) ).
thf(107,plain,
( ( ! [X: $i,Y: $i,W: $i] :
( ~ ( product1 @ X @ Y @ W )
| ! [Z: $i] :
( ~ ( product1 @ X @ Y @ Z )
| ( equalish @ W @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[60]) ).
thf(108,plain,
( ( ! [X: $i] :
( ~ ( group_element @ X )
| ! [Y: $i] :
( ~ ( group_element @ Y )
| ( product1 @ X @ Y @ e_1 )
| ( product1 @ X @ Y @ e_2 )
| ( product1 @ X @ Y @ e_3 )
| ( product1 @ X @ Y @ e_4 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[61]) ).
thf(109,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)],[78]) ).
thf(110,plain,
( ( ! [X: $i] :
( ~ ( cycle @ X @ e_0 )
| ! [Y: $i] :
( ~ ( product @ X @ e_1 @ Y )
| ~ ( greater @ Y @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[79]) ).
thf(111,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)],[80]) ).
thf(112,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)],[81]) ).
thf(113,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( cycle @ X @ Y )
| ! [Z: $i] :
( ~ ( cycle @ X @ Z )
| ( equalish @ Y @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[84]) ).
thf(114,plain,
( ( ! [X: $i,Y: $i,Z1: $i] :
( ~ ( product1 @ X @ Y @ Z1 )
| ! [Z2: $i] :
( ~ ( product1 @ Z1 @ X @ Z2 )
| ( product2 @ Z2 @ Y @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[99]) ).
thf(115,plain,
( ( ! [X: $i,Y: $i,Z1: $i] :
( ~ ( product1 @ X @ Y @ Z1 )
| ! [Z2: $i] :
( ~ ( product1 @ Z1 @ X @ Z2 )
| ( product2 @ Z2 @ Y @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(116,plain,
( ( next @ e_0 @ e_1 )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(117,plain,
( ( next @ e_1 @ e_2 )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(118,plain,
( ( next @ e_2 @ e_3 )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(119,plain,
( ( next @ e_3 @ e_4 )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(120,plain,
( ( greater @ e_1 @ e_0 )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(121,plain,
( ( greater @ e_2 @ e_0 )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(122,plain,
( ( greater @ e_3 @ e_0 )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(123,plain,
( ( greater @ e_4 @ e_0 )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(124,plain,
( ( greater @ e_2 @ e_1 )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(125,plain,
( ( greater @ e_3 @ e_1 )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(126,plain,
( ( greater @ e_4 @ e_1 )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(127,plain,
( ( greater @ e_3 @ e_2 )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(128,plain,
( ( greater @ e_4 @ e_2 )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(129,plain,
( ( greater @ e_4 @ e_3 )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(130,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( cycle @ X @ Y )
| ! [Z: $i] :
( ~ ( cycle @ X @ Z )
| ( equalish @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(131,plain,
( ( ! [X: $i] :
( ~ ( group_element @ X )
| ( cycle @ X @ e_0 )
| ( cycle @ X @ e_1 )
| ( cycle @ X @ e_2 )
| ( cycle @ X @ e_3 ) ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(132,plain,
( ( cycle @ e_4 @ e_0 )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(133,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)],[112]) ).
thf(134,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)],[111]) ).
thf(135,plain,
( ( ! [X: $i] :
( ~ ( cycle @ X @ e_0 )
| ! [Y: $i] :
( ~ ( product @ X @ e_1 @ Y )
| ~ ( greater @ Y @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(136,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)],[109]) ).
thf(137,plain,
( ( group_element @ e_1 )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(138,plain,
( ( group_element @ e_2 )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(139,plain,
( ( group_element @ e_3 )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(140,plain,
( ( group_element @ e_4 )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(141,plain,
( ( ~ ( equalish @ e_1 @ e_2 ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(142,plain,
( ( ~ ( equalish @ e_1 @ e_3 ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(143,plain,
( ( ~ ( equalish @ e_1 @ e_4 ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(144,plain,
( ( ~ ( equalish @ e_2 @ e_1 ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(145,plain,
( ( ~ ( equalish @ e_2 @ e_3 ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(146,plain,
( ( ~ ( equalish @ e_2 @ e_4 ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(147,plain,
( ( ~ ( equalish @ e_3 @ e_1 ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(148,plain,
( ( ~ ( equalish @ e_3 @ e_2 ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(149,plain,
( ( ~ ( equalish @ e_3 @ e_4 ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(150,plain,
( ( ~ ( equalish @ e_4 @ e_1 ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(151,plain,
( ( ~ ( equalish @ e_4 @ e_2 ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(152,plain,
( ( ~ ( equalish @ e_4 @ e_3 ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(153,plain,
( ( ! [X: $i] :
( ~ ( group_element @ X )
| ! [Y: $i] :
( ~ ( group_element @ Y )
| ( product1 @ X @ Y @ e_1 )
| ( product1 @ X @ Y @ e_2 )
| ( product1 @ X @ Y @ e_3 )
| ( product1 @ X @ Y @ e_4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(154,plain,
( ( ! [X: $i,Y: $i,W: $i] :
( ~ ( product1 @ X @ Y @ W )
| ! [Z: $i] :
( ~ ( product1 @ X @ Y @ Z )
| ( equalish @ W @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(155,plain,
( ( ! [X: $i,W: $i,Y: $i] :
( ~ ( product1 @ X @ W @ Y )
| ! [Z: $i] :
( ~ ( product1 @ X @ Z @ Y )
| ( equalish @ W @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(156,plain,
( ( ! [W: $i,Y: $i,X: $i] :
( ~ ( product1 @ W @ Y @ X )
| ! [Z: $i] :
( ~ ( product1 @ Z @ Y @ X )
| ( equalish @ W @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(157,plain,
( ( ! [X: $i] : ( product1 @ X @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(158,plain,
( ( ! [X: $i] :
( ~ ( group_element @ X )
| ! [Y: $i] :
( ~ ( group_element @ Y )
| ( product2 @ X @ Y @ e_1 )
| ( product2 @ X @ Y @ e_2 )
| ( product2 @ X @ Y @ e_3 )
| ( product2 @ X @ Y @ e_4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(159,plain,
( ( ! [X: $i,Y: $i,W: $i] :
( ~ ( product2 @ X @ Y @ W )
| ! [Z: $i] :
( ~ ( product2 @ X @ Y @ Z )
| ( equalish @ W @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(160,plain,
( ( ! [X: $i,W: $i,Y: $i] :
( ~ ( product2 @ X @ W @ Y )
| ! [Z: $i] :
( ~ ( product2 @ X @ Z @ Y )
| ( equalish @ W @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(161,plain,
( ( ! [W: $i,Y: $i,X: $i] :
( ~ ( product2 @ W @ Y @ X )
| ! [Z: $i] :
( ~ ( product2 @ Z @ Y @ X )
| ( equalish @ W @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(162,plain,
( ( ! [X: $i] : ( product2 @ X @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(163,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[100]) ).
thf(164,plain,
! [SV1: $i] :
( ( ! [SY54: $i,SY55: $i] :
( ~ ( product1 @ SV1 @ SY54 @ SY55 )
| ! [SY56: $i] :
( ~ ( product1 @ SY55 @ SV1 @ SY56 )
| ( product2 @ SY56 @ SY54 @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(165,plain,
! [SV2: $i] :
( ( ! [SY57: $i] :
( ~ ( cycle @ SV2 @ SY57 )
| ! [SY58: $i] :
( ~ ( cycle @ SV2 @ SY58 )
| ( equalish @ SY57 @ SY58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(166,plain,
! [SV3: $i] :
( ( ~ ( group_element @ SV3 )
| ( cycle @ SV3 @ e_0 )
| ( cycle @ SV3 @ e_1 )
| ( cycle @ SV3 @ e_2 )
| ( cycle @ SV3 @ e_3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(167,plain,
! [SV4: $i] :
( ( ! [SY59: $i,SY60: $i] :
( ~ ( cycle @ SV4 @ SY59 )
| ! [SY61: $i] :
( ~ ( cycle @ SY60 @ SY61 )
| ~ ( next @ SV4 @ SY60 )
| ~ ( greater @ SY59 @ e_0 )
| ! [Z1: $i] :
( ~ ( next @ SY61 @ Z1 )
| ( equalish @ SY59 @ Z1 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(168,plain,
! [SV5: $i] :
( ( ! [SY63: $i,SY64: $i] :
( ~ ( cycle @ SV5 @ SY63 )
| ~ ( cycle @ SY64 @ e_0 )
| ! [SY65: $i,SY66: $i] :
( ~ ( cycle @ SY65 @ SY66 )
| ~ ( next @ SY64 @ SY65 )
| ~ ( greater @ SY64 @ SV5 )
| ~ ( greater @ SY63 @ SY66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(169,plain,
! [SV6: $i] :
( ( ~ ( cycle @ SV6 @ e_0 )
| ! [SY67: $i] :
( ~ ( product @ SV6 @ e_1 @ SY67 )
| ~ ( greater @ SY67 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(170,plain,
! [SV7: $i] :
( ( ! [SY68: $i] :
( ~ ( cycle @ SV7 @ SY68 )
| ! [SY69: $i] :
( ~ ( product @ SV7 @ e_1 @ SY69 )
| ~ ( greater @ SY68 @ e_0 )
| ! [SY70: $i] :
( ~ ( next @ SV7 @ SY70 )
| ( equalish @ SY69 @ SY70 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(171,plain,
( ( equalish @ e_1 @ e_2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(172,plain,
( ( equalish @ e_1 @ e_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(173,plain,
( ( equalish @ e_1 @ e_4 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(174,plain,
( ( equalish @ e_2 @ e_1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(175,plain,
( ( equalish @ e_2 @ e_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(176,plain,
( ( equalish @ e_2 @ e_4 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(177,plain,
( ( equalish @ e_3 @ e_1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(178,plain,
( ( equalish @ e_3 @ e_2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(179,plain,
( ( equalish @ e_3 @ e_4 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(180,plain,
( ( equalish @ e_4 @ e_1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(181,plain,
( ( equalish @ e_4 @ e_2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(182,plain,
( ( equalish @ e_4 @ e_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(183,plain,
! [SV8: $i] :
( ( ~ ( group_element @ SV8 )
| ! [SY71: $i] :
( ~ ( group_element @ SY71 )
| ( product1 @ SV8 @ SY71 @ e_1 )
| ( product1 @ SV8 @ SY71 @ e_2 )
| ( product1 @ SV8 @ SY71 @ e_3 )
| ( product1 @ SV8 @ SY71 @ e_4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(184,plain,
! [SV9: $i] :
( ( ! [SY72: $i,SY73: $i] :
( ~ ( product1 @ SV9 @ SY72 @ SY73 )
| ! [SY74: $i] :
( ~ ( product1 @ SV9 @ SY72 @ SY74 )
| ( equalish @ SY73 @ SY74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(185,plain,
! [SV10: $i] :
( ( ! [SY75: $i,SY76: $i] :
( ~ ( product1 @ SV10 @ SY75 @ SY76 )
| ! [SY77: $i] :
( ~ ( product1 @ SV10 @ SY77 @ SY76 )
| ( equalish @ SY75 @ SY77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(186,plain,
! [SV11: $i] :
( ( ! [SY78: $i,SY79: $i] :
( ~ ( product1 @ SV11 @ SY78 @ SY79 )
| ! [SY80: $i] :
( ~ ( product1 @ SY80 @ SY78 @ SY79 )
| ( equalish @ SV11 @ SY80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(187,plain,
! [SV12: $i] :
( ( product1 @ SV12 @ SV12 @ SV12 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(188,plain,
! [SV13: $i] :
( ( ~ ( group_element @ SV13 )
| ! [SY81: $i] :
( ~ ( group_element @ SY81 )
| ( product2 @ SV13 @ SY81 @ e_1 )
| ( product2 @ SV13 @ SY81 @ e_2 )
| ( product2 @ SV13 @ SY81 @ e_3 )
| ( product2 @ SV13 @ SY81 @ e_4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(189,plain,
! [SV14: $i] :
( ( ! [SY82: $i,SY83: $i] :
( ~ ( product2 @ SV14 @ SY82 @ SY83 )
| ! [SY84: $i] :
( ~ ( product2 @ SV14 @ SY82 @ SY84 )
| ( equalish @ SY83 @ SY84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(190,plain,
! [SV15: $i] :
( ( ! [SY85: $i,SY86: $i] :
( ~ ( product2 @ SV15 @ SY85 @ SY86 )
| ! [SY87: $i] :
( ~ ( product2 @ SV15 @ SY87 @ SY86 )
| ( equalish @ SY85 @ SY87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(191,plain,
! [SV16: $i] :
( ( ! [SY88: $i,SY89: $i] :
( ~ ( product2 @ SV16 @ SY88 @ SY89 )
| ! [SY90: $i] :
( ~ ( product2 @ SY90 @ SY88 @ SY89 )
| ( equalish @ SV16 @ SY90 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(192,plain,
! [SV17: $i] :
( ( product2 @ SV17 @ SV17 @ SV17 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(193,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(194,plain,
! [SV18: $i,SV1: $i] :
( ( ! [SY91: $i] :
( ~ ( product1 @ SV1 @ SV18 @ SY91 )
| ! [SY92: $i] :
( ~ ( product1 @ SY91 @ SV1 @ SY92 )
| ( product2 @ SY92 @ SV18 @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(195,plain,
! [SV19: $i,SV2: $i] :
( ( ~ ( cycle @ SV2 @ SV19 )
| ! [SY93: $i] :
( ~ ( cycle @ SV2 @ SY93 )
| ( equalish @ SV19 @ SY93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(196,plain,
! [SV3: $i] :
( ( ( ~ ( group_element @ SV3 ) )
= $true )
| ( ( ( cycle @ SV3 @ e_0 )
| ( cycle @ SV3 @ e_1 )
| ( cycle @ SV3 @ e_2 )
| ( cycle @ SV3 @ e_3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(197,plain,
! [SV20: $i,SV4: $i] :
( ( ! [SY94: $i] :
( ~ ( cycle @ SV4 @ SV20 )
| ! [SY95: $i] :
( ~ ( cycle @ SY94 @ SY95 )
| ~ ( next @ SV4 @ SY94 )
| ~ ( greater @ SV20 @ e_0 )
| ! [SY96: $i] :
( ~ ( next @ SY95 @ SY96 )
| ( equalish @ SV20 @ SY96 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(198,plain,
! [SV21: $i,SV5: $i] :
( ( ! [SY97: $i] :
( ~ ( cycle @ SV5 @ SV21 )
| ~ ( cycle @ SY97 @ e_0 )
| ! [SY98: $i,SY99: $i] :
( ~ ( cycle @ SY98 @ SY99 )
| ~ ( next @ SY97 @ SY98 )
| ~ ( greater @ SY97 @ SV5 )
| ~ ( greater @ SV21 @ SY99 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(199,plain,
! [SV6: $i] :
( ( ( ~ ( cycle @ SV6 @ e_0 ) )
= $true )
| ( ( ! [SY67: $i] :
( ~ ( product @ SV6 @ e_1 @ SY67 )
| ~ ( greater @ SY67 @ SV6 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(200,plain,
! [SV22: $i,SV7: $i] :
( ( ~ ( cycle @ SV7 @ SV22 )
| ! [SY100: $i] :
( ~ ( product @ SV7 @ e_1 @ SY100 )
| ~ ( greater @ SV22 @ e_0 )
| ! [SY70: $i] :
( ~ ( next @ SV7 @ SY70 )
| ( equalish @ SY100 @ SY70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(201,plain,
! [SV8: $i] :
( ( ( ~ ( group_element @ SV8 ) )
= $true )
| ( ( ! [SY71: $i] :
( ~ ( group_element @ SY71 )
| ( product1 @ SV8 @ SY71 @ e_1 )
| ( product1 @ SV8 @ SY71 @ e_2 )
| ( product1 @ SV8 @ SY71 @ e_3 )
| ( product1 @ SV8 @ SY71 @ e_4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(202,plain,
! [SV23: $i,SV9: $i] :
( ( ! [SY102: $i] :
( ~ ( product1 @ SV9 @ SV23 @ SY102 )
| ! [SY103: $i] :
( ~ ( product1 @ SV9 @ SV23 @ SY103 )
| ( equalish @ SY102 @ SY103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(203,plain,
! [SV24: $i,SV10: $i] :
( ( ! [SY104: $i] :
( ~ ( product1 @ SV10 @ SV24 @ SY104 )
| ! [SY105: $i] :
( ~ ( product1 @ SV10 @ SY105 @ SY104 )
| ( equalish @ SV24 @ SY105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(204,plain,
! [SV25: $i,SV11: $i] :
( ( ! [SY106: $i] :
( ~ ( product1 @ SV11 @ SV25 @ SY106 )
| ! [SY107: $i] :
( ~ ( product1 @ SY107 @ SV25 @ SY106 )
| ( equalish @ SV11 @ SY107 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(205,plain,
! [SV13: $i] :
( ( ( ~ ( group_element @ SV13 ) )
= $true )
| ( ( ! [SY81: $i] :
( ~ ( group_element @ SY81 )
| ( product2 @ SV13 @ SY81 @ e_1 )
| ( product2 @ SV13 @ SY81 @ e_2 )
| ( product2 @ SV13 @ SY81 @ e_3 )
| ( product2 @ SV13 @ SY81 @ e_4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(206,plain,
! [SV26: $i,SV14: $i] :
( ( ! [SY108: $i] :
( ~ ( product2 @ SV14 @ SV26 @ SY108 )
| ! [SY109: $i] :
( ~ ( product2 @ SV14 @ SV26 @ SY109 )
| ( equalish @ SY108 @ SY109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(207,plain,
! [SV27: $i,SV15: $i] :
( ( ! [SY110: $i] :
( ~ ( product2 @ SV15 @ SV27 @ SY110 )
| ! [SY111: $i] :
( ~ ( product2 @ SV15 @ SY111 @ SY110 )
| ( equalish @ SV27 @ SY111 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(208,plain,
! [SV28: $i,SV16: $i] :
( ( ! [SY112: $i] :
( ~ ( product2 @ SV16 @ SV28 @ SY112 )
| ! [SY113: $i] :
( ~ ( product2 @ SY113 @ SV28 @ SY112 )
| ( equalish @ SV16 @ SY113 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(209,plain,
! [SV29: $i,SV18: $i,SV1: $i] :
( ( ~ ( product1 @ SV1 @ SV18 @ SV29 )
| ! [SY114: $i] :
( ~ ( product1 @ SV29 @ SV1 @ SY114 )
| ( product2 @ SY114 @ SV18 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(210,plain,
! [SV19: $i,SV2: $i] :
( ( ( ~ ( cycle @ SV2 @ SV19 ) )
= $true )
| ( ( ! [SY93: $i] :
( ~ ( cycle @ SV2 @ SY93 )
| ( equalish @ SV19 @ SY93 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(211,plain,
! [SV3: $i] :
( ( ( group_element @ SV3 )
= $false )
| ( ( ( cycle @ SV3 @ e_0 )
| ( cycle @ SV3 @ e_1 )
| ( cycle @ SV3 @ e_2 )
| ( cycle @ SV3 @ e_3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(212,plain,
! [SV30: $i,SV20: $i,SV4: $i] :
( ( ~ ( cycle @ SV4 @ SV20 )
| ! [SY115: $i] :
( ~ ( cycle @ SV30 @ SY115 )
| ~ ( next @ SV4 @ SV30 )
| ~ ( greater @ SV20 @ e_0 )
| ! [SY96: $i] :
( ~ ( next @ SY115 @ SY96 )
| ( equalish @ SV20 @ SY96 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(213,plain,
! [SV31: $i,SV21: $i,SV5: $i] :
( ( ~ ( cycle @ SV5 @ SV21 )
| ~ ( cycle @ SV31 @ e_0 )
| ! [SY117: $i,SY118: $i] :
( ~ ( cycle @ SY117 @ SY118 )
| ~ ( next @ SV31 @ SY117 )
| ~ ( greater @ SV31 @ SV5 )
| ~ ( greater @ SV21 @ SY118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(214,plain,
! [SV6: $i] :
( ( ( cycle @ SV6 @ e_0 )
= $false )
| ( ( ! [SY67: $i] :
( ~ ( product @ SV6 @ e_1 @ SY67 )
| ~ ( greater @ SY67 @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(215,plain,
! [SV22: $i,SV7: $i] :
( ( ( ~ ( cycle @ SV7 @ SV22 ) )
= $true )
| ( ( ! [SY100: $i] :
( ~ ( product @ SV7 @ e_1 @ SY100 )
| ~ ( greater @ SV22 @ e_0 )
| ! [SY70: $i] :
( ~ ( next @ SV7 @ SY70 )
| ( equalish @ SY100 @ SY70 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[200]) ).
thf(216,plain,
! [SV8: $i] :
( ( ( group_element @ SV8 )
= $false )
| ( ( ! [SY71: $i] :
( ~ ( group_element @ SY71 )
| ( product1 @ SV8 @ SY71 @ e_1 )
| ( product1 @ SV8 @ SY71 @ e_2 )
| ( product1 @ SV8 @ SY71 @ e_3 )
| ( product1 @ SV8 @ SY71 @ e_4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(217,plain,
! [SV32: $i,SV23: $i,SV9: $i] :
( ( ~ ( product1 @ SV9 @ SV23 @ SV32 )
| ! [SY119: $i] :
( ~ ( product1 @ SV9 @ SV23 @ SY119 )
| ( equalish @ SV32 @ SY119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(218,plain,
! [SV33: $i,SV24: $i,SV10: $i] :
( ( ~ ( product1 @ SV10 @ SV24 @ SV33 )
| ! [SY120: $i] :
( ~ ( product1 @ SV10 @ SY120 @ SV33 )
| ( equalish @ SV24 @ SY120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(219,plain,
! [SV34: $i,SV25: $i,SV11: $i] :
( ( ~ ( product1 @ SV11 @ SV25 @ SV34 )
| ! [SY121: $i] :
( ~ ( product1 @ SY121 @ SV25 @ SV34 )
| ( equalish @ SV11 @ SY121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(220,plain,
! [SV13: $i] :
( ( ( group_element @ SV13 )
= $false )
| ( ( ! [SY81: $i] :
( ~ ( group_element @ SY81 )
| ( product2 @ SV13 @ SY81 @ e_1 )
| ( product2 @ SV13 @ SY81 @ e_2 )
| ( product2 @ SV13 @ SY81 @ e_3 )
| ( product2 @ SV13 @ SY81 @ e_4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(221,plain,
! [SV35: $i,SV26: $i,SV14: $i] :
( ( ~ ( product2 @ SV14 @ SV26 @ SV35 )
| ! [SY122: $i] :
( ~ ( product2 @ SV14 @ SV26 @ SY122 )
| ( equalish @ SV35 @ SY122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(222,plain,
! [SV36: $i,SV27: $i,SV15: $i] :
( ( ~ ( product2 @ SV15 @ SV27 @ SV36 )
| ! [SY123: $i] :
( ~ ( product2 @ SV15 @ SY123 @ SV36 )
| ( equalish @ SV27 @ SY123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(223,plain,
! [SV37: $i,SV28: $i,SV16: $i] :
( ( ~ ( product2 @ SV16 @ SV28 @ SV37 )
| ! [SY124: $i] :
( ~ ( product2 @ SY124 @ SV28 @ SV37 )
| ( equalish @ SV16 @ SY124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(224,plain,
! [SV29: $i,SV18: $i,SV1: $i] :
( ( ( ~ ( product1 @ SV1 @ SV18 @ SV29 ) )
= $true )
| ( ( ! [SY114: $i] :
( ~ ( product1 @ SV29 @ SV1 @ SY114 )
| ( product2 @ SY114 @ SV18 @ SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(225,plain,
! [SV19: $i,SV2: $i] :
( ( ( cycle @ SV2 @ SV19 )
= $false )
| ( ( ! [SY93: $i] :
( ~ ( cycle @ SV2 @ SY93 )
| ( equalish @ SV19 @ SY93 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(226,plain,
! [SV3: $i] :
( ( ( cycle @ SV3 @ e_0 )
= $true )
| ( ( ( cycle @ SV3 @ e_1 )
| ( cycle @ SV3 @ e_2 )
| ( cycle @ SV3 @ e_3 ) )
= $true )
| ( ( group_element @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(227,plain,
! [SV30: $i,SV20: $i,SV4: $i] :
( ( ( ~ ( cycle @ SV4 @ SV20 ) )
= $true )
| ( ( ! [SY115: $i] :
( ~ ( cycle @ SV30 @ SY115 )
| ~ ( next @ SV4 @ SV30 )
| ~ ( greater @ SV20 @ e_0 )
| ! [SY96: $i] :
( ~ ( next @ SY115 @ SY96 )
| ( equalish @ SV20 @ SY96 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(228,plain,
! [SV31: $i,SV21: $i,SV5: $i] :
( ( ( ~ ( cycle @ SV5 @ SV21 ) )
= $true )
| ( ( ~ ( cycle @ SV31 @ e_0 )
| ! [SY117: $i,SY118: $i] :
( ~ ( cycle @ SY117 @ SY118 )
| ~ ( next @ SV31 @ SY117 )
| ~ ( greater @ SV31 @ SV5 )
| ~ ( greater @ SV21 @ SY118 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(229,plain,
! [SV38: $i,SV6: $i] :
( ( ( ~ ( product @ SV6 @ e_1 @ SV38 )
| ~ ( greater @ SV38 @ SV6 ) )
= $true )
| ( ( cycle @ SV6 @ e_0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(230,plain,
! [SV22: $i,SV7: $i] :
( ( ( cycle @ SV7 @ SV22 )
= $false )
| ( ( ! [SY100: $i] :
( ~ ( product @ SV7 @ e_1 @ SY100 )
| ~ ( greater @ SV22 @ e_0 )
| ! [SY70: $i] :
( ~ ( next @ SV7 @ SY70 )
| ( equalish @ SY100 @ SY70 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(231,plain,
! [SV8: $i,SV39: $i] :
( ( ( ~ ( group_element @ SV39 )
| ( product1 @ SV8 @ SV39 @ e_1 )
| ( product1 @ SV8 @ SV39 @ e_2 )
| ( product1 @ SV8 @ SV39 @ e_3 )
| ( product1 @ SV8 @ SV39 @ e_4 ) )
= $true )
| ( ( group_element @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(232,plain,
! [SV32: $i,SV23: $i,SV9: $i] :
( ( ( ~ ( product1 @ SV9 @ SV23 @ SV32 ) )
= $true )
| ( ( ! [SY119: $i] :
( ~ ( product1 @ SV9 @ SV23 @ SY119 )
| ( equalish @ SV32 @ SY119 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(233,plain,
! [SV33: $i,SV24: $i,SV10: $i] :
( ( ( ~ ( product1 @ SV10 @ SV24 @ SV33 ) )
= $true )
| ( ( ! [SY120: $i] :
( ~ ( product1 @ SV10 @ SY120 @ SV33 )
| ( equalish @ SV24 @ SY120 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(234,plain,
! [SV34: $i,SV25: $i,SV11: $i] :
( ( ( ~ ( product1 @ SV11 @ SV25 @ SV34 ) )
= $true )
| ( ( ! [SY121: $i] :
( ~ ( product1 @ SY121 @ SV25 @ SV34 )
| ( equalish @ SV11 @ SY121 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(235,plain,
! [SV13: $i,SV40: $i] :
( ( ( ~ ( group_element @ SV40 )
| ( product2 @ SV13 @ SV40 @ e_1 )
| ( product2 @ SV13 @ SV40 @ e_2 )
| ( product2 @ SV13 @ SV40 @ e_3 )
| ( product2 @ SV13 @ SV40 @ e_4 ) )
= $true )
| ( ( group_element @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(236,plain,
! [SV35: $i,SV26: $i,SV14: $i] :
( ( ( ~ ( product2 @ SV14 @ SV26 @ SV35 ) )
= $true )
| ( ( ! [SY122: $i] :
( ~ ( product2 @ SV14 @ SV26 @ SY122 )
| ( equalish @ SV35 @ SY122 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(237,plain,
! [SV36: $i,SV27: $i,SV15: $i] :
( ( ( ~ ( product2 @ SV15 @ SV27 @ SV36 ) )
= $true )
| ( ( ! [SY123: $i] :
( ~ ( product2 @ SV15 @ SY123 @ SV36 )
| ( equalish @ SV27 @ SY123 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(238,plain,
! [SV37: $i,SV28: $i,SV16: $i] :
( ( ( ~ ( product2 @ SV16 @ SV28 @ SV37 ) )
= $true )
| ( ( ! [SY124: $i] :
( ~ ( product2 @ SY124 @ SV28 @ SV37 )
| ( equalish @ SV16 @ SY124 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(239,plain,
! [SV29: $i,SV18: $i,SV1: $i] :
( ( ( product1 @ SV1 @ SV18 @ SV29 )
= $false )
| ( ( ! [SY114: $i] :
( ~ ( product1 @ SV29 @ SV1 @ SY114 )
| ( product2 @ SY114 @ SV18 @ SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(240,plain,
! [SV19: $i,SV41: $i,SV2: $i] :
( ( ( ~ ( cycle @ SV2 @ SV41 )
| ( equalish @ SV19 @ SV41 ) )
= $true )
| ( ( cycle @ SV2 @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(241,plain,
! [SV3: $i] :
( ( ( cycle @ SV3 @ e_1 )
= $true )
| ( ( ( cycle @ SV3 @ e_2 )
| ( cycle @ SV3 @ e_3 ) )
= $true )
| ( ( cycle @ SV3 @ e_0 )
= $true )
| ( ( group_element @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(242,plain,
! [SV30: $i,SV20: $i,SV4: $i] :
( ( ( cycle @ SV4 @ SV20 )
= $false )
| ( ( ! [SY115: $i] :
( ~ ( cycle @ SV30 @ SY115 )
| ~ ( next @ SV4 @ SV30 )
| ~ ( greater @ SV20 @ e_0 )
| ! [SY96: $i] :
( ~ ( next @ SY115 @ SY96 )
| ( equalish @ SV20 @ SY96 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(243,plain,
! [SV31: $i,SV21: $i,SV5: $i] :
( ( ( cycle @ SV5 @ SV21 )
= $false )
| ( ( ~ ( cycle @ SV31 @ e_0 )
| ! [SY117: $i,SY118: $i] :
( ~ ( cycle @ SY117 @ SY118 )
| ~ ( next @ SV31 @ SY117 )
| ~ ( greater @ SV31 @ SV5 )
| ~ ( greater @ SV21 @ SY118 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(244,plain,
! [SV38: $i,SV6: $i] :
( ( ( ~ ( product @ SV6 @ e_1 @ SV38 ) )
= $true )
| ( ( ~ ( greater @ SV38 @ SV6 ) )
= $true )
| ( ( cycle @ SV6 @ e_0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[229]) ).
thf(245,plain,
! [SV22: $i,SV42: $i,SV7: $i] :
( ( ( ~ ( product @ SV7 @ e_1 @ SV42 )
| ~ ( greater @ SV22 @ e_0 )
| ! [SY125: $i] :
( ~ ( next @ SV7 @ SY125 )
| ( equalish @ SV42 @ SY125 ) ) )
= $true )
| ( ( cycle @ SV7 @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(246,plain,
! [SV8: $i,SV39: $i] :
( ( ( ~ ( group_element @ SV39 ) )
= $true )
| ( ( ( product1 @ SV8 @ SV39 @ e_1 )
| ( product1 @ SV8 @ SV39 @ e_2 )
| ( product1 @ SV8 @ SV39 @ e_3 )
| ( product1 @ SV8 @ SV39 @ e_4 ) )
= $true )
| ( ( group_element @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[231]) ).
thf(247,plain,
! [SV32: $i,SV23: $i,SV9: $i] :
( ( ( product1 @ SV9 @ SV23 @ SV32 )
= $false )
| ( ( ! [SY119: $i] :
( ~ ( product1 @ SV9 @ SV23 @ SY119 )
| ( equalish @ SV32 @ SY119 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(248,plain,
! [SV33: $i,SV24: $i,SV10: $i] :
( ( ( product1 @ SV10 @ SV24 @ SV33 )
= $false )
| ( ( ! [SY120: $i] :
( ~ ( product1 @ SV10 @ SY120 @ SV33 )
| ( equalish @ SV24 @ SY120 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(249,plain,
! [SV34: $i,SV25: $i,SV11: $i] :
( ( ( product1 @ SV11 @ SV25 @ SV34 )
= $false )
| ( ( ! [SY121: $i] :
( ~ ( product1 @ SY121 @ SV25 @ SV34 )
| ( equalish @ SV11 @ SY121 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(250,plain,
! [SV13: $i,SV40: $i] :
( ( ( ~ ( group_element @ SV40 ) )
= $true )
| ( ( ( product2 @ SV13 @ SV40 @ e_1 )
| ( product2 @ SV13 @ SV40 @ e_2 )
| ( product2 @ SV13 @ SV40 @ e_3 )
| ( product2 @ SV13 @ SV40 @ e_4 ) )
= $true )
| ( ( group_element @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(251,plain,
! [SV35: $i,SV26: $i,SV14: $i] :
( ( ( product2 @ SV14 @ SV26 @ SV35 )
= $false )
| ( ( ! [SY122: $i] :
( ~ ( product2 @ SV14 @ SV26 @ SY122 )
| ( equalish @ SV35 @ SY122 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(252,plain,
! [SV36: $i,SV27: $i,SV15: $i] :
( ( ( product2 @ SV15 @ SV27 @ SV36 )
= $false )
| ( ( ! [SY123: $i] :
( ~ ( product2 @ SV15 @ SY123 @ SV36 )
| ( equalish @ SV27 @ SY123 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(253,plain,
! [SV37: $i,SV28: $i,SV16: $i] :
( ( ( product2 @ SV16 @ SV28 @ SV37 )
= $false )
| ( ( ! [SY124: $i] :
( ~ ( product2 @ SY124 @ SV28 @ SV37 )
| ( equalish @ SV16 @ SY124 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(254,plain,
! [SV18: $i,SV43: $i,SV1: $i,SV29: $i] :
( ( ( ~ ( product1 @ SV29 @ SV1 @ SV43 )
| ( product2 @ SV43 @ SV18 @ SV1 ) )
= $true )
| ( ( product1 @ SV1 @ SV18 @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(255,plain,
! [SV19: $i,SV41: $i,SV2: $i] :
( ( ( ~ ( cycle @ SV2 @ SV41 ) )
= $true )
| ( ( equalish @ SV19 @ SV41 )
= $true )
| ( ( cycle @ SV2 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[240]) ).
thf(256,plain,
! [SV3: $i] :
( ( ( cycle @ SV3 @ e_2 )
= $true )
| ( ( cycle @ SV3 @ e_3 )
= $true )
| ( ( cycle @ SV3 @ e_1 )
= $true )
| ( ( cycle @ SV3 @ e_0 )
= $true )
| ( ( group_element @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[241]) ).
thf(257,plain,
! [SV20: $i,SV4: $i,SV44: $i,SV30: $i] :
( ( ( ~ ( cycle @ SV30 @ SV44 )
| ~ ( next @ SV4 @ SV30 )
| ~ ( greater @ SV20 @ e_0 )
| ! [SY126: $i] :
( ~ ( next @ SV44 @ SY126 )
| ( equalish @ SV20 @ SY126 ) ) )
= $true )
| ( ( cycle @ SV4 @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(258,plain,
! [SV21: $i,SV5: $i,SV31: $i] :
( ( ( ~ ( cycle @ SV31 @ e_0 ) )
= $true )
| ( ( ! [SY117: $i,SY118: $i] :
( ~ ( cycle @ SY117 @ SY118 )
| ~ ( next @ SV31 @ SY117 )
| ~ ( greater @ SV31 @ SV5 )
| ~ ( greater @ SV21 @ SY118 ) ) )
= $true )
| ( ( cycle @ SV5 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[243]) ).
thf(259,plain,
! [SV38: $i,SV6: $i] :
( ( ( product @ SV6 @ e_1 @ SV38 )
= $false )
| ( ( ~ ( greater @ SV38 @ SV6 ) )
= $true )
| ( ( cycle @ SV6 @ e_0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(260,plain,
! [SV22: $i,SV42: $i,SV7: $i] :
( ( ( ~ ( product @ SV7 @ e_1 @ SV42 ) )
= $true )
| ( ( ~ ( greater @ SV22 @ e_0 )
| ! [SY125: $i] :
( ~ ( next @ SV7 @ SY125 )
| ( equalish @ SV42 @ SY125 ) ) )
= $true )
| ( ( cycle @ SV7 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(261,plain,
! [SV8: $i,SV39: $i] :
( ( ( group_element @ SV39 )
= $false )
| ( ( ( product1 @ SV8 @ SV39 @ e_1 )
| ( product1 @ SV8 @ SV39 @ e_2 )
| ( product1 @ SV8 @ SV39 @ e_3 )
| ( product1 @ SV8 @ SV39 @ e_4 ) )
= $true )
| ( ( group_element @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(262,plain,
! [SV32: $i,SV45: $i,SV23: $i,SV9: $i] :
( ( ( ~ ( product1 @ SV9 @ SV23 @ SV45 )
| ( equalish @ SV32 @ SV45 ) )
= $true )
| ( ( product1 @ SV9 @ SV23 @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(263,plain,
! [SV24: $i,SV33: $i,SV46: $i,SV10: $i] :
( ( ( ~ ( product1 @ SV10 @ SV46 @ SV33 )
| ( equalish @ SV24 @ SV46 ) )
= $true )
| ( ( product1 @ SV10 @ SV24 @ SV33 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(264,plain,
! [SV11: $i,SV34: $i,SV25: $i,SV47: $i] :
( ( ( ~ ( product1 @ SV47 @ SV25 @ SV34 )
| ( equalish @ SV11 @ SV47 ) )
= $true )
| ( ( product1 @ SV11 @ SV25 @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(265,plain,
! [SV13: $i,SV40: $i] :
( ( ( group_element @ SV40 )
= $false )
| ( ( ( product2 @ SV13 @ SV40 @ e_1 )
| ( product2 @ SV13 @ SV40 @ e_2 )
| ( product2 @ SV13 @ SV40 @ e_3 )
| ( product2 @ SV13 @ SV40 @ e_4 ) )
= $true )
| ( ( group_element @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(266,plain,
! [SV35: $i,SV48: $i,SV26: $i,SV14: $i] :
( ( ( ~ ( product2 @ SV14 @ SV26 @ SV48 )
| ( equalish @ SV35 @ SV48 ) )
= $true )
| ( ( product2 @ SV14 @ SV26 @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(267,plain,
! [SV27: $i,SV36: $i,SV49: $i,SV15: $i] :
( ( ( ~ ( product2 @ SV15 @ SV49 @ SV36 )
| ( equalish @ SV27 @ SV49 ) )
= $true )
| ( ( product2 @ SV15 @ SV27 @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[252]) ).
thf(268,plain,
! [SV16: $i,SV37: $i,SV28: $i,SV50: $i] :
( ( ( ~ ( product2 @ SV50 @ SV28 @ SV37 )
| ( equalish @ SV16 @ SV50 ) )
= $true )
| ( ( product2 @ SV16 @ SV28 @ SV37 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(269,plain,
! [SV18: $i,SV43: $i,SV1: $i,SV29: $i] :
( ( ( ~ ( product1 @ SV29 @ SV1 @ SV43 ) )
= $true )
| ( ( product2 @ SV43 @ SV18 @ SV1 )
= $true )
| ( ( product1 @ SV1 @ SV18 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[254]) ).
thf(270,plain,
! [SV19: $i,SV41: $i,SV2: $i] :
( ( ( cycle @ SV2 @ SV41 )
= $false )
| ( ( equalish @ SV19 @ SV41 )
= $true )
| ( ( cycle @ SV2 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(271,plain,
! [SV20: $i,SV4: $i,SV44: $i,SV30: $i] :
( ( ( ~ ( cycle @ SV30 @ SV44 ) )
= $true )
| ( ( ~ ( next @ SV4 @ SV30 )
| ~ ( greater @ SV20 @ e_0 )
| ! [SY126: $i] :
( ~ ( next @ SV44 @ SY126 )
| ( equalish @ SV20 @ SY126 ) ) )
= $true )
| ( ( cycle @ SV4 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[257]) ).
thf(272,plain,
! [SV21: $i,SV5: $i,SV31: $i] :
( ( ( cycle @ SV31 @ e_0 )
= $false )
| ( ( ! [SY117: $i,SY118: $i] :
( ~ ( cycle @ SY117 @ SY118 )
| ~ ( next @ SV31 @ SY117 )
| ~ ( greater @ SV31 @ SV5 )
| ~ ( greater @ SV21 @ SY118 ) ) )
= $true )
| ( ( cycle @ SV5 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(273,plain,
! [SV6: $i,SV38: $i] :
( ( ( greater @ SV38 @ SV6 )
= $false )
| ( ( product @ SV6 @ e_1 @ SV38 )
= $false )
| ( ( cycle @ SV6 @ e_0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(274,plain,
! [SV22: $i,SV42: $i,SV7: $i] :
( ( ( product @ SV7 @ e_1 @ SV42 )
= $false )
| ( ( ~ ( greater @ SV22 @ e_0 )
| ! [SY125: $i] :
( ~ ( next @ SV7 @ SY125 )
| ( equalish @ SV42 @ SY125 ) ) )
= $true )
| ( ( cycle @ SV7 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(275,plain,
! [SV39: $i,SV8: $i] :
( ( ( product1 @ SV8 @ SV39 @ e_1 )
= $true )
| ( ( ( product1 @ SV8 @ SV39 @ e_2 )
| ( product1 @ SV8 @ SV39 @ e_3 )
| ( product1 @ SV8 @ SV39 @ e_4 ) )
= $true )
| ( ( group_element @ SV39 )
= $false )
| ( ( group_element @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[261]) ).
thf(276,plain,
! [SV32: $i,SV45: $i,SV23: $i,SV9: $i] :
( ( ( ~ ( product1 @ SV9 @ SV23 @ SV45 ) )
= $true )
| ( ( equalish @ SV32 @ SV45 )
= $true )
| ( ( product1 @ SV9 @ SV23 @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[262]) ).
thf(277,plain,
! [SV24: $i,SV33: $i,SV46: $i,SV10: $i] :
( ( ( ~ ( product1 @ SV10 @ SV46 @ SV33 ) )
= $true )
| ( ( equalish @ SV24 @ SV46 )
= $true )
| ( ( product1 @ SV10 @ SV24 @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[263]) ).
thf(278,plain,
! [SV11: $i,SV34: $i,SV25: $i,SV47: $i] :
( ( ( ~ ( product1 @ SV47 @ SV25 @ SV34 ) )
= $true )
| ( ( equalish @ SV11 @ SV47 )
= $true )
| ( ( product1 @ SV11 @ SV25 @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[264]) ).
thf(279,plain,
! [SV40: $i,SV13: $i] :
( ( ( product2 @ SV13 @ SV40 @ e_1 )
= $true )
| ( ( ( product2 @ SV13 @ SV40 @ e_2 )
| ( product2 @ SV13 @ SV40 @ e_3 )
| ( product2 @ SV13 @ SV40 @ e_4 ) )
= $true )
| ( ( group_element @ SV40 )
= $false )
| ( ( group_element @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(280,plain,
! [SV35: $i,SV48: $i,SV26: $i,SV14: $i] :
( ( ( ~ ( product2 @ SV14 @ SV26 @ SV48 ) )
= $true )
| ( ( equalish @ SV35 @ SV48 )
= $true )
| ( ( product2 @ SV14 @ SV26 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(281,plain,
! [SV27: $i,SV36: $i,SV49: $i,SV15: $i] :
( ( ( ~ ( product2 @ SV15 @ SV49 @ SV36 ) )
= $true )
| ( ( equalish @ SV27 @ SV49 )
= $true )
| ( ( product2 @ SV15 @ SV27 @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[267]) ).
thf(282,plain,
! [SV16: $i,SV37: $i,SV28: $i,SV50: $i] :
( ( ( ~ ( product2 @ SV50 @ SV28 @ SV37 ) )
= $true )
| ( ( equalish @ SV16 @ SV50 )
= $true )
| ( ( product2 @ SV16 @ SV28 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[268]) ).
thf(283,plain,
! [SV18: $i,SV43: $i,SV1: $i,SV29: $i] :
( ( ( product1 @ SV29 @ SV1 @ SV43 )
= $false )
| ( ( product2 @ SV43 @ SV18 @ SV1 )
= $true )
| ( ( product1 @ SV1 @ SV18 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(284,plain,
! [SV20: $i,SV4: $i,SV44: $i,SV30: $i] :
( ( ( cycle @ SV30 @ SV44 )
= $false )
| ( ( ~ ( next @ SV4 @ SV30 )
| ~ ( greater @ SV20 @ e_0 )
| ! [SY126: $i] :
( ~ ( next @ SV44 @ SY126 )
| ( equalish @ SV20 @ SY126 ) ) )
= $true )
| ( ( cycle @ SV4 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(285,plain,
! [SV21: $i,SV5: $i,SV31: $i,SV51: $i] :
( ( ( ! [SY127: $i] :
( ~ ( cycle @ SV51 @ SY127 )
| ~ ( next @ SV31 @ SV51 )
| ~ ( greater @ SV31 @ SV5 )
| ~ ( greater @ SV21 @ SY127 ) ) )
= $true )
| ( ( cycle @ SV31 @ e_0 )
= $false )
| ( ( cycle @ SV5 @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(286,plain,
! [SV42: $i,SV7: $i,SV22: $i] :
( ( ( ~ ( greater @ SV22 @ e_0 ) )
= $true )
| ( ( ! [SY125: $i] :
( ~ ( next @ SV7 @ SY125 )
| ( equalish @ SV42 @ SY125 ) ) )
= $true )
| ( ( product @ SV7 @ e_1 @ SV42 )
= $false )
| ( ( cycle @ SV7 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(287,plain,
! [SV39: $i,SV8: $i] :
( ( ( product1 @ SV8 @ SV39 @ e_2 )
= $true )
| ( ( ( product1 @ SV8 @ SV39 @ e_3 )
| ( product1 @ SV8 @ SV39 @ e_4 ) )
= $true )
| ( ( product1 @ SV8 @ SV39 @ e_1 )
= $true )
| ( ( group_element @ SV39 )
= $false )
| ( ( group_element @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[275]) ).
thf(288,plain,
! [SV32: $i,SV45: $i,SV23: $i,SV9: $i] :
( ( ( product1 @ SV9 @ SV23 @ SV45 )
= $false )
| ( ( equalish @ SV32 @ SV45 )
= $true )
| ( ( product1 @ SV9 @ SV23 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(289,plain,
! [SV24: $i,SV33: $i,SV46: $i,SV10: $i] :
( ( ( product1 @ SV10 @ SV46 @ SV33 )
= $false )
| ( ( equalish @ SV24 @ SV46 )
= $true )
| ( ( product1 @ SV10 @ SV24 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(290,plain,
! [SV11: $i,SV34: $i,SV25: $i,SV47: $i] :
( ( ( product1 @ SV47 @ SV25 @ SV34 )
= $false )
| ( ( equalish @ SV11 @ SV47 )
= $true )
| ( ( product1 @ SV11 @ SV25 @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(291,plain,
! [SV40: $i,SV13: $i] :
( ( ( product2 @ SV13 @ SV40 @ e_2 )
= $true )
| ( ( ( product2 @ SV13 @ SV40 @ e_3 )
| ( product2 @ SV13 @ SV40 @ e_4 ) )
= $true )
| ( ( product2 @ SV13 @ SV40 @ e_1 )
= $true )
| ( ( group_element @ SV40 )
= $false )
| ( ( group_element @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[279]) ).
thf(292,plain,
! [SV35: $i,SV48: $i,SV26: $i,SV14: $i] :
( ( ( product2 @ SV14 @ SV26 @ SV48 )
= $false )
| ( ( equalish @ SV35 @ SV48 )
= $true )
| ( ( product2 @ SV14 @ SV26 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(293,plain,
! [SV27: $i,SV36: $i,SV49: $i,SV15: $i] :
( ( ( product2 @ SV15 @ SV49 @ SV36 )
= $false )
| ( ( equalish @ SV27 @ SV49 )
= $true )
| ( ( product2 @ SV15 @ SV27 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(294,plain,
! [SV16: $i,SV37: $i,SV28: $i,SV50: $i] :
( ( ( product2 @ SV50 @ SV28 @ SV37 )
= $false )
| ( ( equalish @ SV16 @ SV50 )
= $true )
| ( ( product2 @ SV16 @ SV28 @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(295,plain,
! [SV44: $i,SV20: $i,SV30: $i,SV4: $i] :
( ( ( ~ ( next @ SV4 @ SV30 ) )
= $true )
| ( ( ~ ( greater @ SV20 @ e_0 )
| ! [SY126: $i] :
( ~ ( next @ SV44 @ SY126 )
| ( equalish @ SV20 @ SY126 ) ) )
= $true )
| ( ( cycle @ SV30 @ SV44 )
= $false )
| ( ( cycle @ SV4 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[284]) ).
thf(296,plain,
! [SV21: $i,SV5: $i,SV31: $i,SV52: $i,SV51: $i] :
( ( ( ~ ( cycle @ SV51 @ SV52 )
| ~ ( next @ SV31 @ SV51 )
| ~ ( greater @ SV31 @ SV5 )
| ~ ( greater @ SV21 @ SV52 ) )
= $true )
| ( ( cycle @ SV31 @ e_0 )
= $false )
| ( ( cycle @ SV5 @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(297,plain,
! [SV42: $i,SV7: $i,SV22: $i] :
( ( ( greater @ SV22 @ e_0 )
= $false )
| ( ( ! [SY125: $i] :
( ~ ( next @ SV7 @ SY125 )
| ( equalish @ SV42 @ SY125 ) ) )
= $true )
| ( ( product @ SV7 @ e_1 @ SV42 )
= $false )
| ( ( cycle @ SV7 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[286]) ).
thf(298,plain,
! [SV39: $i,SV8: $i] :
( ( ( product1 @ SV8 @ SV39 @ e_3 )
= $true )
| ( ( product1 @ SV8 @ SV39 @ e_4 )
= $true )
| ( ( product1 @ SV8 @ SV39 @ e_2 )
= $true )
| ( ( product1 @ SV8 @ SV39 @ e_1 )
= $true )
| ( ( group_element @ SV39 )
= $false )
| ( ( group_element @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[287]) ).
thf(299,plain,
! [SV40: $i,SV13: $i] :
( ( ( product2 @ SV13 @ SV40 @ e_3 )
= $true )
| ( ( product2 @ SV13 @ SV40 @ e_4 )
= $true )
| ( ( product2 @ SV13 @ SV40 @ e_2 )
= $true )
| ( ( product2 @ SV13 @ SV40 @ e_1 )
= $true )
| ( ( group_element @ SV40 )
= $false )
| ( ( group_element @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[291]) ).
thf(300,plain,
! [SV44: $i,SV20: $i,SV30: $i,SV4: $i] :
( ( ( next @ SV4 @ SV30 )
= $false )
| ( ( ~ ( greater @ SV20 @ e_0 )
| ! [SY126: $i] :
( ~ ( next @ SV44 @ SY126 )
| ( equalish @ SV20 @ SY126 ) ) )
= $true )
| ( ( cycle @ SV30 @ SV44 )
= $false )
| ( ( cycle @ SV4 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(301,plain,
! [SV21: $i,SV5: $i,SV31: $i,SV52: $i,SV51: $i] :
( ( ( ~ ( cycle @ SV51 @ SV52 ) )
= $true )
| ( ( ~ ( next @ SV31 @ SV51 )
| ~ ( greater @ SV31 @ SV5 )
| ~ ( greater @ SV21 @ SV52 ) )
= $true )
| ( ( cycle @ SV31 @ e_0 )
= $false )
| ( ( cycle @ SV5 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[296]) ).
thf(302,plain,
! [SV22: $i,SV42: $i,SV53: $i,SV7: $i] :
( ( ( ~ ( next @ SV7 @ SV53 )
| ( equalish @ SV42 @ SV53 ) )
= $true )
| ( ( greater @ SV22 @ e_0 )
= $false )
| ( ( product @ SV7 @ e_1 @ SV42 )
= $false )
| ( ( cycle @ SV7 @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(303,plain,
! [SV30: $i,SV4: $i,SV44: $i,SV20: $i] :
( ( ( ~ ( greater @ SV20 @ e_0 ) )
= $true )
| ( ( ! [SY126: $i] :
( ~ ( next @ SV44 @ SY126 )
| ( equalish @ SV20 @ SY126 ) ) )
= $true )
| ( ( next @ SV4 @ SV30 )
= $false )
| ( ( cycle @ SV30 @ SV44 )
= $false )
| ( ( cycle @ SV4 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[300]) ).
thf(304,plain,
! [SV21: $i,SV5: $i,SV31: $i,SV52: $i,SV51: $i] :
( ( ( cycle @ SV51 @ SV52 )
= $false )
| ( ( ~ ( next @ SV31 @ SV51 )
| ~ ( greater @ SV31 @ SV5 )
| ~ ( greater @ SV21 @ SV52 ) )
= $true )
| ( ( cycle @ SV31 @ e_0 )
= $false )
| ( ( cycle @ SV5 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(305,plain,
! [SV22: $i,SV42: $i,SV53: $i,SV7: $i] :
( ( ( ~ ( next @ SV7 @ SV53 ) )
= $true )
| ( ( equalish @ SV42 @ SV53 )
= $true )
| ( ( greater @ SV22 @ e_0 )
= $false )
| ( ( product @ SV7 @ e_1 @ SV42 )
= $false )
| ( ( cycle @ SV7 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(306,plain,
! [SV30: $i,SV4: $i,SV44: $i,SV20: $i] :
( ( ( greater @ SV20 @ e_0 )
= $false )
| ( ( ! [SY126: $i] :
( ~ ( next @ SV44 @ SY126 )
| ( equalish @ SV20 @ SY126 ) ) )
= $true )
| ( ( next @ SV4 @ SV30 )
= $false )
| ( ( cycle @ SV30 @ SV44 )
= $false )
| ( ( cycle @ SV4 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(307,plain,
! [SV52: $i,SV21: $i,SV5: $i,SV51: $i,SV31: $i] :
( ( ( ~ ( next @ SV31 @ SV51 ) )
= $true )
| ( ( ~ ( greater @ SV31 @ SV5 )
| ~ ( greater @ SV21 @ SV52 ) )
= $true )
| ( ( cycle @ SV51 @ SV52 )
= $false )
| ( ( cycle @ SV31 @ e_0 )
= $false )
| ( ( cycle @ SV5 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[304]) ).
thf(308,plain,
! [SV22: $i,SV42: $i,SV53: $i,SV7: $i] :
( ( ( next @ SV7 @ SV53 )
= $false )
| ( ( equalish @ SV42 @ SV53 )
= $true )
| ( ( greater @ SV22 @ e_0 )
= $false )
| ( ( product @ SV7 @ e_1 @ SV42 )
= $false )
| ( ( cycle @ SV7 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(309,plain,
! [SV30: $i,SV4: $i,SV20: $i,SV54: $i,SV44: $i] :
( ( ( ~ ( next @ SV44 @ SV54 )
| ( equalish @ SV20 @ SV54 ) )
= $true )
| ( ( greater @ SV20 @ e_0 )
= $false )
| ( ( next @ SV4 @ SV30 )
= $false )
| ( ( cycle @ SV30 @ SV44 )
= $false )
| ( ( cycle @ SV4 @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(310,plain,
! [SV52: $i,SV21: $i,SV5: $i,SV51: $i,SV31: $i] :
( ( ( next @ SV31 @ SV51 )
= $false )
| ( ( ~ ( greater @ SV31 @ SV5 )
| ~ ( greater @ SV21 @ SV52 ) )
= $true )
| ( ( cycle @ SV51 @ SV52 )
= $false )
| ( ( cycle @ SV31 @ e_0 )
= $false )
| ( ( cycle @ SV5 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(311,plain,
! [SV30: $i,SV4: $i,SV20: $i,SV54: $i,SV44: $i] :
( ( ( ~ ( next @ SV44 @ SV54 ) )
= $true )
| ( ( equalish @ SV20 @ SV54 )
= $true )
| ( ( greater @ SV20 @ e_0 )
= $false )
| ( ( next @ SV4 @ SV30 )
= $false )
| ( ( cycle @ SV30 @ SV44 )
= $false )
| ( ( cycle @ SV4 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[309]) ).
thf(312,plain,
! [SV51: $i,SV52: $i,SV21: $i,SV5: $i,SV31: $i] :
( ( ( ~ ( greater @ SV31 @ SV5 ) )
= $true )
| ( ( ~ ( greater @ SV21 @ SV52 ) )
= $true )
| ( ( next @ SV31 @ SV51 )
= $false )
| ( ( cycle @ SV51 @ SV52 )
= $false )
| ( ( cycle @ SV31 @ e_0 )
= $false )
| ( ( cycle @ SV5 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[310]) ).
thf(313,plain,
! [SV30: $i,SV4: $i,SV20: $i,SV54: $i,SV44: $i] :
( ( ( next @ SV44 @ SV54 )
= $false )
| ( ( equalish @ SV20 @ SV54 )
= $true )
| ( ( greater @ SV20 @ e_0 )
= $false )
| ( ( next @ SV4 @ SV30 )
= $false )
| ( ( cycle @ SV30 @ SV44 )
= $false )
| ( ( cycle @ SV4 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(314,plain,
! [SV51: $i,SV52: $i,SV21: $i,SV5: $i,SV31: $i] :
( ( ( greater @ SV31 @ SV5 )
= $false )
| ( ( ~ ( greater @ SV21 @ SV52 ) )
= $true )
| ( ( next @ SV31 @ SV51 )
= $false )
| ( ( cycle @ SV51 @ SV52 )
= $false )
| ( ( cycle @ SV31 @ e_0 )
= $false )
| ( ( cycle @ SV5 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(315,plain,
! [SV51: $i,SV5: $i,SV31: $i,SV52: $i,SV21: $i] :
( ( ( greater @ SV21 @ SV52 )
= $false )
| ( ( greater @ SV31 @ SV5 )
= $false )
| ( ( next @ SV31 @ SV51 )
= $false )
| ( ( cycle @ SV51 @ SV52 )
= $false )
| ( ( cycle @ SV31 @ e_0 )
= $false )
| ( ( cycle @ SV5 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(316,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[116,315,313,308,299,298,294,293,292,290,289,288,283,273,270,256,193,192,187,182,181,180,179,178,177,176,175,174,173,172,171,140,139,138,137,132,129,128,127,126,125,124,123,122,121,120,119,118,117]) ).
thf(317,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[316]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP124-8.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.16 % Computer : n026.cluster.edu
% 0.07/0.16 % Model : x86_64 x86_64
% 0.07/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.16 % Memory : 8046.5625MB
% 0.07/0.16 % OS : Linux 6.8.0-71-generic
% 0.07/0.16 % CPULimit : 300
% 0.07/0.16 % WCLimit : 300
% 0.07/0.16 % DateTime : Tue Oct 6 10:38:02 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.15/0.42
% 1.15/0.42 No.of.Axioms: 48
% 1.15/0.42
% 1.15/0.42 Length.of.Defs: 0
% 1.15/0.42
% 1.15/0.42 Contains.Choice.Funs: false
% 1.15/0.42 .........
% 1.15/0.42
% 1.15/0.42 ********************************
% 1.15/0.42 * All subproblems solved! *
% 1.15/0.42 ********************************
% 1.15/0.42 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:48,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:5,ordering:none,proof_output:1,protocol_output:false,clause_count:316,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.15/0.42
% 1.15/0.42 %**** Beginning of derivation protocol ****
% 1.15/0.42 % SZS output start CNFRefutation
% See solution above
% 1.15/0.42
% 1.15/0.42 %**** End of derivation protocol ****
% 1.15/0.42 %**** no. of clauses in derivation: 317 ****
% 1.15/0.42 %**** clause counter: 316 ****
% 1.15/0.42
% 1.15/0.42 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:48,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:5,ordering:none,proof_output:1,protocol_output:false,clause_count:316,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------