TSTP Solution File: GRP124-4.004 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GRP124-4.004 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n022.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 10:16:05 EDT 2022
% Result : Unsatisfiable 0.20s 0.58s
% Output : CNFRefutation 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 33
% Syntax : Number of formulae : 190 ( 116 unt; 7 typ; 0 def)
% Number of atoms : 1154 ( 280 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 2115 ( 246 ~; 411 |; 0 &;1458 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-3 aty)
% Number of variables : 442 ( 0 ^ 442 !; 0 ?; 442 :)
% Comments :
%------------------------------------------------------------------------------
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_group_element,type,
group_element: $i > $o ).
thf(tp_product,type,
product: $i > $i > $i > $o ).
thf(1,axiom,
! [X: $i] : ( product @ X @ X @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_idempotence) ).
thf(2,axiom,
! [W: $i,Y: $i,X: $i,Z: $i] :
( ~ ( product @ W @ Y @ X )
| ~ ( product @ Z @ Y @ X )
| ( equalish @ W @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
thf(3,axiom,
! [X: $i,W: $i,Y: $i,Z: $i] :
( ~ ( product @ X @ W @ Y )
| ~ ( product @ X @ Z @ Y )
| ( equalish @ W @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
thf(4,axiom,
! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( product @ X @ Y @ W )
| ~ ( product @ X @ Y @ Z )
| ( equalish @ W @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function2) ).
thf(5,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 )
| ( product @ X @ Y @ e_4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function1) ).
thf(6,axiom,
~ ( equalish @ e_4 @ e_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_3) ).
thf(7,axiom,
~ ( equalish @ e_4 @ e_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_2) ).
thf(8,axiom,
~ ( equalish @ e_4 @ e_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_1) ).
thf(9,axiom,
~ ( equalish @ e_3 @ e_4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
thf(10,axiom,
~ ( equalish @ e_3 @ e_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
thf(11,axiom,
~ ( equalish @ e_3 @ e_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
thf(12,axiom,
~ ( equalish @ e_2 @ e_4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_4) ).
thf(13,axiom,
~ ( equalish @ e_2 @ e_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
thf(14,axiom,
~ ( equalish @ e_2 @ e_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
thf(15,axiom,
~ ( equalish @ e_1 @ e_4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_4) ).
thf(16,axiom,
~ ( equalish @ e_1 @ e_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
thf(17,axiom,
~ ( equalish @ e_1 @ e_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
thf(18,axiom,
group_element @ e_4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_4) ).
thf(19,axiom,
group_element @ e_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
thf(20,axiom,
group_element @ e_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
thf(21,axiom,
group_element @ e_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
thf(22,axiom,
! [X: $i,Y: $i] :
( ~ ( group_element @ X )
| ~ ( group_element @ Y )
| ( product @ X @ e_1 @ Y )
| ( product @ X @ e_2 @ Y )
| ( product @ X @ e_3 @ Y )
| ( product @ X @ e_4 @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',column_surjectivity) ).
thf(23,axiom,
! [X: $i,Y: $i] :
( ~ ( group_element @ X )
| ~ ( group_element @ Y )
| ( product @ e_1 @ X @ Y )
| ( product @ e_2 @ X @ Y )
| ( product @ e_3 @ X @ Y )
| ( product @ e_4 @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',row_surjectivity) ).
thf(24,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(25,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[24]) ).
thf(26,negated_conjecture,
! [X1: $i,Y1: $i,Z1: $i,X2: $i,Y2: $i,Z2: $i] :
( ~ ( product @ X1 @ Y1 @ Z1 )
| ~ ( product @ X2 @ Y2 @ Z1 )
| ~ ( product @ Z2 @ X1 @ Y1 )
| ~ ( product @ Z2 @ X2 @ Y2 )
| ( equalish @ Y1 @ Y2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg2_2) ).
thf(27,negated_conjecture,
! [X1: $i,Y1: $i,Z1: $i,X2: $i,Y2: $i,Z2: $i] :
( ~ ( product @ X1 @ Y1 @ Z1 )
| ~ ( product @ X2 @ Y2 @ Z1 )
| ~ ( product @ Z2 @ X1 @ Y1 )
| ~ ( product @ Z2 @ X2 @ Y2 )
| ( equalish @ X1 @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg2_1) ).
thf(28,plain,
$false = $false,
inference(unfold_def,[status(thm)],[25]) ).
thf(29,plain,
( ( ! [X: $i] : ( product @ X @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(30,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)],[2]) ).
thf(31,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)],[3]) ).
thf(32,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)],[4]) ).
thf(33,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 )
| ( product @ X @ Y @ e_4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(34,plain,
( ( ~ ( equalish @ e_4 @ e_3 ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(35,plain,
( ( ~ ( equalish @ e_4 @ e_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(36,plain,
( ( ~ ( equalish @ e_4 @ e_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(37,plain,
( ( ~ ( equalish @ e_3 @ e_4 ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(38,plain,
( ( ~ ( equalish @ e_3 @ e_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(39,plain,
( ( ~ ( equalish @ e_3 @ e_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(40,plain,
( ( ~ ( equalish @ e_2 @ e_4 ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(41,plain,
( ( ~ ( equalish @ e_2 @ e_3 ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(42,plain,
( ( ~ ( equalish @ e_2 @ e_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(43,plain,
( ( ~ ( equalish @ e_1 @ e_4 ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(44,plain,
( ( ~ ( equalish @ e_1 @ e_3 ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(45,plain,
( ( ~ ( equalish @ e_1 @ e_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(46,plain,
( ( group_element @ e_4 )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(47,plain,
( ( group_element @ e_3 )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(48,plain,
( ( group_element @ e_2 )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(49,plain,
( ( group_element @ e_1 )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(50,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( group_element @ X )
| ~ ( group_element @ Y )
| ( product @ X @ e_1 @ Y )
| ( product @ X @ e_2 @ Y )
| ( product @ X @ e_3 @ Y )
| ( product @ X @ e_4 @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(51,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( group_element @ X )
| ~ ( group_element @ Y )
| ( product @ e_1 @ X @ Y )
| ( product @ e_2 @ X @ Y )
| ( product @ e_3 @ X @ Y )
| ( product @ e_4 @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(52,plain,
( ( ! [X1: $i,Y1: $i,Z1: $i,X2: $i,Y2: $i,Z2: $i] :
( ~ ( product @ X1 @ Y1 @ Z1 )
| ~ ( product @ X2 @ Y2 @ Z1 )
| ~ ( product @ Z2 @ X1 @ Y1 )
| ~ ( product @ Z2 @ X2 @ Y2 )
| ( equalish @ Y1 @ Y2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(53,plain,
( ( ! [X1: $i,Y1: $i,Z1: $i,X2: $i,Y2: $i,Z2: $i] :
( ~ ( product @ X1 @ Y1 @ Z1 )
| ~ ( product @ X2 @ Y2 @ Z1 )
| ~ ( product @ Z2 @ X1 @ Y1 )
| ~ ( product @ Z2 @ X2 @ Y2 )
| ( equalish @ X1 @ X2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(54,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[28]) ).
thf(55,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)],[30]) ).
thf(56,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)],[31]) ).
thf(57,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)],[32]) ).
thf(58,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 )
| ( product @ X @ Y @ e_4 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[33]) ).
thf(59,plain,
( ( ! [X: $i] :
( ~ ( group_element @ X )
| ! [Y: $i] :
( ~ ( group_element @ Y )
| ( product @ X @ e_1 @ Y )
| ( product @ X @ e_2 @ Y )
| ( product @ X @ e_3 @ Y )
| ( product @ X @ e_4 @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[50]) ).
thf(60,plain,
( ( ! [X: $i] :
( ~ ( group_element @ X )
| ! [Y: $i] :
( ~ ( group_element @ Y )
| ( product @ e_1 @ X @ Y )
| ( product @ e_2 @ X @ Y )
| ( product @ e_3 @ X @ Y )
| ( product @ e_4 @ X @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[51]) ).
thf(61,plain,
( ( ! [X1: $i,Y1: $i,Z1: $i,X2: $i] :
( ~ ( product @ X1 @ Y1 @ Z1 )
| ! [Y2: $i] :
( ~ ( product @ X2 @ Y2 @ Z1 )
| ! [Z2: $i] :
( ~ ( product @ Z2 @ X1 @ Y1 )
| ~ ( product @ Z2 @ X2 @ Y2 )
| ( equalish @ Y1 @ Y2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[52]) ).
thf(62,plain,
( ( ! [X1: $i,Y1: $i,Z1: $i,X2: $i] :
( ~ ( product @ X1 @ Y1 @ Z1 )
| ! [Y2: $i] :
( ~ ( product @ X2 @ Y2 @ Z1 )
| ! [Z2: $i] :
( ~ ( product @ Z2 @ X1 @ Y1 )
| ~ ( product @ Z2 @ X2 @ Y2 )
| ( equalish @ X1 @ X2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[53]) ).
thf(63,plain,
( ( ! [X1: $i,Y1: $i,Z1: $i,X2: $i] :
( ~ ( product @ X1 @ Y1 @ Z1 )
| ! [Y2: $i] :
( ~ ( product @ X2 @ Y2 @ Z1 )
| ! [Z2: $i] :
( ~ ( product @ Z2 @ X1 @ Y1 )
| ~ ( product @ Z2 @ X2 @ Y2 )
| ( equalish @ X1 @ X2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(64,plain,
( ( ! [X1: $i,Y1: $i,Z1: $i,X2: $i] :
( ~ ( product @ X1 @ Y1 @ Z1 )
| ! [Y2: $i] :
( ~ ( product @ X2 @ Y2 @ Z1 )
| ! [Z2: $i] :
( ~ ( product @ Z2 @ X1 @ Y1 )
| ~ ( product @ Z2 @ X2 @ Y2 )
| ( equalish @ Y1 @ Y2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(65,plain,
( ( ! [X: $i] :
( ~ ( group_element @ X )
| ! [Y: $i] :
( ~ ( group_element @ Y )
| ( product @ e_1 @ X @ Y )
| ( product @ e_2 @ X @ Y )
| ( product @ e_3 @ X @ Y )
| ( product @ e_4 @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(66,plain,
( ( ! [X: $i] :
( ~ ( group_element @ X )
| ! [Y: $i] :
( ~ ( group_element @ Y )
| ( product @ X @ e_1 @ Y )
| ( product @ X @ e_2 @ Y )
| ( product @ X @ e_3 @ Y )
| ( product @ X @ e_4 @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(67,plain,
( ( group_element @ e_1 )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(68,plain,
( ( group_element @ e_2 )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(69,plain,
( ( group_element @ e_3 )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(70,plain,
( ( group_element @ e_4 )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(71,plain,
( ( ~ ( equalish @ e_1 @ e_2 ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(72,plain,
( ( ~ ( equalish @ e_1 @ e_3 ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(73,plain,
( ( ~ ( equalish @ e_1 @ e_4 ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(74,plain,
( ( ~ ( equalish @ e_2 @ e_1 ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(75,plain,
( ( ~ ( equalish @ e_2 @ e_3 ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(76,plain,
( ( ~ ( equalish @ e_2 @ e_4 ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(77,plain,
( ( ~ ( equalish @ e_3 @ e_1 ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(78,plain,
( ( ~ ( equalish @ e_3 @ e_2 ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(79,plain,
( ( ~ ( equalish @ e_3 @ e_4 ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(80,plain,
( ( ~ ( equalish @ e_4 @ e_1 ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(81,plain,
( ( ~ ( equalish @ e_4 @ e_2 ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(82,plain,
( ( ~ ( equalish @ e_4 @ e_3 ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(83,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 )
| ( product @ X @ Y @ e_4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(84,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)],[57]) ).
thf(85,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)],[56]) ).
thf(86,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)],[55]) ).
thf(87,plain,
( ( ! [X: $i] : ( product @ X @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(88,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(89,plain,
! [SV1: $i] :
( ( ! [SY31: $i,SY32: $i,SY33: $i] :
( ~ ( product @ SV1 @ SY31 @ SY32 )
| ! [SY34: $i] :
( ~ ( product @ SY33 @ SY34 @ SY32 )
| ! [SY35: $i] :
( ~ ( product @ SY35 @ SV1 @ SY31 )
| ~ ( product @ SY35 @ SY33 @ SY34 )
| ( equalish @ SV1 @ SY33 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(90,plain,
! [SV2: $i] :
( ( ! [SY36: $i,SY37: $i,SY38: $i] :
( ~ ( product @ SV2 @ SY36 @ SY37 )
| ! [SY39: $i] :
( ~ ( product @ SY38 @ SY39 @ SY37 )
| ! [SY40: $i] :
( ~ ( product @ SY40 @ SV2 @ SY36 )
| ~ ( product @ SY40 @ SY38 @ SY39 )
| ( equalish @ SY36 @ SY39 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(91,plain,
! [SV3: $i] :
( ( ~ ( group_element @ SV3 )
| ! [SY41: $i] :
( ~ ( group_element @ SY41 )
| ( product @ e_1 @ SV3 @ SY41 )
| ( product @ e_2 @ SV3 @ SY41 )
| ( product @ e_3 @ SV3 @ SY41 )
| ( product @ e_4 @ SV3 @ SY41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(92,plain,
! [SV4: $i] :
( ( ~ ( group_element @ SV4 )
| ! [SY42: $i] :
( ~ ( group_element @ SY42 )
| ( product @ SV4 @ e_1 @ SY42 )
| ( product @ SV4 @ e_2 @ SY42 )
| ( product @ SV4 @ e_3 @ SY42 )
| ( product @ SV4 @ e_4 @ SY42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(93,plain,
( ( equalish @ e_1 @ e_2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(94,plain,
( ( equalish @ e_1 @ e_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(95,plain,
( ( equalish @ e_1 @ e_4 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(96,plain,
( ( equalish @ e_2 @ e_1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(97,plain,
( ( equalish @ e_2 @ e_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(98,plain,
( ( equalish @ e_2 @ e_4 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(99,plain,
( ( equalish @ e_3 @ e_1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(100,plain,
( ( equalish @ e_3 @ e_2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(101,plain,
( ( equalish @ e_3 @ e_4 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(102,plain,
( ( equalish @ e_4 @ e_1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(103,plain,
( ( equalish @ e_4 @ e_2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(104,plain,
( ( equalish @ e_4 @ e_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(105,plain,
! [SV5: $i] :
( ( ~ ( group_element @ SV5 )
| ! [SY43: $i] :
( ~ ( group_element @ SY43 )
| ( product @ SV5 @ SY43 @ e_1 )
| ( product @ SV5 @ SY43 @ e_2 )
| ( product @ SV5 @ SY43 @ e_3 )
| ( product @ SV5 @ SY43 @ e_4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(106,plain,
! [SV6: $i] :
( ( ! [SY44: $i,SY45: $i] :
( ~ ( product @ SV6 @ SY44 @ SY45 )
| ! [SY46: $i] :
( ~ ( product @ SV6 @ SY44 @ SY46 )
| ( equalish @ SY45 @ SY46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(107,plain,
! [SV7: $i] :
( ( ! [SY47: $i,SY48: $i] :
( ~ ( product @ SV7 @ SY47 @ SY48 )
| ! [SY49: $i] :
( ~ ( product @ SV7 @ SY49 @ SY48 )
| ( equalish @ SY47 @ SY49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(108,plain,
! [SV8: $i] :
( ( ! [SY50: $i,SY51: $i] :
( ~ ( product @ SV8 @ SY50 @ SY51 )
| ! [SY52: $i] :
( ~ ( product @ SY52 @ SY50 @ SY51 )
| ( equalish @ SV8 @ SY52 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(109,plain,
! [SV9: $i] :
( ( product @ SV9 @ SV9 @ SV9 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(110,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(111,plain,
! [SV10: $i,SV1: $i] :
( ( ! [SY53: $i,SY54: $i] :
( ~ ( product @ SV1 @ SV10 @ SY53 )
| ! [SY55: $i] :
( ~ ( product @ SY54 @ SY55 @ SY53 )
| ! [SY56: $i] :
( ~ ( product @ SY56 @ SV1 @ SV10 )
| ~ ( product @ SY56 @ SY54 @ SY55 )
| ( equalish @ SV1 @ SY54 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(112,plain,
! [SV11: $i,SV2: $i] :
( ( ! [SY57: $i,SY58: $i] :
( ~ ( product @ SV2 @ SV11 @ SY57 )
| ! [SY59: $i] :
( ~ ( product @ SY58 @ SY59 @ SY57 )
| ! [SY60: $i] :
( ~ ( product @ SY60 @ SV2 @ SV11 )
| ~ ( product @ SY60 @ SY58 @ SY59 )
| ( equalish @ SV11 @ SY59 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(113,plain,
! [SV3: $i] :
( ( ( ~ ( group_element @ SV3 ) )
= $true )
| ( ( ! [SY41: $i] :
( ~ ( group_element @ SY41 )
| ( product @ e_1 @ SV3 @ SY41 )
| ( product @ e_2 @ SV3 @ SY41 )
| ( product @ e_3 @ SV3 @ SY41 )
| ( product @ e_4 @ SV3 @ SY41 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(114,plain,
! [SV4: $i] :
( ( ( ~ ( group_element @ SV4 ) )
= $true )
| ( ( ! [SY42: $i] :
( ~ ( group_element @ SY42 )
| ( product @ SV4 @ e_1 @ SY42 )
| ( product @ SV4 @ e_2 @ SY42 )
| ( product @ SV4 @ e_3 @ SY42 )
| ( product @ SV4 @ e_4 @ SY42 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(115,plain,
! [SV5: $i] :
( ( ( ~ ( group_element @ SV5 ) )
= $true )
| ( ( ! [SY43: $i] :
( ~ ( group_element @ SY43 )
| ( product @ SV5 @ SY43 @ e_1 )
| ( product @ SV5 @ SY43 @ e_2 )
| ( product @ SV5 @ SY43 @ e_3 )
| ( product @ SV5 @ SY43 @ e_4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(116,plain,
! [SV12: $i,SV6: $i] :
( ( ! [SY61: $i] :
( ~ ( product @ SV6 @ SV12 @ SY61 )
| ! [SY62: $i] :
( ~ ( product @ SV6 @ SV12 @ SY62 )
| ( equalish @ SY61 @ SY62 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(117,plain,
! [SV13: $i,SV7: $i] :
( ( ! [SY63: $i] :
( ~ ( product @ SV7 @ SV13 @ SY63 )
| ! [SY64: $i] :
( ~ ( product @ SV7 @ SY64 @ SY63 )
| ( equalish @ SV13 @ SY64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(118,plain,
! [SV14: $i,SV8: $i] :
( ( ! [SY65: $i] :
( ~ ( product @ SV8 @ SV14 @ SY65 )
| ! [SY66: $i] :
( ~ ( product @ SY66 @ SV14 @ SY65 )
| ( equalish @ SV8 @ SY66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(119,plain,
! [SV15: $i,SV10: $i,SV1: $i] :
( ( ! [SY67: $i] :
( ~ ( product @ SV1 @ SV10 @ SV15 )
| ! [SY68: $i] :
( ~ ( product @ SY67 @ SY68 @ SV15 )
| ! [SY56: $i] :
( ~ ( product @ SY56 @ SV1 @ SV10 )
| ~ ( product @ SY56 @ SY67 @ SY68 )
| ( equalish @ SV1 @ SY67 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(120,plain,
! [SV16: $i,SV11: $i,SV2: $i] :
( ( ! [SY70: $i] :
( ~ ( product @ SV2 @ SV11 @ SV16 )
| ! [SY71: $i] :
( ~ ( product @ SY70 @ SY71 @ SV16 )
| ! [SY60: $i] :
( ~ ( product @ SY60 @ SV2 @ SV11 )
| ~ ( product @ SY60 @ SY70 @ SY71 )
| ( equalish @ SV11 @ SY71 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(121,plain,
! [SV3: $i] :
( ( ( group_element @ SV3 )
= $false )
| ( ( ! [SY41: $i] :
( ~ ( group_element @ SY41 )
| ( product @ e_1 @ SV3 @ SY41 )
| ( product @ e_2 @ SV3 @ SY41 )
| ( product @ e_3 @ SV3 @ SY41 )
| ( product @ e_4 @ SV3 @ SY41 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(122,plain,
! [SV4: $i] :
( ( ( group_element @ SV4 )
= $false )
| ( ( ! [SY42: $i] :
( ~ ( group_element @ SY42 )
| ( product @ SV4 @ e_1 @ SY42 )
| ( product @ SV4 @ e_2 @ SY42 )
| ( product @ SV4 @ e_3 @ SY42 )
| ( product @ SV4 @ e_4 @ SY42 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(123,plain,
! [SV5: $i] :
( ( ( group_element @ SV5 )
= $false )
| ( ( ! [SY43: $i] :
( ~ ( group_element @ SY43 )
| ( product @ SV5 @ SY43 @ e_1 )
| ( product @ SV5 @ SY43 @ e_2 )
| ( product @ SV5 @ SY43 @ e_3 )
| ( product @ SV5 @ SY43 @ e_4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(124,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ~ ( product @ SV6 @ SV12 @ SV17 )
| ! [SY73: $i] :
( ~ ( product @ SV6 @ SV12 @ SY73 )
| ( equalish @ SV17 @ SY73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(125,plain,
! [SV18: $i,SV13: $i,SV7: $i] :
( ( ~ ( product @ SV7 @ SV13 @ SV18 )
| ! [SY74: $i] :
( ~ ( product @ SV7 @ SY74 @ SV18 )
| ( equalish @ SV13 @ SY74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(126,plain,
! [SV19: $i,SV14: $i,SV8: $i] :
( ( ~ ( product @ SV8 @ SV14 @ SV19 )
| ! [SY75: $i] :
( ~ ( product @ SY75 @ SV14 @ SV19 )
| ( equalish @ SV8 @ SY75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(127,plain,
! [SV20: $i,SV15: $i,SV10: $i,SV1: $i] :
( ( ~ ( product @ SV1 @ SV10 @ SV15 )
| ! [SY76: $i] :
( ~ ( product @ SV20 @ SY76 @ SV15 )
| ! [SY77: $i] :
( ~ ( product @ SY77 @ SV1 @ SV10 )
| ~ ( product @ SY77 @ SV20 @ SY76 )
| ( equalish @ SV1 @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(128,plain,
! [SV21: $i,SV16: $i,SV11: $i,SV2: $i] :
( ( ~ ( product @ SV2 @ SV11 @ SV16 )
| ! [SY78: $i] :
( ~ ( product @ SV21 @ SY78 @ SV16 )
| ! [SY79: $i] :
( ~ ( product @ SY79 @ SV2 @ SV11 )
| ~ ( product @ SY79 @ SV21 @ SY78 )
| ( equalish @ SV11 @ SY78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(129,plain,
! [SV3: $i,SV22: $i] :
( ( ( ~ ( group_element @ SV22 )
| ( product @ e_1 @ SV3 @ SV22 )
| ( product @ e_2 @ SV3 @ SV22 )
| ( product @ e_3 @ SV3 @ SV22 )
| ( product @ e_4 @ SV3 @ SV22 ) )
= $true )
| ( ( group_element @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(130,plain,
! [SV4: $i,SV23: $i] :
( ( ( ~ ( group_element @ SV23 )
| ( product @ SV4 @ e_1 @ SV23 )
| ( product @ SV4 @ e_2 @ SV23 )
| ( product @ SV4 @ e_3 @ SV23 )
| ( product @ SV4 @ e_4 @ SV23 ) )
= $true )
| ( ( group_element @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(131,plain,
! [SV5: $i,SV24: $i] :
( ( ( ~ ( group_element @ SV24 )
| ( product @ SV5 @ SV24 @ e_1 )
| ( product @ SV5 @ SV24 @ e_2 )
| ( product @ SV5 @ SV24 @ e_3 )
| ( product @ SV5 @ SV24 @ e_4 ) )
= $true )
| ( ( group_element @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(132,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ( ~ ( product @ SV6 @ SV12 @ SV17 ) )
= $true )
| ( ( ! [SY73: $i] :
( ~ ( product @ SV6 @ SV12 @ SY73 )
| ( equalish @ SV17 @ SY73 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(133,plain,
! [SV18: $i,SV13: $i,SV7: $i] :
( ( ( ~ ( product @ SV7 @ SV13 @ SV18 ) )
= $true )
| ( ( ! [SY74: $i] :
( ~ ( product @ SV7 @ SY74 @ SV18 )
| ( equalish @ SV13 @ SY74 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(134,plain,
! [SV19: $i,SV14: $i,SV8: $i] :
( ( ( ~ ( product @ SV8 @ SV14 @ SV19 ) )
= $true )
| ( ( ! [SY75: $i] :
( ~ ( product @ SY75 @ SV14 @ SV19 )
| ( equalish @ SV8 @ SY75 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(135,plain,
! [SV20: $i,SV15: $i,SV10: $i,SV1: $i] :
( ( ( ~ ( product @ SV1 @ SV10 @ SV15 ) )
= $true )
| ( ( ! [SY76: $i] :
( ~ ( product @ SV20 @ SY76 @ SV15 )
| ! [SY77: $i] :
( ~ ( product @ SY77 @ SV1 @ SV10 )
| ~ ( product @ SY77 @ SV20 @ SY76 )
| ( equalish @ SV1 @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(136,plain,
! [SV21: $i,SV16: $i,SV11: $i,SV2: $i] :
( ( ( ~ ( product @ SV2 @ SV11 @ SV16 ) )
= $true )
| ( ( ! [SY78: $i] :
( ~ ( product @ SV21 @ SY78 @ SV16 )
| ! [SY79: $i] :
( ~ ( product @ SY79 @ SV2 @ SV11 )
| ~ ( product @ SY79 @ SV21 @ SY78 )
| ( equalish @ SV11 @ SY78 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(137,plain,
! [SV3: $i,SV22: $i] :
( ( ( ~ ( group_element @ SV22 ) )
= $true )
| ( ( ( product @ e_1 @ SV3 @ SV22 )
| ( product @ e_2 @ SV3 @ SV22 )
| ( product @ e_3 @ SV3 @ SV22 )
| ( product @ e_4 @ SV3 @ SV22 ) )
= $true )
| ( ( group_element @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(138,plain,
! [SV4: $i,SV23: $i] :
( ( ( ~ ( group_element @ SV23 ) )
= $true )
| ( ( ( product @ SV4 @ e_1 @ SV23 )
| ( product @ SV4 @ e_2 @ SV23 )
| ( product @ SV4 @ e_3 @ SV23 )
| ( product @ SV4 @ e_4 @ SV23 ) )
= $true )
| ( ( group_element @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(139,plain,
! [SV5: $i,SV24: $i] :
( ( ( ~ ( group_element @ SV24 ) )
= $true )
| ( ( ( product @ SV5 @ SV24 @ e_1 )
| ( product @ SV5 @ SV24 @ e_2 )
| ( product @ SV5 @ SV24 @ e_3 )
| ( product @ SV5 @ SV24 @ e_4 ) )
= $true )
| ( ( group_element @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(140,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ( product @ SV6 @ SV12 @ SV17 )
= $false )
| ( ( ! [SY73: $i] :
( ~ ( product @ SV6 @ SV12 @ SY73 )
| ( equalish @ SV17 @ SY73 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(141,plain,
! [SV18: $i,SV13: $i,SV7: $i] :
( ( ( product @ SV7 @ SV13 @ SV18 )
= $false )
| ( ( ! [SY74: $i] :
( ~ ( product @ SV7 @ SY74 @ SV18 )
| ( equalish @ SV13 @ SY74 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(142,plain,
! [SV19: $i,SV14: $i,SV8: $i] :
( ( ( product @ SV8 @ SV14 @ SV19 )
= $false )
| ( ( ! [SY75: $i] :
( ~ ( product @ SY75 @ SV14 @ SV19 )
| ( equalish @ SV8 @ SY75 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(143,plain,
! [SV20: $i,SV15: $i,SV10: $i,SV1: $i] :
( ( ( product @ SV1 @ SV10 @ SV15 )
= $false )
| ( ( ! [SY76: $i] :
( ~ ( product @ SV20 @ SY76 @ SV15 )
| ! [SY77: $i] :
( ~ ( product @ SY77 @ SV1 @ SV10 )
| ~ ( product @ SY77 @ SV20 @ SY76 )
| ( equalish @ SV1 @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(144,plain,
! [SV21: $i,SV16: $i,SV11: $i,SV2: $i] :
( ( ( product @ SV2 @ SV11 @ SV16 )
= $false )
| ( ( ! [SY78: $i] :
( ~ ( product @ SV21 @ SY78 @ SV16 )
| ! [SY79: $i] :
( ~ ( product @ SY79 @ SV2 @ SV11 )
| ~ ( product @ SY79 @ SV21 @ SY78 )
| ( equalish @ SV11 @ SY78 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(145,plain,
! [SV3: $i,SV22: $i] :
( ( ( group_element @ SV22 )
= $false )
| ( ( ( product @ e_1 @ SV3 @ SV22 )
| ( product @ e_2 @ SV3 @ SV22 )
| ( product @ e_3 @ SV3 @ SV22 )
| ( product @ e_4 @ SV3 @ SV22 ) )
= $true )
| ( ( group_element @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(146,plain,
! [SV4: $i,SV23: $i] :
( ( ( group_element @ SV23 )
= $false )
| ( ( ( product @ SV4 @ e_1 @ SV23 )
| ( product @ SV4 @ e_2 @ SV23 )
| ( product @ SV4 @ e_3 @ SV23 )
| ( product @ SV4 @ e_4 @ SV23 ) )
= $true )
| ( ( group_element @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(147,plain,
! [SV5: $i,SV24: $i] :
( ( ( group_element @ SV24 )
= $false )
| ( ( ( product @ SV5 @ SV24 @ e_1 )
| ( product @ SV5 @ SV24 @ e_2 )
| ( product @ SV5 @ SV24 @ e_3 )
| ( product @ SV5 @ SV24 @ e_4 ) )
= $true )
| ( ( group_element @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(148,plain,
! [SV17: $i,SV25: $i,SV12: $i,SV6: $i] :
( ( ( ~ ( product @ SV6 @ SV12 @ SV25 )
| ( equalish @ SV17 @ SV25 ) )
= $true )
| ( ( product @ SV6 @ SV12 @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(149,plain,
! [SV13: $i,SV18: $i,SV26: $i,SV7: $i] :
( ( ( ~ ( product @ SV7 @ SV26 @ SV18 )
| ( equalish @ SV13 @ SV26 ) )
= $true )
| ( ( product @ SV7 @ SV13 @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(150,plain,
! [SV8: $i,SV19: $i,SV14: $i,SV27: $i] :
( ( ( ~ ( product @ SV27 @ SV14 @ SV19 )
| ( equalish @ SV8 @ SV27 ) )
= $true )
| ( ( product @ SV8 @ SV14 @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(151,plain,
! [SV10: $i,SV1: $i,SV15: $i,SV28: $i,SV20: $i] :
( ( ( ~ ( product @ SV20 @ SV28 @ SV15 )
| ! [SY80: $i] :
( ~ ( product @ SY80 @ SV1 @ SV10 )
| ~ ( product @ SY80 @ SV20 @ SV28 )
| ( equalish @ SV1 @ SV20 ) ) )
= $true )
| ( ( product @ SV1 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(152,plain,
! [SV11: $i,SV2: $i,SV16: $i,SV29: $i,SV21: $i] :
( ( ( ~ ( product @ SV21 @ SV29 @ SV16 )
| ! [SY81: $i] :
( ~ ( product @ SY81 @ SV2 @ SV11 )
| ~ ( product @ SY81 @ SV21 @ SV29 )
| ( equalish @ SV11 @ SV29 ) ) )
= $true )
| ( ( product @ SV2 @ SV11 @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(153,plain,
! [SV22: $i,SV3: $i] :
( ( ( product @ e_1 @ SV3 @ SV22 )
= $true )
| ( ( ( product @ e_2 @ SV3 @ SV22 )
| ( product @ e_3 @ SV3 @ SV22 )
| ( product @ e_4 @ SV3 @ SV22 ) )
= $true )
| ( ( group_element @ SV22 )
= $false )
| ( ( group_element @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(154,plain,
! [SV23: $i,SV4: $i] :
( ( ( product @ SV4 @ e_1 @ SV23 )
= $true )
| ( ( ( product @ SV4 @ e_2 @ SV23 )
| ( product @ SV4 @ e_3 @ SV23 )
| ( product @ SV4 @ e_4 @ SV23 ) )
= $true )
| ( ( group_element @ SV23 )
= $false )
| ( ( group_element @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(155,plain,
! [SV24: $i,SV5: $i] :
( ( ( product @ SV5 @ SV24 @ e_1 )
= $true )
| ( ( ( product @ SV5 @ SV24 @ e_2 )
| ( product @ SV5 @ SV24 @ e_3 )
| ( product @ SV5 @ SV24 @ e_4 ) )
= $true )
| ( ( group_element @ SV24 )
= $false )
| ( ( group_element @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(156,plain,
! [SV17: $i,SV25: $i,SV12: $i,SV6: $i] :
( ( ( ~ ( product @ SV6 @ SV12 @ SV25 ) )
= $true )
| ( ( equalish @ SV17 @ SV25 )
= $true )
| ( ( product @ SV6 @ SV12 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(157,plain,
! [SV13: $i,SV18: $i,SV26: $i,SV7: $i] :
( ( ( ~ ( product @ SV7 @ SV26 @ SV18 ) )
= $true )
| ( ( equalish @ SV13 @ SV26 )
= $true )
| ( ( product @ SV7 @ SV13 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(158,plain,
! [SV8: $i,SV19: $i,SV14: $i,SV27: $i] :
( ( ( ~ ( product @ SV27 @ SV14 @ SV19 ) )
= $true )
| ( ( equalish @ SV8 @ SV27 )
= $true )
| ( ( product @ SV8 @ SV14 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(159,plain,
! [SV10: $i,SV1: $i,SV15: $i,SV28: $i,SV20: $i] :
( ( ( ~ ( product @ SV20 @ SV28 @ SV15 ) )
= $true )
| ( ( ! [SY80: $i] :
( ~ ( product @ SY80 @ SV1 @ SV10 )
| ~ ( product @ SY80 @ SV20 @ SV28 )
| ( equalish @ SV1 @ SV20 ) ) )
= $true )
| ( ( product @ SV1 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(160,plain,
! [SV11: $i,SV2: $i,SV16: $i,SV29: $i,SV21: $i] :
( ( ( ~ ( product @ SV21 @ SV29 @ SV16 ) )
= $true )
| ( ( ! [SY81: $i] :
( ~ ( product @ SY81 @ SV2 @ SV11 )
| ~ ( product @ SY81 @ SV21 @ SV29 )
| ( equalish @ SV11 @ SV29 ) ) )
= $true )
| ( ( product @ SV2 @ SV11 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(161,plain,
! [SV22: $i,SV3: $i] :
( ( ( product @ e_2 @ SV3 @ SV22 )
= $true )
| ( ( ( product @ e_3 @ SV3 @ SV22 )
| ( product @ e_4 @ SV3 @ SV22 ) )
= $true )
| ( ( product @ e_1 @ SV3 @ SV22 )
= $true )
| ( ( group_element @ SV22 )
= $false )
| ( ( group_element @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(162,plain,
! [SV23: $i,SV4: $i] :
( ( ( product @ SV4 @ e_2 @ SV23 )
= $true )
| ( ( ( product @ SV4 @ e_3 @ SV23 )
| ( product @ SV4 @ e_4 @ SV23 ) )
= $true )
| ( ( product @ SV4 @ e_1 @ SV23 )
= $true )
| ( ( group_element @ SV23 )
= $false )
| ( ( group_element @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(163,plain,
! [SV24: $i,SV5: $i] :
( ( ( product @ SV5 @ SV24 @ e_2 )
= $true )
| ( ( ( product @ SV5 @ SV24 @ e_3 )
| ( product @ SV5 @ SV24 @ e_4 ) )
= $true )
| ( ( product @ SV5 @ SV24 @ e_1 )
= $true )
| ( ( group_element @ SV24 )
= $false )
| ( ( group_element @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(164,plain,
! [SV17: $i,SV25: $i,SV12: $i,SV6: $i] :
( ( ( product @ SV6 @ SV12 @ SV25 )
= $false )
| ( ( equalish @ SV17 @ SV25 )
= $true )
| ( ( product @ SV6 @ SV12 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(165,plain,
! [SV13: $i,SV18: $i,SV26: $i,SV7: $i] :
( ( ( product @ SV7 @ SV26 @ SV18 )
= $false )
| ( ( equalish @ SV13 @ SV26 )
= $true )
| ( ( product @ SV7 @ SV13 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(166,plain,
! [SV8: $i,SV19: $i,SV14: $i,SV27: $i] :
( ( ( product @ SV27 @ SV14 @ SV19 )
= $false )
| ( ( equalish @ SV8 @ SV27 )
= $true )
| ( ( product @ SV8 @ SV14 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(167,plain,
! [SV10: $i,SV1: $i,SV15: $i,SV28: $i,SV20: $i] :
( ( ( product @ SV20 @ SV28 @ SV15 )
= $false )
| ( ( ! [SY80: $i] :
( ~ ( product @ SY80 @ SV1 @ SV10 )
| ~ ( product @ SY80 @ SV20 @ SV28 )
| ( equalish @ SV1 @ SV20 ) ) )
= $true )
| ( ( product @ SV1 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(168,plain,
! [SV11: $i,SV2: $i,SV16: $i,SV29: $i,SV21: $i] :
( ( ( product @ SV21 @ SV29 @ SV16 )
= $false )
| ( ( ! [SY81: $i] :
( ~ ( product @ SY81 @ SV2 @ SV11 )
| ~ ( product @ SY81 @ SV21 @ SV29 )
| ( equalish @ SV11 @ SV29 ) ) )
= $true )
| ( ( product @ SV2 @ SV11 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(169,plain,
! [SV22: $i,SV3: $i] :
( ( ( product @ e_3 @ SV3 @ SV22 )
= $true )
| ( ( product @ e_4 @ SV3 @ SV22 )
= $true )
| ( ( product @ e_2 @ SV3 @ SV22 )
= $true )
| ( ( product @ e_1 @ SV3 @ SV22 )
= $true )
| ( ( group_element @ SV22 )
= $false )
| ( ( group_element @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(170,plain,
! [SV23: $i,SV4: $i] :
( ( ( product @ SV4 @ e_3 @ SV23 )
= $true )
| ( ( product @ SV4 @ e_4 @ SV23 )
= $true )
| ( ( product @ SV4 @ e_2 @ SV23 )
= $true )
| ( ( product @ SV4 @ e_1 @ SV23 )
= $true )
| ( ( group_element @ SV23 )
= $false )
| ( ( group_element @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(171,plain,
! [SV24: $i,SV5: $i] :
( ( ( product @ SV5 @ SV24 @ e_3 )
= $true )
| ( ( product @ SV5 @ SV24 @ e_4 )
= $true )
| ( ( product @ SV5 @ SV24 @ e_2 )
= $true )
| ( ( product @ SV5 @ SV24 @ e_1 )
= $true )
| ( ( group_element @ SV24 )
= $false )
| ( ( group_element @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(172,plain,
! [SV15: $i,SV28: $i,SV20: $i,SV10: $i,SV1: $i,SV30: $i] :
( ( ( ~ ( product @ SV30 @ SV1 @ SV10 )
| ~ ( product @ SV30 @ SV20 @ SV28 )
| ( equalish @ SV1 @ SV20 ) )
= $true )
| ( ( product @ SV20 @ SV28 @ SV15 )
= $false )
| ( ( product @ SV1 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(173,plain,
! [SV16: $i,SV29: $i,SV21: $i,SV11: $i,SV2: $i,SV31: $i] :
( ( ( ~ ( product @ SV31 @ SV2 @ SV11 )
| ~ ( product @ SV31 @ SV21 @ SV29 )
| ( equalish @ SV11 @ SV29 ) )
= $true )
| ( ( product @ SV21 @ SV29 @ SV16 )
= $false )
| ( ( product @ SV2 @ SV11 @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(174,plain,
! [SV15: $i,SV28: $i,SV20: $i,SV10: $i,SV1: $i,SV30: $i] :
( ( ( ~ ( product @ SV30 @ SV1 @ SV10 ) )
= $true )
| ( ( ~ ( product @ SV30 @ SV20 @ SV28 )
| ( equalish @ SV1 @ SV20 ) )
= $true )
| ( ( product @ SV20 @ SV28 @ SV15 )
= $false )
| ( ( product @ SV1 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(175,plain,
! [SV16: $i,SV29: $i,SV21: $i,SV11: $i,SV2: $i,SV31: $i] :
( ( ( ~ ( product @ SV31 @ SV2 @ SV11 ) )
= $true )
| ( ( ~ ( product @ SV31 @ SV21 @ SV29 )
| ( equalish @ SV11 @ SV29 ) )
= $true )
| ( ( product @ SV21 @ SV29 @ SV16 )
= $false )
| ( ( product @ SV2 @ SV11 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(176,plain,
! [SV15: $i,SV28: $i,SV20: $i,SV10: $i,SV1: $i,SV30: $i] :
( ( ( product @ SV30 @ SV1 @ SV10 )
= $false )
| ( ( ~ ( product @ SV30 @ SV20 @ SV28 )
| ( equalish @ SV1 @ SV20 ) )
= $true )
| ( ( product @ SV20 @ SV28 @ SV15 )
= $false )
| ( ( product @ SV1 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(177,plain,
! [SV16: $i,SV29: $i,SV21: $i,SV11: $i,SV2: $i,SV31: $i] :
( ( ( product @ SV31 @ SV2 @ SV11 )
= $false )
| ( ( ~ ( product @ SV31 @ SV21 @ SV29 )
| ( equalish @ SV11 @ SV29 ) )
= $true )
| ( ( product @ SV21 @ SV29 @ SV16 )
= $false )
| ( ( product @ SV2 @ SV11 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(178,plain,
! [SV15: $i,SV10: $i,SV1: $i,SV28: $i,SV20: $i,SV30: $i] :
( ( ( ~ ( product @ SV30 @ SV20 @ SV28 ) )
= $true )
| ( ( equalish @ SV1 @ SV20 )
= $true )
| ( ( product @ SV30 @ SV1 @ SV10 )
= $false )
| ( ( product @ SV20 @ SV28 @ SV15 )
= $false )
| ( ( product @ SV1 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(179,plain,
! [SV16: $i,SV2: $i,SV11: $i,SV29: $i,SV21: $i,SV31: $i] :
( ( ( ~ ( product @ SV31 @ SV21 @ SV29 ) )
= $true )
| ( ( equalish @ SV11 @ SV29 )
= $true )
| ( ( product @ SV31 @ SV2 @ SV11 )
= $false )
| ( ( product @ SV21 @ SV29 @ SV16 )
= $false )
| ( ( product @ SV2 @ SV11 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(180,plain,
! [SV15: $i,SV10: $i,SV1: $i,SV28: $i,SV20: $i,SV30: $i] :
( ( ( product @ SV30 @ SV20 @ SV28 )
= $false )
| ( ( equalish @ SV1 @ SV20 )
= $true )
| ( ( product @ SV30 @ SV1 @ SV10 )
= $false )
| ( ( product @ SV20 @ SV28 @ SV15 )
= $false )
| ( ( product @ SV1 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(181,plain,
! [SV16: $i,SV2: $i,SV11: $i,SV29: $i,SV21: $i,SV31: $i] :
( ( ( product @ SV31 @ SV21 @ SV29 )
= $false )
| ( ( equalish @ SV11 @ SV29 )
= $true )
| ( ( product @ SV31 @ SV2 @ SV11 )
= $false )
| ( ( product @ SV21 @ SV29 @ SV16 )
= $false )
| ( ( product @ SV2 @ SV11 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(182,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[67,181,180,171,170,169,166,165,164,110,109,104,103,102,101,100,99,98,97,96,95,94,93,70,69,68]) ).
thf(183,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[182]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP124-4.004 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 14 07:32:03 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36
% 0.13/0.36 No.of.Axioms: 25
% 0.13/0.36
% 0.13/0.36 Length.of.Defs: 0
% 0.13/0.36
% 0.13/0.36 Contains.Choice.Funs: false
% 0.13/0.38 (rf:0,axioms:25,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:27,loop_count:0,foatp_calls:0,translation:fof_full).........
% 0.20/0.58
% 0.20/0.58 ********************************
% 0.20/0.58 * All subproblems solved! *
% 0.20/0.58 ********************************
% 0.20/0.58 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:25,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:182,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.41/0.59
% 0.41/0.59 %**** Beginning of derivation protocol ****
% 0.41/0.59 % SZS output start CNFRefutation
% See solution above
% 0.41/0.59
% 0.41/0.59 %**** End of derivation protocol ****
% 0.41/0.59 %**** no. of clauses in derivation: 183 ****
% 0.41/0.59 %**** clause counter: 182 ****
% 0.41/0.59
% 0.41/0.59 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:25,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:182,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------