TSTP Solution File: GRP025-1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GRP025-1 : 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 : n008.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 10:15:28 EDT 2022
% Result : Unsatisfiable 0.36s 0.58s
% Output : CNFRefutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 48
% Syntax : Number of formulae : 195 ( 133 unt; 15 typ; 0 def)
% Number of atoms : 801 ( 254 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 1615 ( 154 ~; 207 |; 0 &;1254 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 11 con; 0-4 aty)
% Number of variables : 441 ( 0 ^ 441 !; 0 ?; 441 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_an_isomorphism,type,
an_isomorphism: $i > $i ).
thf(tp_b,type,
b: $i ).
thf(tp_c,type,
c: $i ).
thf(tp_d,type,
d: $i ).
thf(tp_d1,type,
d1: $i ).
thf(tp_d2,type,
d2: $i ).
thf(tp_d3,type,
d3: $i ).
thf(tp_g1,type,
g1: $i ).
thf(tp_g2,type,
g2: $i ).
thf(tp_group_member,type,
group_member: $i > $i > $o ).
thf(tp_identity_for,type,
identity_for: $i > $i ).
thf(tp_inverse,type,
inverse: $i > $i > $i ).
thf(tp_multiply,type,
multiply: $i > $i > $i > $i ).
thf(tp_product,type,
product: $i > $i > $i > $i > $o ).
thf(1,axiom,
! [Xg: $i,X: $i,Y: $i,Xy: $i,Z: $i,Yz: $i,Xyz: $i] :
( ~ ( product @ Xg @ X @ Y @ Xy )
| ~ ( product @ Xg @ Y @ Z @ Yz )
| ~ ( product @ Xg @ X @ Yz @ Xyz )
| ( product @ Xg @ Xy @ Z @ Xyz ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity2) ).
thf(2,axiom,
! [Xg: $i,X: $i,Y: $i,Xy: $i,Z: $i,Yz: $i,Xyz: $i] :
( ~ ( product @ Xg @ X @ Y @ Xy )
| ~ ( product @ Xg @ Y @ Z @ Yz )
| ~ ( product @ Xg @ Xy @ Z @ Xyz )
| ( product @ Xg @ X @ Yz @ Xyz ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity1) ).
thf(3,axiom,
! [Xg: $i,X: $i,Y: $i,Z: $i,W: $i] :
( ~ ( product @ Xg @ X @ Y @ Z )
| ~ ( product @ Xg @ X @ Y @ W )
| ( W = Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function2) ).
thf(4,axiom,
! [X: $i,Xg: $i,Y: $i] :
( ~ ( group_member @ X @ Xg )
| ~ ( group_member @ Y @ Xg )
| ( group_member @ ( multiply @ Xg @ X @ Y ) @ Xg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function1_2) ).
thf(5,axiom,
! [X: $i,Xg: $i,Y: $i] :
( ~ ( group_member @ X @ Xg )
| ~ ( group_member @ Y @ Xg )
| ( product @ Xg @ X @ Y @ ( multiply @ Xg @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function1_1) ).
thf(6,axiom,
! [Xg: $i,X: $i] : ( product @ Xg @ X @ ( inverse @ Xg @ X ) @ ( identity_for @ Xg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
thf(7,axiom,
! [Xg: $i,X: $i] : ( product @ Xg @ ( inverse @ Xg @ X ) @ X @ ( identity_for @ Xg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
thf(8,axiom,
! [X: $i,Xg: $i] :
( ~ ( group_member @ X @ Xg )
| ( group_member @ ( inverse @ Xg @ X ) @ Xg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_in_group) ).
thf(9,axiom,
! [Xg: $i,X: $i] : ( product @ Xg @ X @ ( identity_for @ Xg ) @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
thf(10,axiom,
! [Xg: $i,X: $i] : ( product @ Xg @ ( identity_for @ Xg ) @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
thf(11,axiom,
! [Xg: $i] : ( group_member @ ( identity_for @ Xg ) @ Xg ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_in_group) ).
thf(12,axiom,
product @ g1 @ d1 @ d2 @ d3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_times_d2_is_d3) ).
thf(13,axiom,
group_member @ d3 @ g1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_member_of_group1) ).
thf(14,axiom,
group_member @ d2 @ g1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_member_of_group1) ).
thf(15,axiom,
group_member @ d1 @ g1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_member_of_group1) ).
thf(16,axiom,
( ( an_isomorphism @ b )
= d ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_maps_to_d) ).
thf(17,axiom,
( ( an_isomorphism @ a )
= c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_maps_to_c) ).
thf(18,axiom,
product @ g2 @ d @ d @ c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_times_d_is_c) ).
thf(19,axiom,
product @ g2 @ d @ c @ d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_times_c_is_d) ).
thf(20,axiom,
product @ g2 @ c @ d @ d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_times_d_is_d) ).
thf(21,axiom,
product @ g2 @ c @ c @ c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_times_c_is_c) ).
thf(22,axiom,
product @ g1 @ b @ b @ a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_b_is_a) ).
thf(23,axiom,
product @ g1 @ b @ a @ b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_a_is_b) ).
thf(24,axiom,
product @ g1 @ a @ b @ b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_b) ).
thf(25,axiom,
product @ g1 @ a @ a @ a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_a_is_a) ).
thf(26,axiom,
! [X: $i] :
( ~ ( group_member @ X @ g2 )
| ( X = c )
| ( X = d ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_and_d_only_members_of_group2) ).
thf(27,axiom,
! [X: $i] :
( ~ ( group_member @ X @ g1 )
| ( X = a )
| ( X = b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_and_b_only_members_of_group1) ).
thf(28,axiom,
group_member @ d @ g2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_member_of_group2) ).
thf(29,axiom,
group_member @ c @ g2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_member_of_group2) ).
thf(30,axiom,
group_member @ b @ g1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_member_of_group1) ).
thf(31,axiom,
group_member @ a @ g1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_member_of_group1) ).
thf(32,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(33,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[32]) ).
thf(34,negated_conjecture,
~ ( product @ g2 @ ( an_isomorphism @ d1 ) @ ( an_isomorphism @ d2 ) @ ( an_isomorphism @ d3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_product_holds_in_group2) ).
thf(35,plain,
$false = $false,
inference(unfold_def,[status(thm)],[33]) ).
thf(36,plain,
( ( ! [Xg: $i,X: $i,Y: $i,Xy: $i,Z: $i,Yz: $i,Xyz: $i] :
( ~ ( product @ Xg @ X @ Y @ Xy )
| ~ ( product @ Xg @ Y @ Z @ Yz )
| ~ ( product @ Xg @ X @ Yz @ Xyz )
| ( product @ Xg @ Xy @ Z @ Xyz ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(37,plain,
( ( ! [Xg: $i,X: $i,Y: $i,Xy: $i,Z: $i,Yz: $i,Xyz: $i] :
( ~ ( product @ Xg @ X @ Y @ Xy )
| ~ ( product @ Xg @ Y @ Z @ Yz )
| ~ ( product @ Xg @ Xy @ Z @ Xyz )
| ( product @ Xg @ X @ Yz @ Xyz ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(38,plain,
( ( ! [Xg: $i,X: $i,Y: $i,Z: $i,W: $i] :
( ~ ( product @ Xg @ X @ Y @ Z )
| ~ ( product @ Xg @ X @ Y @ W )
| ( W = Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(39,plain,
( ( ! [X: $i,Xg: $i,Y: $i] :
( ~ ( group_member @ X @ Xg )
| ~ ( group_member @ Y @ Xg )
| ( group_member @ ( multiply @ Xg @ X @ Y ) @ Xg ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(40,plain,
( ( ! [X: $i,Xg: $i,Y: $i] :
( ~ ( group_member @ X @ Xg )
| ~ ( group_member @ Y @ Xg )
| ( product @ Xg @ X @ Y @ ( multiply @ Xg @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(41,plain,
( ( ! [Xg: $i,X: $i] : ( product @ Xg @ X @ ( inverse @ Xg @ X ) @ ( identity_for @ Xg ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(42,plain,
( ( ! [Xg: $i,X: $i] : ( product @ Xg @ ( inverse @ Xg @ X ) @ X @ ( identity_for @ Xg ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(43,plain,
( ( ! [X: $i,Xg: $i] :
( ~ ( group_member @ X @ Xg )
| ( group_member @ ( inverse @ Xg @ X ) @ Xg ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(44,plain,
( ( ! [Xg: $i,X: $i] : ( product @ Xg @ X @ ( identity_for @ Xg ) @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(45,plain,
( ( ! [Xg: $i,X: $i] : ( product @ Xg @ ( identity_for @ Xg ) @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(46,plain,
( ( ! [Xg: $i] : ( group_member @ ( identity_for @ Xg ) @ Xg ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(47,plain,
( ( product @ g1 @ d1 @ d2 @ d3 )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(48,plain,
( ( group_member @ d3 @ g1 )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(49,plain,
( ( group_member @ d2 @ g1 )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(50,plain,
( ( group_member @ d1 @ g1 )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(51,plain,
( ( ( an_isomorphism @ b )
= d )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(52,plain,
( ( ( an_isomorphism @ a )
= c )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(53,plain,
( ( product @ g2 @ d @ d @ c )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(54,plain,
( ( product @ g2 @ d @ c @ d )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(55,plain,
( ( product @ g2 @ c @ d @ d )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(56,plain,
( ( product @ g2 @ c @ c @ c )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(57,plain,
( ( product @ g1 @ b @ b @ a )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(58,plain,
( ( product @ g1 @ b @ a @ b )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(59,plain,
( ( product @ g1 @ a @ b @ b )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(60,plain,
( ( product @ g1 @ a @ a @ a )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(61,plain,
( ( ! [X: $i] :
( ~ ( group_member @ X @ g2 )
| ( X = c )
| ( X = d ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(62,plain,
( ( ! [X: $i] :
( ~ ( group_member @ X @ g1 )
| ( X = a )
| ( X = b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(63,plain,
( ( group_member @ d @ g2 )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(64,plain,
( ( group_member @ c @ g2 )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(65,plain,
( ( group_member @ b @ g1 )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(66,plain,
( ( group_member @ a @ g1 )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(67,plain,
( ( ~ ( product @ g2 @ ( an_isomorphism @ d1 ) @ ( an_isomorphism @ d2 ) @ ( an_isomorphism @ d3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(68,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[35]) ).
thf(69,plain,
( ( ! [Xg: $i,X: $i,Y: $i,Xy: $i,Z: $i] :
( ~ ( product @ Xg @ X @ Y @ Xy )
| ! [Yz: $i] :
( ~ ( product @ Xg @ Y @ Z @ Yz )
| ! [Xyz: $i] :
( ~ ( product @ Xg @ X @ Yz @ Xyz )
| ( product @ Xg @ Xy @ Z @ Xyz ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[36]) ).
thf(70,plain,
( ( ! [Xg: $i,X: $i,Y: $i,Xy: $i,Z: $i] :
( ~ ( product @ Xg @ X @ Y @ Xy )
| ! [Yz: $i] :
( ~ ( product @ Xg @ Y @ Z @ Yz )
| ! [Xyz: $i] :
( ~ ( product @ Xg @ Xy @ Z @ Xyz )
| ( product @ Xg @ X @ Yz @ Xyz ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[37]) ).
thf(71,plain,
( ( ! [Xg: $i,X: $i,Y: $i,Z: $i] :
( ~ ( product @ Xg @ X @ Y @ Z )
| ! [W: $i] :
( ~ ( product @ Xg @ X @ Y @ W )
| ( W = Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[38]) ).
thf(72,plain,
( ( ! [X: $i,Xg: $i] :
( ~ ( group_member @ X @ Xg )
| ! [Y: $i] :
( ~ ( group_member @ Y @ Xg )
| ( group_member @ ( multiply @ Xg @ X @ Y ) @ Xg ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[39]) ).
thf(73,plain,
( ( ! [X: $i,Xg: $i] :
( ~ ( group_member @ X @ Xg )
| ! [Y: $i] :
( ~ ( group_member @ Y @ Xg )
| ( product @ Xg @ X @ Y @ ( multiply @ Xg @ X @ Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[40]) ).
thf(74,plain,
( ( ~ ( product @ g2 @ ( an_isomorphism @ d1 ) @ ( an_isomorphism @ d2 ) @ ( an_isomorphism @ d3 ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(75,plain,
( ( group_member @ a @ g1 )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(76,plain,
( ( group_member @ b @ g1 )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(77,plain,
( ( group_member @ c @ g2 )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(78,plain,
( ( group_member @ d @ g2 )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(79,plain,
( ( ! [X: $i] :
( ~ ( group_member @ X @ g1 )
| ( X = a )
| ( X = b ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(80,plain,
( ( ! [X: $i] :
( ~ ( group_member @ X @ g2 )
| ( X = c )
| ( X = d ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(81,plain,
( ( product @ g1 @ a @ a @ a )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(82,plain,
( ( product @ g1 @ a @ b @ b )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(83,plain,
( ( product @ g1 @ b @ a @ b )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(84,plain,
( ( product @ g1 @ b @ b @ a )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(85,plain,
( ( product @ g2 @ c @ c @ c )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(86,plain,
( ( product @ g2 @ c @ d @ d )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(87,plain,
( ( product @ g2 @ d @ c @ d )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(88,plain,
( ( product @ g2 @ d @ d @ c )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(89,plain,
( ( ( an_isomorphism @ a )
= c )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(90,plain,
( ( ( an_isomorphism @ b )
= d )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(91,plain,
( ( group_member @ d1 @ g1 )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(92,plain,
( ( group_member @ d2 @ g1 )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(93,plain,
( ( group_member @ d3 @ g1 )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(94,plain,
( ( product @ g1 @ d1 @ d2 @ d3 )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(95,plain,
( ( ! [Xg: $i] : ( group_member @ ( identity_for @ Xg ) @ Xg ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(96,plain,
( ( ! [Xg: $i,X: $i] : ( product @ Xg @ ( identity_for @ Xg ) @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(97,plain,
( ( ! [Xg: $i,X: $i] : ( product @ Xg @ X @ ( identity_for @ Xg ) @ X ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(98,plain,
( ( ! [X: $i,Xg: $i] :
( ~ ( group_member @ X @ Xg )
| ( group_member @ ( inverse @ Xg @ X ) @ Xg ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(99,plain,
( ( ! [Xg: $i,X: $i] : ( product @ Xg @ ( inverse @ Xg @ X ) @ X @ ( identity_for @ Xg ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(100,plain,
( ( ! [Xg: $i,X: $i] : ( product @ Xg @ X @ ( inverse @ Xg @ X ) @ ( identity_for @ Xg ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(101,plain,
( ( ! [X: $i,Xg: $i] :
( ~ ( group_member @ X @ Xg )
| ! [Y: $i] :
( ~ ( group_member @ Y @ Xg )
| ( product @ Xg @ X @ Y @ ( multiply @ Xg @ X @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(102,plain,
( ( ! [X: $i,Xg: $i] :
( ~ ( group_member @ X @ Xg )
| ! [Y: $i] :
( ~ ( group_member @ Y @ Xg )
| ( group_member @ ( multiply @ Xg @ X @ Y ) @ Xg ) ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(103,plain,
( ( ! [Xg: $i,X: $i,Y: $i,Z: $i] :
( ~ ( product @ Xg @ X @ Y @ Z )
| ! [W: $i] :
( ~ ( product @ Xg @ X @ Y @ W )
| ( W = Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(104,plain,
( ( ! [Xg: $i,X: $i,Y: $i,Xy: $i,Z: $i] :
( ~ ( product @ Xg @ X @ Y @ Xy )
| ! [Yz: $i] :
( ~ ( product @ Xg @ Y @ Z @ Yz )
| ! [Xyz: $i] :
( ~ ( product @ Xg @ Xy @ Z @ Xyz )
| ( product @ Xg @ X @ Yz @ Xyz ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(105,plain,
( ( ! [Xg: $i,X: $i,Y: $i,Xy: $i,Z: $i] :
( ~ ( product @ Xg @ X @ Y @ Xy )
| ! [Yz: $i] :
( ~ ( product @ Xg @ Y @ Z @ Yz )
| ! [Xyz: $i] :
( ~ ( product @ Xg @ X @ Yz @ Xyz )
| ( product @ Xg @ Xy @ Z @ Xyz ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(106,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(107,plain,
( ( product @ g2 @ ( an_isomorphism @ d1 ) @ ( an_isomorphism @ d2 ) @ ( an_isomorphism @ d3 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(108,plain,
! [SV1: $i] :
( ( ~ ( group_member @ SV1 @ g1 )
| ( SV1 = a )
| ( SV1 = b ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(109,plain,
! [SV2: $i] :
( ( ~ ( group_member @ SV2 @ g2 )
| ( SV2 = c )
| ( SV2 = d ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(110,plain,
! [SV3: $i] :
( ( group_member @ ( identity_for @ SV3 ) @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(111,plain,
! [SV4: $i] :
( ( ! [SY38: $i] : ( product @ SV4 @ ( identity_for @ SV4 ) @ SY38 @ SY38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(112,plain,
! [SV5: $i] :
( ( ! [SY39: $i] : ( product @ SV5 @ SY39 @ ( identity_for @ SV5 ) @ SY39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(113,plain,
! [SV6: $i] :
( ( ! [SY40: $i] :
( ~ ( group_member @ SV6 @ SY40 )
| ( group_member @ ( inverse @ SY40 @ SV6 ) @ SY40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(114,plain,
! [SV7: $i] :
( ( ! [SY41: $i] : ( product @ SV7 @ ( inverse @ SV7 @ SY41 ) @ SY41 @ ( identity_for @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(115,plain,
! [SV8: $i] :
( ( ! [SY42: $i] : ( product @ SV8 @ SY42 @ ( inverse @ SV8 @ SY42 ) @ ( identity_for @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(116,plain,
! [SV9: $i] :
( ( ! [SY43: $i] :
( ~ ( group_member @ SV9 @ SY43 )
| ! [SY44: $i] :
( ~ ( group_member @ SY44 @ SY43 )
| ( product @ SY43 @ SV9 @ SY44 @ ( multiply @ SY43 @ SV9 @ SY44 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(117,plain,
! [SV10: $i] :
( ( ! [SY45: $i] :
( ~ ( group_member @ SV10 @ SY45 )
| ! [SY46: $i] :
( ~ ( group_member @ SY46 @ SY45 )
| ( group_member @ ( multiply @ SY45 @ SV10 @ SY46 ) @ SY45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(118,plain,
! [SV11: $i] :
( ( ! [SY47: $i,SY48: $i,SY49: $i] :
( ~ ( product @ SV11 @ SY47 @ SY48 @ SY49 )
| ! [SY50: $i] :
( ~ ( product @ SV11 @ SY47 @ SY48 @ SY50 )
| ( SY50 = SY49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(119,plain,
! [SV12: $i] :
( ( ! [SY51: $i,SY52: $i,SY53: $i,SY54: $i] :
( ~ ( product @ SV12 @ SY51 @ SY52 @ SY53 )
| ! [SY55: $i] :
( ~ ( product @ SV12 @ SY52 @ SY54 @ SY55 )
| ! [SY56: $i] :
( ~ ( product @ SV12 @ SY53 @ SY54 @ SY56 )
| ( product @ SV12 @ SY51 @ SY55 @ SY56 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(120,plain,
! [SV13: $i] :
( ( ! [SY57: $i,SY58: $i,SY59: $i,SY60: $i] :
( ~ ( product @ SV13 @ SY57 @ SY58 @ SY59 )
| ! [SY61: $i] :
( ~ ( product @ SV13 @ SY58 @ SY60 @ SY61 )
| ! [SY62: $i] :
( ~ ( product @ SV13 @ SY57 @ SY61 @ SY62 )
| ( product @ SV13 @ SY59 @ SY60 @ SY62 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(121,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(122,plain,
! [SV1: $i] :
( ( ( ~ ( group_member @ SV1 @ g1 ) )
= $true )
| ( ( ( SV1 = a )
| ( SV1 = b ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(123,plain,
! [SV2: $i] :
( ( ( ~ ( group_member @ SV2 @ g2 ) )
= $true )
| ( ( ( SV2 = c )
| ( SV2 = d ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(124,plain,
! [SV14: $i,SV4: $i] :
( ( product @ SV4 @ ( identity_for @ SV4 ) @ SV14 @ SV14 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(125,plain,
! [SV15: $i,SV5: $i] :
( ( product @ SV5 @ SV15 @ ( identity_for @ SV5 ) @ SV15 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(126,plain,
! [SV16: $i,SV6: $i] :
( ( ~ ( group_member @ SV6 @ SV16 )
| ( group_member @ ( inverse @ SV16 @ SV6 ) @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(127,plain,
! [SV17: $i,SV7: $i] :
( ( product @ SV7 @ ( inverse @ SV7 @ SV17 ) @ SV17 @ ( identity_for @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(128,plain,
! [SV18: $i,SV8: $i] :
( ( product @ SV8 @ SV18 @ ( inverse @ SV8 @ SV18 ) @ ( identity_for @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(129,plain,
! [SV19: $i,SV9: $i] :
( ( ~ ( group_member @ SV9 @ SV19 )
| ! [SY63: $i] :
( ~ ( group_member @ SY63 @ SV19 )
| ( product @ SV19 @ SV9 @ SY63 @ ( multiply @ SV19 @ SV9 @ SY63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(130,plain,
! [SV20: $i,SV10: $i] :
( ( ~ ( group_member @ SV10 @ SV20 )
| ! [SY64: $i] :
( ~ ( group_member @ SY64 @ SV20 )
| ( group_member @ ( multiply @ SV20 @ SV10 @ SY64 ) @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(131,plain,
! [SV21: $i,SV11: $i] :
( ( ! [SY65: $i,SY66: $i] :
( ~ ( product @ SV11 @ SV21 @ SY65 @ SY66 )
| ! [SY67: $i] :
( ~ ( product @ SV11 @ SV21 @ SY65 @ SY67 )
| ( SY67 = SY66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(132,plain,
! [SV22: $i,SV12: $i] :
( ( ! [SY68: $i,SY69: $i,SY70: $i] :
( ~ ( product @ SV12 @ SV22 @ SY68 @ SY69 )
| ! [SY71: $i] :
( ~ ( product @ SV12 @ SY68 @ SY70 @ SY71 )
| ! [SY72: $i] :
( ~ ( product @ SV12 @ SY69 @ SY70 @ SY72 )
| ( product @ SV12 @ SV22 @ SY71 @ SY72 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(133,plain,
! [SV23: $i,SV13: $i] :
( ( ! [SY73: $i,SY74: $i,SY75: $i] :
( ~ ( product @ SV13 @ SV23 @ SY73 @ SY74 )
| ! [SY76: $i] :
( ~ ( product @ SV13 @ SY73 @ SY75 @ SY76 )
| ! [SY77: $i] :
( ~ ( product @ SV13 @ SV23 @ SY76 @ SY77 )
| ( product @ SV13 @ SY74 @ SY75 @ SY77 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(134,plain,
! [SV1: $i] :
( ( ( group_member @ SV1 @ g1 )
= $false )
| ( ( ( SV1 = a )
| ( SV1 = b ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(135,plain,
! [SV2: $i] :
( ( ( group_member @ SV2 @ g2 )
= $false )
| ( ( ( SV2 = c )
| ( SV2 = d ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(136,plain,
! [SV16: $i,SV6: $i] :
( ( ( ~ ( group_member @ SV6 @ SV16 ) )
= $true )
| ( ( group_member @ ( inverse @ SV16 @ SV6 ) @ SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(137,plain,
! [SV19: $i,SV9: $i] :
( ( ( ~ ( group_member @ SV9 @ SV19 ) )
= $true )
| ( ( ! [SY63: $i] :
( ~ ( group_member @ SY63 @ SV19 )
| ( product @ SV19 @ SV9 @ SY63 @ ( multiply @ SV19 @ SV9 @ SY63 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(138,plain,
! [SV20: $i,SV10: $i] :
( ( ( ~ ( group_member @ SV10 @ SV20 ) )
= $true )
| ( ( ! [SY64: $i] :
( ~ ( group_member @ SY64 @ SV20 )
| ( group_member @ ( multiply @ SV20 @ SV10 @ SY64 ) @ SV20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(139,plain,
! [SV24: $i,SV21: $i,SV11: $i] :
( ( ! [SY78: $i] :
( ~ ( product @ SV11 @ SV21 @ SV24 @ SY78 )
| ! [SY79: $i] :
( ~ ( product @ SV11 @ SV21 @ SV24 @ SY79 )
| ( SY79 = SY78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(140,plain,
! [SV25: $i,SV22: $i,SV12: $i] :
( ( ! [SY80: $i,SY81: $i] :
( ~ ( product @ SV12 @ SV22 @ SV25 @ SY80 )
| ! [SY82: $i] :
( ~ ( product @ SV12 @ SV25 @ SY81 @ SY82 )
| ! [SY72: $i] :
( ~ ( product @ SV12 @ SY80 @ SY81 @ SY72 )
| ( product @ SV12 @ SV22 @ SY82 @ SY72 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(141,plain,
! [SV26: $i,SV23: $i,SV13: $i] :
( ( ! [SY84: $i,SY85: $i] :
( ~ ( product @ SV13 @ SV23 @ SV26 @ SY84 )
| ! [SY86: $i] :
( ~ ( product @ SV13 @ SV26 @ SY85 @ SY86 )
| ! [SY77: $i] :
( ~ ( product @ SV13 @ SV23 @ SY86 @ SY77 )
| ( product @ SV13 @ SY84 @ SY85 @ SY77 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(142,plain,
! [SV1: $i] :
( ( ( SV1 = a )
= $true )
| ( ( SV1 = b )
= $true )
| ( ( group_member @ SV1 @ g1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(143,plain,
! [SV2: $i] :
( ( ( SV2 = c )
= $true )
| ( ( SV2 = d )
= $true )
| ( ( group_member @ SV2 @ g2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(144,plain,
! [SV16: $i,SV6: $i] :
( ( ( group_member @ SV6 @ SV16 )
= $false )
| ( ( group_member @ ( inverse @ SV16 @ SV6 ) @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(145,plain,
! [SV19: $i,SV9: $i] :
( ( ( group_member @ SV9 @ SV19 )
= $false )
| ( ( ! [SY63: $i] :
( ~ ( group_member @ SY63 @ SV19 )
| ( product @ SV19 @ SV9 @ SY63 @ ( multiply @ SV19 @ SV9 @ SY63 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(146,plain,
! [SV20: $i,SV10: $i] :
( ( ( group_member @ SV10 @ SV20 )
= $false )
| ( ( ! [SY64: $i] :
( ~ ( group_member @ SY64 @ SV20 )
| ( group_member @ ( multiply @ SV20 @ SV10 @ SY64 ) @ SV20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(147,plain,
! [SV27: $i,SV24: $i,SV21: $i,SV11: $i] :
( ( ~ ( product @ SV11 @ SV21 @ SV24 @ SV27 )
| ! [SY88: $i] :
( ~ ( product @ SV11 @ SV21 @ SV24 @ SY88 )
| ( SY88 = SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(148,plain,
! [SV28: $i,SV25: $i,SV22: $i,SV12: $i] :
( ( ! [SY89: $i] :
( ~ ( product @ SV12 @ SV22 @ SV25 @ SV28 )
| ! [SY90: $i] :
( ~ ( product @ SV12 @ SV25 @ SY89 @ SY90 )
| ! [SY91: $i] :
( ~ ( product @ SV12 @ SV28 @ SY89 @ SY91 )
| ( product @ SV12 @ SV22 @ SY90 @ SY91 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(149,plain,
! [SV29: $i,SV26: $i,SV23: $i,SV13: $i] :
( ( ! [SY92: $i] :
( ~ ( product @ SV13 @ SV23 @ SV26 @ SV29 )
| ! [SY93: $i] :
( ~ ( product @ SV13 @ SV26 @ SY92 @ SY93 )
| ! [SY94: $i] :
( ~ ( product @ SV13 @ SV23 @ SY93 @ SY94 )
| ( product @ SV13 @ SV29 @ SY92 @ SY94 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(150,plain,
! [SV9: $i,SV19: $i,SV30: $i] :
( ( ( ~ ( group_member @ SV30 @ SV19 )
| ( product @ SV19 @ SV9 @ SV30 @ ( multiply @ SV19 @ SV9 @ SV30 ) ) )
= $true )
| ( ( group_member @ SV9 @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(151,plain,
! [SV10: $i,SV20: $i,SV31: $i] :
( ( ( ~ ( group_member @ SV31 @ SV20 )
| ( group_member @ ( multiply @ SV20 @ SV10 @ SV31 ) @ SV20 ) )
= $true )
| ( ( group_member @ SV10 @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(152,plain,
! [SV27: $i,SV24: $i,SV21: $i,SV11: $i] :
( ( ( ~ ( product @ SV11 @ SV21 @ SV24 @ SV27 ) )
= $true )
| ( ( ! [SY88: $i] :
( ~ ( product @ SV11 @ SV21 @ SV24 @ SY88 )
| ( SY88 = SV27 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(153,plain,
! [SV32: $i,SV28: $i,SV25: $i,SV22: $i,SV12: $i] :
( ( ~ ( product @ SV12 @ SV22 @ SV25 @ SV28 )
| ! [SY95: $i] :
( ~ ( product @ SV12 @ SV25 @ SV32 @ SY95 )
| ! [SY96: $i] :
( ~ ( product @ SV12 @ SV28 @ SV32 @ SY96 )
| ( product @ SV12 @ SV22 @ SY95 @ SY96 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(154,plain,
! [SV33: $i,SV29: $i,SV26: $i,SV23: $i,SV13: $i] :
( ( ~ ( product @ SV13 @ SV23 @ SV26 @ SV29 )
| ! [SY97: $i] :
( ~ ( product @ SV13 @ SV26 @ SV33 @ SY97 )
| ! [SY98: $i] :
( ~ ( product @ SV13 @ SV23 @ SY97 @ SY98 )
| ( product @ SV13 @ SV29 @ SV33 @ SY98 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(155,plain,
! [SV9: $i,SV19: $i,SV30: $i] :
( ( ( ~ ( group_member @ SV30 @ SV19 ) )
= $true )
| ( ( product @ SV19 @ SV9 @ SV30 @ ( multiply @ SV19 @ SV9 @ SV30 ) )
= $true )
| ( ( group_member @ SV9 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(156,plain,
! [SV10: $i,SV20: $i,SV31: $i] :
( ( ( ~ ( group_member @ SV31 @ SV20 ) )
= $true )
| ( ( group_member @ ( multiply @ SV20 @ SV10 @ SV31 ) @ SV20 )
= $true )
| ( ( group_member @ SV10 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(157,plain,
! [SV27: $i,SV24: $i,SV21: $i,SV11: $i] :
( ( ( product @ SV11 @ SV21 @ SV24 @ SV27 )
= $false )
| ( ( ! [SY88: $i] :
( ~ ( product @ SV11 @ SV21 @ SV24 @ SY88 )
| ( SY88 = SV27 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(158,plain,
! [SV32: $i,SV28: $i,SV25: $i,SV22: $i,SV12: $i] :
( ( ( ~ ( product @ SV12 @ SV22 @ SV25 @ SV28 ) )
= $true )
| ( ( ! [SY95: $i] :
( ~ ( product @ SV12 @ SV25 @ SV32 @ SY95 )
| ! [SY96: $i] :
( ~ ( product @ SV12 @ SV28 @ SV32 @ SY96 )
| ( product @ SV12 @ SV22 @ SY95 @ SY96 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(159,plain,
! [SV33: $i,SV29: $i,SV26: $i,SV23: $i,SV13: $i] :
( ( ( ~ ( product @ SV13 @ SV23 @ SV26 @ SV29 ) )
= $true )
| ( ( ! [SY97: $i] :
( ~ ( product @ SV13 @ SV26 @ SV33 @ SY97 )
| ! [SY98: $i] :
( ~ ( product @ SV13 @ SV23 @ SY97 @ SY98 )
| ( product @ SV13 @ SV29 @ SV33 @ SY98 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(160,plain,
! [SV9: $i,SV19: $i,SV30: $i] :
( ( ( group_member @ SV30 @ SV19 )
= $false )
| ( ( product @ SV19 @ SV9 @ SV30 @ ( multiply @ SV19 @ SV9 @ SV30 ) )
= $true )
| ( ( group_member @ SV9 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(161,plain,
! [SV10: $i,SV20: $i,SV31: $i] :
( ( ( group_member @ SV31 @ SV20 )
= $false )
| ( ( group_member @ ( multiply @ SV20 @ SV10 @ SV31 ) @ SV20 )
= $true )
| ( ( group_member @ SV10 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(162,plain,
! [SV27: $i,SV34: $i,SV24: $i,SV21: $i,SV11: $i] :
( ( ( ~ ( product @ SV11 @ SV21 @ SV24 @ SV34 )
| ( SV34 = SV27 ) )
= $true )
| ( ( product @ SV11 @ SV21 @ SV24 @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(163,plain,
! [SV32: $i,SV28: $i,SV25: $i,SV22: $i,SV12: $i] :
( ( ( product @ SV12 @ SV22 @ SV25 @ SV28 )
= $false )
| ( ( ! [SY95: $i] :
( ~ ( product @ SV12 @ SV25 @ SV32 @ SY95 )
| ! [SY96: $i] :
( ~ ( product @ SV12 @ SV28 @ SV32 @ SY96 )
| ( product @ SV12 @ SV22 @ SY95 @ SY96 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(164,plain,
! [SV33: $i,SV29: $i,SV26: $i,SV23: $i,SV13: $i] :
( ( ( product @ SV13 @ SV23 @ SV26 @ SV29 )
= $false )
| ( ( ! [SY97: $i] :
( ~ ( product @ SV13 @ SV26 @ SV33 @ SY97 )
| ! [SY98: $i] :
( ~ ( product @ SV13 @ SV23 @ SY97 @ SY98 )
| ( product @ SV13 @ SV29 @ SV33 @ SY98 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(165,plain,
! [SV27: $i,SV34: $i,SV24: $i,SV21: $i,SV11: $i] :
( ( ( ~ ( product @ SV11 @ SV21 @ SV24 @ SV34 ) )
= $true )
| ( ( SV34 = SV27 )
= $true )
| ( ( product @ SV11 @ SV21 @ SV24 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(166,plain,
! [SV22: $i,SV28: $i,SV35: $i,SV32: $i,SV25: $i,SV12: $i] :
( ( ( ~ ( product @ SV12 @ SV25 @ SV32 @ SV35 )
| ! [SY99: $i] :
( ~ ( product @ SV12 @ SV28 @ SV32 @ SY99 )
| ( product @ SV12 @ SV22 @ SV35 @ SY99 ) ) )
= $true )
| ( ( product @ SV12 @ SV22 @ SV25 @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(167,plain,
! [SV29: $i,SV23: $i,SV36: $i,SV33: $i,SV26: $i,SV13: $i] :
( ( ( ~ ( product @ SV13 @ SV26 @ SV33 @ SV36 )
| ! [SY100: $i] :
( ~ ( product @ SV13 @ SV23 @ SV36 @ SY100 )
| ( product @ SV13 @ SV29 @ SV33 @ SY100 ) ) )
= $true )
| ( ( product @ SV13 @ SV23 @ SV26 @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(168,plain,
! [SV27: $i,SV34: $i,SV24: $i,SV21: $i,SV11: $i] :
( ( ( product @ SV11 @ SV21 @ SV24 @ SV34 )
= $false )
| ( ( SV34 = SV27 )
= $true )
| ( ( product @ SV11 @ SV21 @ SV24 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(169,plain,
! [SV22: $i,SV28: $i,SV35: $i,SV32: $i,SV25: $i,SV12: $i] :
( ( ( ~ ( product @ SV12 @ SV25 @ SV32 @ SV35 ) )
= $true )
| ( ( ! [SY99: $i] :
( ~ ( product @ SV12 @ SV28 @ SV32 @ SY99 )
| ( product @ SV12 @ SV22 @ SV35 @ SY99 ) ) )
= $true )
| ( ( product @ SV12 @ SV22 @ SV25 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(170,plain,
! [SV29: $i,SV23: $i,SV36: $i,SV33: $i,SV26: $i,SV13: $i] :
( ( ( ~ ( product @ SV13 @ SV26 @ SV33 @ SV36 ) )
= $true )
| ( ( ! [SY100: $i] :
( ~ ( product @ SV13 @ SV23 @ SV36 @ SY100 )
| ( product @ SV13 @ SV29 @ SV33 @ SY100 ) ) )
= $true )
| ( ( product @ SV13 @ SV23 @ SV26 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(171,plain,
! [SV22: $i,SV28: $i,SV35: $i,SV32: $i,SV25: $i,SV12: $i] :
( ( ( product @ SV12 @ SV25 @ SV32 @ SV35 )
= $false )
| ( ( ! [SY99: $i] :
( ~ ( product @ SV12 @ SV28 @ SV32 @ SY99 )
| ( product @ SV12 @ SV22 @ SV35 @ SY99 ) ) )
= $true )
| ( ( product @ SV12 @ SV22 @ SV25 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(172,plain,
! [SV29: $i,SV23: $i,SV36: $i,SV33: $i,SV26: $i,SV13: $i] :
( ( ( product @ SV13 @ SV26 @ SV33 @ SV36 )
= $false )
| ( ( ! [SY100: $i] :
( ~ ( product @ SV13 @ SV23 @ SV36 @ SY100 )
| ( product @ SV13 @ SV29 @ SV33 @ SY100 ) ) )
= $true )
| ( ( product @ SV13 @ SV23 @ SV26 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(173,plain,
! [SV25: $i,SV35: $i,SV22: $i,SV37: $i,SV32: $i,SV28: $i,SV12: $i] :
( ( ( ~ ( product @ SV12 @ SV28 @ SV32 @ SV37 )
| ( product @ SV12 @ SV22 @ SV35 @ SV37 ) )
= $true )
| ( ( product @ SV12 @ SV25 @ SV32 @ SV35 )
= $false )
| ( ( product @ SV12 @ SV22 @ SV25 @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(174,plain,
! [SV26: $i,SV33: $i,SV29: $i,SV38: $i,SV36: $i,SV23: $i,SV13: $i] :
( ( ( ~ ( product @ SV13 @ SV23 @ SV36 @ SV38 )
| ( product @ SV13 @ SV29 @ SV33 @ SV38 ) )
= $true )
| ( ( product @ SV13 @ SV26 @ SV33 @ SV36 )
= $false )
| ( ( product @ SV13 @ SV23 @ SV26 @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(175,plain,
! [SV25: $i,SV35: $i,SV22: $i,SV37: $i,SV32: $i,SV28: $i,SV12: $i] :
( ( ( ~ ( product @ SV12 @ SV28 @ SV32 @ SV37 ) )
= $true )
| ( ( product @ SV12 @ SV22 @ SV35 @ SV37 )
= $true )
| ( ( product @ SV12 @ SV25 @ SV32 @ SV35 )
= $false )
| ( ( product @ SV12 @ SV22 @ SV25 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(176,plain,
! [SV26: $i,SV33: $i,SV29: $i,SV38: $i,SV36: $i,SV23: $i,SV13: $i] :
( ( ( ~ ( product @ SV13 @ SV23 @ SV36 @ SV38 ) )
= $true )
| ( ( product @ SV13 @ SV29 @ SV33 @ SV38 )
= $true )
| ( ( product @ SV13 @ SV26 @ SV33 @ SV36 )
= $false )
| ( ( product @ SV13 @ SV23 @ SV26 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(177,plain,
! [SV25: $i,SV35: $i,SV22: $i,SV37: $i,SV32: $i,SV28: $i,SV12: $i] :
( ( ( product @ SV12 @ SV28 @ SV32 @ SV37 )
= $false )
| ( ( product @ SV12 @ SV22 @ SV35 @ SV37 )
= $true )
| ( ( product @ SV12 @ SV25 @ SV32 @ SV35 )
= $false )
| ( ( product @ SV12 @ SV22 @ SV25 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(178,plain,
! [SV26: $i,SV33: $i,SV29: $i,SV38: $i,SV36: $i,SV23: $i,SV13: $i] :
( ( ( product @ SV13 @ SV23 @ SV36 @ SV38 )
= $false )
| ( ( product @ SV13 @ SV29 @ SV33 @ SV38 )
= $true )
| ( ( product @ SV13 @ SV26 @ SV33 @ SV36 )
= $false )
| ( ( product @ SV13 @ SV23 @ SV26 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(179,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[75,178,177,168,161,160,144,143,142,128,127,125,124,121,110,107,94,93,92,91,90,89,88,87,86,85,84,83,82,81,78,77,76]) ).
thf(180,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[179]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP025-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.06/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n008.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 : Mon Jun 13 05:27:07 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.37
% 0.13/0.37 No.of.Axioms: 32
% 0.13/0.37
% 0.13/0.37 Length.of.Defs: 0
% 0.13/0.37
% 0.13/0.37 Contains.Choice.Funs: false
% 0.13/0.38 (rf:0,axioms:32,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:34,loop_count:0,foatp_calls:0,translation:fof_full).........
% 0.36/0.58
% 0.36/0.58 ********************************
% 0.36/0.58 * All subproblems solved! *
% 0.36/0.58 ********************************
% 0.36/0.58 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:32,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:179,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.36/0.60
% 0.36/0.60 %**** Beginning of derivation protocol ****
% 0.36/0.60 % SZS output start CNFRefutation
% See solution above
% 0.36/0.60
% 0.36/0.60 %**** End of derivation protocol ****
% 0.36/0.60 %**** no. of clauses in derivation: 180 ****
% 0.36/0.60 %**** clause counter: 179 ****
% 0.36/0.60
% 0.36/0.60 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:32,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:179,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------