TSTP Solution File: GRP033-3 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GRP033-3 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n014.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 10:15:32 EDT 2022
% Result : Unsatisfiable 0.18s 0.46s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 31
% Syntax : Number of formulae : 204 ( 108 unt; 8 typ; 0 def)
% Number of atoms : 1085 ( 281 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 1967 ( 256 ~; 327 |; 0 &;1384 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 601 ( 0 ^ 601 !; 0 ?; 601 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_equalish,type,
equalish: $i > $i > $o ).
thf(tp_identity,type,
identity: $i ).
thf(tp_inverse,type,
inverse: $i > $i ).
thf(tp_j,type,
j: $i > $i ).
thf(tp_multiply,type,
multiply: $i > $i > $i ).
thf(tp_product,type,
product: $i > $i > $i > $o ).
thf(tp_subgroup_member,type,
subgroup_member: $i > $o ).
thf(1,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( subgroup_member @ A )
| ~ ( subgroup_member @ B )
| ~ ( product @ A @ ( inverse @ B ) @ C )
| ( subgroup_member @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_product_and_inverse) ).
thf(2,axiom,
! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
( ~ ( product @ X @ Y @ U )
| ~ ( product @ Y @ Z @ V )
| ~ ( product @ X @ V @ W )
| ( product @ U @ Z @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity2) ).
thf(3,axiom,
! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
( ~ ( product @ X @ Y @ U )
| ~ ( product @ Y @ Z @ V )
| ~ ( product @ U @ Z @ W )
| ( product @ X @ V @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity1) ).
thf(4,axiom,
! [X: $i,Y: $i,Z: $i,W: $i] :
( ~ ( product @ X @ Y @ Z )
| ~ ( product @ X @ Y @ W )
| ( equalish @ Z @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function2) ).
thf(5,axiom,
! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function1) ).
thf(6,axiom,
! [X: $i] : ( product @ X @ ( inverse @ X ) @ identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
thf(7,axiom,
! [X: $i] : ( product @ ( inverse @ X ) @ X @ identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(8,axiom,
! [X: $i] : ( product @ X @ identity @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
thf(9,axiom,
! [X: $i] : ( product @ identity @ X @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ~ ( equalish @ A @ B )
| ~ ( subgroup_member @ A )
| ( subgroup_member @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subgroup_member_substitution) ).
thf(11,axiom,
! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( product @ W @ Z @ X )
| ( product @ W @ Z @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution3) ).
thf(12,axiom,
! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( product @ W @ X @ Z )
| ( product @ W @ Y @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution2) ).
thf(13,axiom,
! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( product @ X @ W @ Z )
| ( product @ Y @ W @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution1) ).
thf(14,axiom,
! [X: $i,Y: $i,W: $i] :
( ~ ( equalish @ X @ Y )
| ( equalish @ ( multiply @ W @ X ) @ ( multiply @ W @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_substitution2) ).
thf(15,axiom,
! [X: $i,Y: $i,W: $i] :
( ~ ( equalish @ X @ Y )
| ( equalish @ ( multiply @ X @ W ) @ ( multiply @ Y @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_substitution1) ).
thf(16,axiom,
! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ( equalish @ ( inverse @ X ) @ ( inverse @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_substitution) ).
thf(17,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( equalish @ Y @ Z )
| ( equalish @ X @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
thf(18,axiom,
! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ( equalish @ Y @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry) ).
thf(19,axiom,
! [X: $i] : ( equalish @ X @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(20,axiom,
! [A: $i] :
( ~ ( subgroup_member @ A )
| ( subgroup_member @ ( j @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subgr2_clause1) ).
thf(21,axiom,
subgroup_member @ a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_in_subgroup) ).
thf(22,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(23,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[22]) ).
thf(24,negated_conjecture,
! [A: $i] :
( ~ ( product @ ( j @ A ) @ A @ ( j @ A ) )
| ~ ( product @ A @ ( j @ A ) @ ( j @ A ) )
| ~ ( subgroup_member @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_subgr2) ).
thf(25,plain,
$false = $false,
inference(unfold_def,[status(thm)],[23]) ).
thf(26,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subgroup_member @ A )
| ~ ( subgroup_member @ B )
| ~ ( product @ A @ ( inverse @ B ) @ C )
| ( subgroup_member @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(27,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
( ~ ( product @ X @ Y @ U )
| ~ ( product @ Y @ Z @ V )
| ~ ( product @ X @ V @ W )
| ( product @ U @ Z @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(28,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
( ~ ( product @ X @ Y @ U )
| ~ ( product @ Y @ Z @ V )
| ~ ( product @ U @ Z @ W )
| ( product @ X @ V @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(29,plain,
( ( ! [X: $i,Y: $i,Z: $i,W: $i] :
( ~ ( product @ X @ Y @ Z )
| ~ ( product @ X @ Y @ W )
| ( equalish @ Z @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(30,plain,
( ( ! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(31,plain,
( ( ! [X: $i] : ( product @ X @ ( inverse @ X ) @ identity ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(32,plain,
( ( ! [X: $i] : ( product @ ( inverse @ X ) @ X @ identity ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(33,plain,
( ( ! [X: $i] : ( product @ X @ identity @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(34,plain,
( ( ! [X: $i] : ( product @ identity @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(35,plain,
( ( ! [A: $i,B: $i] :
( ~ ( equalish @ A @ B )
| ~ ( subgroup_member @ A )
| ( subgroup_member @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(36,plain,
( ( ! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( product @ W @ Z @ X )
| ( product @ W @ Z @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(37,plain,
( ( ! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( product @ W @ X @ Z )
| ( product @ W @ Y @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(38,plain,
( ( ! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( product @ X @ W @ Z )
| ( product @ Y @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(39,plain,
( ( ! [X: $i,Y: $i,W: $i] :
( ~ ( equalish @ X @ Y )
| ( equalish @ ( multiply @ W @ X ) @ ( multiply @ W @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(40,plain,
( ( ! [X: $i,Y: $i,W: $i] :
( ~ ( equalish @ X @ Y )
| ( equalish @ ( multiply @ X @ W ) @ ( multiply @ Y @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(41,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ( equalish @ ( inverse @ X ) @ ( inverse @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(42,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( equalish @ Y @ Z )
| ( equalish @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(43,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ( equalish @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(44,plain,
( ( ! [X: $i] : ( equalish @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(45,plain,
( ( ! [A: $i] :
( ~ ( subgroup_member @ A )
| ( subgroup_member @ ( j @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(46,plain,
( ( subgroup_member @ a )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(47,plain,
( ( ! [A: $i] :
( ~ ( product @ ( j @ A ) @ A @ ( j @ A ) )
| ~ ( product @ A @ ( j @ A ) @ ( j @ A ) )
| ~ ( subgroup_member @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(48,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[25]) ).
thf(49,plain,
( ( ! [A: $i] :
( ~ ( subgroup_member @ A )
| ! [B: $i] :
( ~ ( subgroup_member @ B )
| ! [C: $i] :
( ~ ( product @ A @ ( inverse @ B ) @ C )
| ( subgroup_member @ C ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(50,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i] :
( ~ ( product @ X @ Y @ U )
| ! [V: $i] :
( ~ ( product @ Y @ Z @ V )
| ! [W: $i] :
( ~ ( product @ X @ V @ W )
| ( product @ U @ Z @ W ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(51,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i] :
( ~ ( product @ X @ Y @ U )
| ! [V: $i] :
( ~ ( product @ Y @ Z @ V )
| ! [W: $i] :
( ~ ( product @ U @ Z @ W )
| ( product @ X @ V @ W ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(52,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( product @ X @ Y @ Z )
| ! [W: $i] :
( ~ ( product @ X @ Y @ W )
| ( equalish @ Z @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[29]) ).
thf(53,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [W: $i,Z: $i] :
( ~ ( product @ W @ Z @ X )
| ( product @ W @ Z @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[36]) ).
thf(54,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [W: $i,Z: $i] :
( ~ ( product @ W @ X @ Z )
| ( product @ W @ Y @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[37]) ).
thf(55,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [W: $i,Z: $i] :
( ~ ( product @ X @ W @ Z )
| ( product @ Y @ W @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[38]) ).
thf(56,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [W: $i] : ( equalish @ ( multiply @ W @ X ) @ ( multiply @ W @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[39]) ).
thf(57,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [W: $i] : ( equalish @ ( multiply @ X @ W ) @ ( multiply @ Y @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[40]) ).
thf(58,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [Z: $i] :
( ~ ( equalish @ Y @ Z )
| ( equalish @ X @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(59,plain,
( ( ! [A: $i] :
( ~ ( product @ ( j @ A ) @ A @ ( j @ A ) )
| ~ ( product @ A @ ( j @ A ) @ ( j @ A ) )
| ~ ( subgroup_member @ A ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(60,plain,
( ( subgroup_member @ a )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(61,plain,
( ( ! [A: $i] :
( ~ ( subgroup_member @ A )
| ( subgroup_member @ ( j @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(62,plain,
( ( ! [X: $i] : ( equalish @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(63,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ( equalish @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(64,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [Z: $i] :
( ~ ( equalish @ Y @ Z )
| ( equalish @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(65,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ( equalish @ ( inverse @ X ) @ ( inverse @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(66,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [W: $i] : ( equalish @ ( multiply @ X @ W ) @ ( multiply @ Y @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(67,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [W: $i] : ( equalish @ ( multiply @ W @ X ) @ ( multiply @ W @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(68,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [W: $i,Z: $i] :
( ~ ( product @ X @ W @ Z )
| ( product @ Y @ W @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(69,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [W: $i,Z: $i] :
( ~ ( product @ W @ X @ Z )
| ( product @ W @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(70,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [W: $i,Z: $i] :
( ~ ( product @ W @ Z @ X )
| ( product @ W @ Z @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(71,plain,
( ( ! [A: $i,B: $i] :
( ~ ( equalish @ A @ B )
| ~ ( subgroup_member @ A )
| ( subgroup_member @ B ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(72,plain,
( ( ! [X: $i] : ( product @ identity @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(73,plain,
( ( ! [X: $i] : ( product @ X @ identity @ X ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(74,plain,
( ( ! [X: $i] : ( product @ ( inverse @ X ) @ X @ identity ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(75,plain,
( ( ! [X: $i] : ( product @ X @ ( inverse @ X ) @ identity ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(76,plain,
( ( ! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(77,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( product @ X @ Y @ Z )
| ! [W: $i] :
( ~ ( product @ X @ Y @ W )
| ( equalish @ Z @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(78,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i] :
( ~ ( product @ X @ Y @ U )
| ! [V: $i] :
( ~ ( product @ Y @ Z @ V )
| ! [W: $i] :
( ~ ( product @ U @ Z @ W )
| ( product @ X @ V @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(79,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i] :
( ~ ( product @ X @ Y @ U )
| ! [V: $i] :
( ~ ( product @ Y @ Z @ V )
| ! [W: $i] :
( ~ ( product @ X @ V @ W )
| ( product @ U @ Z @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(80,plain,
( ( ! [A: $i] :
( ~ ( subgroup_member @ A )
| ! [B: $i] :
( ~ ( subgroup_member @ B )
| ! [C: $i] :
( ~ ( product @ A @ ( inverse @ B ) @ C )
| ( subgroup_member @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(81,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(82,plain,
! [SV1: $i] :
( ( ~ ( product @ ( j @ SV1 ) @ SV1 @ ( j @ SV1 ) )
| ~ ( product @ SV1 @ ( j @ SV1 ) @ ( j @ SV1 ) )
| ~ ( subgroup_member @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(83,plain,
! [SV2: $i] :
( ( ~ ( subgroup_member @ SV2 )
| ( subgroup_member @ ( j @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(84,plain,
! [SV3: $i] :
( ( equalish @ SV3 @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(85,plain,
! [SV4: $i] :
( ( ! [SY55: $i] :
( ~ ( equalish @ SV4 @ SY55 )
| ( equalish @ SY55 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(86,plain,
! [SV5: $i] :
( ( ! [SY56: $i] :
( ~ ( equalish @ SV5 @ SY56 )
| ! [SY57: $i] :
( ~ ( equalish @ SY56 @ SY57 )
| ( equalish @ SV5 @ SY57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(87,plain,
! [SV6: $i] :
( ( ! [SY58: $i] :
( ~ ( equalish @ SV6 @ SY58 )
| ( equalish @ ( inverse @ SV6 ) @ ( inverse @ SY58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(88,plain,
! [SV7: $i] :
( ( ! [SY59: $i] :
( ~ ( equalish @ SV7 @ SY59 )
| ! [SY60: $i] : ( equalish @ ( multiply @ SV7 @ SY60 ) @ ( multiply @ SY59 @ SY60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(89,plain,
! [SV8: $i] :
( ( ! [SY61: $i] :
( ~ ( equalish @ SV8 @ SY61 )
| ! [SY62: $i] : ( equalish @ ( multiply @ SY62 @ SV8 ) @ ( multiply @ SY62 @ SY61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(90,plain,
! [SV9: $i] :
( ( ! [SY63: $i] :
( ~ ( equalish @ SV9 @ SY63 )
| ! [SY64: $i,SY65: $i] :
( ~ ( product @ SV9 @ SY64 @ SY65 )
| ( product @ SY63 @ SY64 @ SY65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(91,plain,
! [SV10: $i] :
( ( ! [SY66: $i] :
( ~ ( equalish @ SV10 @ SY66 )
| ! [SY67: $i,SY68: $i] :
( ~ ( product @ SY67 @ SV10 @ SY68 )
| ( product @ SY67 @ SY66 @ SY68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(92,plain,
! [SV11: $i] :
( ( ! [SY69: $i] :
( ~ ( equalish @ SV11 @ SY69 )
| ! [SY70: $i,SY71: $i] :
( ~ ( product @ SY70 @ SY71 @ SV11 )
| ( product @ SY70 @ SY71 @ SY69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(93,plain,
! [SV12: $i] :
( ( ! [SY72: $i] :
( ~ ( equalish @ SV12 @ SY72 )
| ~ ( subgroup_member @ SV12 )
| ( subgroup_member @ SY72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(94,plain,
! [SV13: $i] :
( ( product @ identity @ SV13 @ SV13 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(95,plain,
! [SV14: $i] :
( ( product @ SV14 @ identity @ SV14 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(96,plain,
! [SV15: $i] :
( ( product @ ( inverse @ SV15 ) @ SV15 @ identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(97,plain,
! [SV16: $i] :
( ( product @ SV16 @ ( inverse @ SV16 ) @ identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(98,plain,
! [SV17: $i] :
( ( ! [SY73: $i] : ( product @ SV17 @ SY73 @ ( multiply @ SV17 @ SY73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(99,plain,
! [SV18: $i] :
( ( ! [SY74: $i,SY75: $i] :
( ~ ( product @ SV18 @ SY74 @ SY75 )
| ! [SY76: $i] :
( ~ ( product @ SV18 @ SY74 @ SY76 )
| ( equalish @ SY75 @ SY76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(100,plain,
! [SV19: $i] :
( ( ! [SY77: $i,SY78: $i,SY79: $i] :
( ~ ( product @ SV19 @ SY77 @ SY78 )
| ! [SY80: $i] :
( ~ ( product @ SY77 @ SY79 @ SY80 )
| ! [SY81: $i] :
( ~ ( product @ SY78 @ SY79 @ SY81 )
| ( product @ SV19 @ SY80 @ SY81 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(101,plain,
! [SV20: $i] :
( ( ! [SY82: $i,SY83: $i,SY84: $i] :
( ~ ( product @ SV20 @ SY82 @ SY83 )
| ! [SY85: $i] :
( ~ ( product @ SY82 @ SY84 @ SY85 )
| ! [SY86: $i] :
( ~ ( product @ SV20 @ SY85 @ SY86 )
| ( product @ SY83 @ SY84 @ SY86 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(102,plain,
! [SV21: $i] :
( ( ~ ( subgroup_member @ SV21 )
| ! [SY87: $i] :
( ~ ( subgroup_member @ SY87 )
| ! [SY88: $i] :
( ~ ( product @ SV21 @ ( inverse @ SY87 ) @ SY88 )
| ( subgroup_member @ SY88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(103,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(104,plain,
! [SV1: $i] :
( ( ( ~ ( product @ ( j @ SV1 ) @ SV1 @ ( j @ SV1 ) ) )
= $true )
| ( ( ~ ( product @ SV1 @ ( j @ SV1 ) @ ( j @ SV1 ) )
| ~ ( subgroup_member @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(105,plain,
! [SV2: $i] :
( ( ( ~ ( subgroup_member @ SV2 ) )
= $true )
| ( ( subgroup_member @ ( j @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(106,plain,
! [SV22: $i,SV4: $i] :
( ( ~ ( equalish @ SV4 @ SV22 )
| ( equalish @ SV22 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(107,plain,
! [SV23: $i,SV5: $i] :
( ( ~ ( equalish @ SV5 @ SV23 )
| ! [SY89: $i] :
( ~ ( equalish @ SV23 @ SY89 )
| ( equalish @ SV5 @ SY89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(108,plain,
! [SV24: $i,SV6: $i] :
( ( ~ ( equalish @ SV6 @ SV24 )
| ( equalish @ ( inverse @ SV6 ) @ ( inverse @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(109,plain,
! [SV25: $i,SV7: $i] :
( ( ~ ( equalish @ SV7 @ SV25 )
| ! [SY90: $i] : ( equalish @ ( multiply @ SV7 @ SY90 ) @ ( multiply @ SV25 @ SY90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(110,plain,
! [SV26: $i,SV8: $i] :
( ( ~ ( equalish @ SV8 @ SV26 )
| ! [SY91: $i] : ( equalish @ ( multiply @ SY91 @ SV8 ) @ ( multiply @ SY91 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(111,plain,
! [SV27: $i,SV9: $i] :
( ( ~ ( equalish @ SV9 @ SV27 )
| ! [SY92: $i,SY93: $i] :
( ~ ( product @ SV9 @ SY92 @ SY93 )
| ( product @ SV27 @ SY92 @ SY93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(112,plain,
! [SV28: $i,SV10: $i] :
( ( ~ ( equalish @ SV10 @ SV28 )
| ! [SY94: $i,SY95: $i] :
( ~ ( product @ SY94 @ SV10 @ SY95 )
| ( product @ SY94 @ SV28 @ SY95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(113,plain,
! [SV29: $i,SV11: $i] :
( ( ~ ( equalish @ SV11 @ SV29 )
| ! [SY96: $i,SY97: $i] :
( ~ ( product @ SY96 @ SY97 @ SV11 )
| ( product @ SY96 @ SY97 @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(114,plain,
! [SV30: $i,SV12: $i] :
( ( ~ ( equalish @ SV12 @ SV30 )
| ~ ( subgroup_member @ SV12 )
| ( subgroup_member @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(115,plain,
! [SV31: $i,SV17: $i] :
( ( product @ SV17 @ SV31 @ ( multiply @ SV17 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(116,plain,
! [SV32: $i,SV18: $i] :
( ( ! [SY98: $i] :
( ~ ( product @ SV18 @ SV32 @ SY98 )
| ! [SY99: $i] :
( ~ ( product @ SV18 @ SV32 @ SY99 )
| ( equalish @ SY98 @ SY99 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(117,plain,
! [SV33: $i,SV19: $i] :
( ( ! [SY100: $i,SY101: $i] :
( ~ ( product @ SV19 @ SV33 @ SY100 )
| ! [SY102: $i] :
( ~ ( product @ SV33 @ SY101 @ SY102 )
| ! [SY81: $i] :
( ~ ( product @ SY100 @ SY101 @ SY81 )
| ( product @ SV19 @ SY102 @ SY81 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(118,plain,
! [SV34: $i,SV20: $i] :
( ( ! [SY104: $i,SY105: $i] :
( ~ ( product @ SV20 @ SV34 @ SY104 )
| ! [SY106: $i] :
( ~ ( product @ SV34 @ SY105 @ SY106 )
| ! [SY86: $i] :
( ~ ( product @ SV20 @ SY106 @ SY86 )
| ( product @ SY104 @ SY105 @ SY86 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(119,plain,
! [SV21: $i] :
( ( ( ~ ( subgroup_member @ SV21 ) )
= $true )
| ( ( ! [SY87: $i] :
( ~ ( subgroup_member @ SY87 )
| ! [SY88: $i] :
( ~ ( product @ SV21 @ ( inverse @ SY87 ) @ SY88 )
| ( subgroup_member @ SY88 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(120,plain,
! [SV1: $i] :
( ( ( product @ ( j @ SV1 ) @ SV1 @ ( j @ SV1 ) )
= $false )
| ( ( ~ ( product @ SV1 @ ( j @ SV1 ) @ ( j @ SV1 ) )
| ~ ( subgroup_member @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(121,plain,
! [SV2: $i] :
( ( ( subgroup_member @ SV2 )
= $false )
| ( ( subgroup_member @ ( j @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(122,plain,
! [SV22: $i,SV4: $i] :
( ( ( ~ ( equalish @ SV4 @ SV22 ) )
= $true )
| ( ( equalish @ SV22 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(123,plain,
! [SV23: $i,SV5: $i] :
( ( ( ~ ( equalish @ SV5 @ SV23 ) )
= $true )
| ( ( ! [SY89: $i] :
( ~ ( equalish @ SV23 @ SY89 )
| ( equalish @ SV5 @ SY89 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(124,plain,
! [SV24: $i,SV6: $i] :
( ( ( ~ ( equalish @ SV6 @ SV24 ) )
= $true )
| ( ( equalish @ ( inverse @ SV6 ) @ ( inverse @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(125,plain,
! [SV25: $i,SV7: $i] :
( ( ( ~ ( equalish @ SV7 @ SV25 ) )
= $true )
| ( ( ! [SY90: $i] : ( equalish @ ( multiply @ SV7 @ SY90 ) @ ( multiply @ SV25 @ SY90 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(126,plain,
! [SV26: $i,SV8: $i] :
( ( ( ~ ( equalish @ SV8 @ SV26 ) )
= $true )
| ( ( ! [SY91: $i] : ( equalish @ ( multiply @ SY91 @ SV8 ) @ ( multiply @ SY91 @ SV26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(127,plain,
! [SV27: $i,SV9: $i] :
( ( ( ~ ( equalish @ SV9 @ SV27 ) )
= $true )
| ( ( ! [SY92: $i,SY93: $i] :
( ~ ( product @ SV9 @ SY92 @ SY93 )
| ( product @ SV27 @ SY92 @ SY93 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(128,plain,
! [SV28: $i,SV10: $i] :
( ( ( ~ ( equalish @ SV10 @ SV28 ) )
= $true )
| ( ( ! [SY94: $i,SY95: $i] :
( ~ ( product @ SY94 @ SV10 @ SY95 )
| ( product @ SY94 @ SV28 @ SY95 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(129,plain,
! [SV29: $i,SV11: $i] :
( ( ( ~ ( equalish @ SV11 @ SV29 ) )
= $true )
| ( ( ! [SY96: $i,SY97: $i] :
( ~ ( product @ SY96 @ SY97 @ SV11 )
| ( product @ SY96 @ SY97 @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(130,plain,
! [SV30: $i,SV12: $i] :
( ( ( ~ ( equalish @ SV12 @ SV30 ) )
= $true )
| ( ( ~ ( subgroup_member @ SV12 )
| ( subgroup_member @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(131,plain,
! [SV35: $i,SV32: $i,SV18: $i] :
( ( ~ ( product @ SV18 @ SV32 @ SV35 )
| ! [SY108: $i] :
( ~ ( product @ SV18 @ SV32 @ SY108 )
| ( equalish @ SV35 @ SY108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(132,plain,
! [SV36: $i,SV33: $i,SV19: $i] :
( ( ! [SY109: $i] :
( ~ ( product @ SV19 @ SV33 @ SV36 )
| ! [SY110: $i] :
( ~ ( product @ SV33 @ SY109 @ SY110 )
| ! [SY111: $i] :
( ~ ( product @ SV36 @ SY109 @ SY111 )
| ( product @ SV19 @ SY110 @ SY111 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(133,plain,
! [SV37: $i,SV34: $i,SV20: $i] :
( ( ! [SY112: $i] :
( ~ ( product @ SV20 @ SV34 @ SV37 )
| ! [SY113: $i] :
( ~ ( product @ SV34 @ SY112 @ SY113 )
| ! [SY114: $i] :
( ~ ( product @ SV20 @ SY113 @ SY114 )
| ( product @ SV37 @ SY112 @ SY114 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(134,plain,
! [SV21: $i] :
( ( ( subgroup_member @ SV21 )
= $false )
| ( ( ! [SY87: $i] :
( ~ ( subgroup_member @ SY87 )
| ! [SY88: $i] :
( ~ ( product @ SV21 @ ( inverse @ SY87 ) @ SY88 )
| ( subgroup_member @ SY88 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(135,plain,
! [SV1: $i] :
( ( ( ~ ( product @ SV1 @ ( j @ SV1 ) @ ( j @ SV1 ) ) )
= $true )
| ( ( ~ ( subgroup_member @ SV1 ) )
= $true )
| ( ( product @ ( j @ SV1 ) @ SV1 @ ( j @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(136,plain,
! [SV22: $i,SV4: $i] :
( ( ( equalish @ SV4 @ SV22 )
= $false )
| ( ( equalish @ SV22 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(137,plain,
! [SV23: $i,SV5: $i] :
( ( ( equalish @ SV5 @ SV23 )
= $false )
| ( ( ! [SY89: $i] :
( ~ ( equalish @ SV23 @ SY89 )
| ( equalish @ SV5 @ SY89 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(138,plain,
! [SV24: $i,SV6: $i] :
( ( ( equalish @ SV6 @ SV24 )
= $false )
| ( ( equalish @ ( inverse @ SV6 ) @ ( inverse @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(139,plain,
! [SV25: $i,SV7: $i] :
( ( ( equalish @ SV7 @ SV25 )
= $false )
| ( ( ! [SY90: $i] : ( equalish @ ( multiply @ SV7 @ SY90 ) @ ( multiply @ SV25 @ SY90 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(140,plain,
! [SV26: $i,SV8: $i] :
( ( ( equalish @ SV8 @ SV26 )
= $false )
| ( ( ! [SY91: $i] : ( equalish @ ( multiply @ SY91 @ SV8 ) @ ( multiply @ SY91 @ SV26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(141,plain,
! [SV27: $i,SV9: $i] :
( ( ( equalish @ SV9 @ SV27 )
= $false )
| ( ( ! [SY92: $i,SY93: $i] :
( ~ ( product @ SV9 @ SY92 @ SY93 )
| ( product @ SV27 @ SY92 @ SY93 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(142,plain,
! [SV28: $i,SV10: $i] :
( ( ( equalish @ SV10 @ SV28 )
= $false )
| ( ( ! [SY94: $i,SY95: $i] :
( ~ ( product @ SY94 @ SV10 @ SY95 )
| ( product @ SY94 @ SV28 @ SY95 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(143,plain,
! [SV29: $i,SV11: $i] :
( ( ( equalish @ SV11 @ SV29 )
= $false )
| ( ( ! [SY96: $i,SY97: $i] :
( ~ ( product @ SY96 @ SY97 @ SV11 )
| ( product @ SY96 @ SY97 @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(144,plain,
! [SV30: $i,SV12: $i] :
( ( ( equalish @ SV12 @ SV30 )
= $false )
| ( ( ~ ( subgroup_member @ SV12 )
| ( subgroup_member @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(145,plain,
! [SV35: $i,SV32: $i,SV18: $i] :
( ( ( ~ ( product @ SV18 @ SV32 @ SV35 ) )
= $true )
| ( ( ! [SY108: $i] :
( ~ ( product @ SV18 @ SV32 @ SY108 )
| ( equalish @ SV35 @ SY108 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(146,plain,
! [SV38: $i,SV36: $i,SV33: $i,SV19: $i] :
( ( ~ ( product @ SV19 @ SV33 @ SV36 )
| ! [SY115: $i] :
( ~ ( product @ SV33 @ SV38 @ SY115 )
| ! [SY116: $i] :
( ~ ( product @ SV36 @ SV38 @ SY116 )
| ( product @ SV19 @ SY115 @ SY116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(147,plain,
! [SV39: $i,SV37: $i,SV34: $i,SV20: $i] :
( ( ~ ( product @ SV20 @ SV34 @ SV37 )
| ! [SY117: $i] :
( ~ ( product @ SV34 @ SV39 @ SY117 )
| ! [SY118: $i] :
( ~ ( product @ SV20 @ SY117 @ SY118 )
| ( product @ SV37 @ SV39 @ SY118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(148,plain,
! [SV21: $i,SV40: $i] :
( ( ( ~ ( subgroup_member @ SV40 )
| ! [SY119: $i] :
( ~ ( product @ SV21 @ ( inverse @ SV40 ) @ SY119 )
| ( subgroup_member @ SY119 ) ) )
= $true )
| ( ( subgroup_member @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(149,plain,
! [SV1: $i] :
( ( ( product @ SV1 @ ( j @ SV1 ) @ ( j @ SV1 ) )
= $false )
| ( ( ~ ( subgroup_member @ SV1 ) )
= $true )
| ( ( product @ ( j @ SV1 ) @ SV1 @ ( j @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(150,plain,
! [SV5: $i,SV41: $i,SV23: $i] :
( ( ( ~ ( equalish @ SV23 @ SV41 )
| ( equalish @ SV5 @ SV41 ) )
= $true )
| ( ( equalish @ SV5 @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(151,plain,
! [SV25: $i,SV42: $i,SV7: $i] :
( ( ( equalish @ ( multiply @ SV7 @ SV42 ) @ ( multiply @ SV25 @ SV42 ) )
= $true )
| ( ( equalish @ SV7 @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(152,plain,
! [SV26: $i,SV8: $i,SV43: $i] :
( ( ( equalish @ ( multiply @ SV43 @ SV8 ) @ ( multiply @ SV43 @ SV26 ) )
= $true )
| ( ( equalish @ SV8 @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(153,plain,
! [SV27: $i,SV44: $i,SV9: $i] :
( ( ( ! [SY120: $i] :
( ~ ( product @ SV9 @ SV44 @ SY120 )
| ( product @ SV27 @ SV44 @ SY120 ) ) )
= $true )
| ( ( equalish @ SV9 @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(154,plain,
! [SV28: $i,SV10: $i,SV45: $i] :
( ( ( ! [SY121: $i] :
( ~ ( product @ SV45 @ SV10 @ SY121 )
| ( product @ SV45 @ SV28 @ SY121 ) ) )
= $true )
| ( ( equalish @ SV10 @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(155,plain,
! [SV29: $i,SV11: $i,SV46: $i] :
( ( ( ! [SY122: $i] :
( ~ ( product @ SV46 @ SY122 @ SV11 )
| ( product @ SV46 @ SY122 @ SV29 ) ) )
= $true )
| ( ( equalish @ SV11 @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(156,plain,
! [SV30: $i,SV12: $i] :
( ( ( ~ ( subgroup_member @ SV12 ) )
= $true )
| ( ( subgroup_member @ SV30 )
= $true )
| ( ( equalish @ SV12 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(157,plain,
! [SV35: $i,SV32: $i,SV18: $i] :
( ( ( product @ SV18 @ SV32 @ SV35 )
= $false )
| ( ( ! [SY108: $i] :
( ~ ( product @ SV18 @ SV32 @ SY108 )
| ( equalish @ SV35 @ SY108 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(158,plain,
! [SV38: $i,SV36: $i,SV33: $i,SV19: $i] :
( ( ( ~ ( product @ SV19 @ SV33 @ SV36 ) )
= $true )
| ( ( ! [SY115: $i] :
( ~ ( product @ SV33 @ SV38 @ SY115 )
| ! [SY116: $i] :
( ~ ( product @ SV36 @ SV38 @ SY116 )
| ( product @ SV19 @ SY115 @ SY116 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(159,plain,
! [SV39: $i,SV37: $i,SV34: $i,SV20: $i] :
( ( ( ~ ( product @ SV20 @ SV34 @ SV37 ) )
= $true )
| ( ( ! [SY117: $i] :
( ~ ( product @ SV34 @ SV39 @ SY117 )
| ! [SY118: $i] :
( ~ ( product @ SV20 @ SY117 @ SY118 )
| ( product @ SV37 @ SV39 @ SY118 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(160,plain,
! [SV21: $i,SV40: $i] :
( ( ( ~ ( subgroup_member @ SV40 ) )
= $true )
| ( ( ! [SY119: $i] :
( ~ ( product @ SV21 @ ( inverse @ SV40 ) @ SY119 )
| ( subgroup_member @ SY119 ) ) )
= $true )
| ( ( subgroup_member @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(161,plain,
! [SV1: $i] :
( ( ( subgroup_member @ SV1 )
= $false )
| ( ( product @ SV1 @ ( j @ SV1 ) @ ( j @ SV1 ) )
= $false )
| ( ( product @ ( j @ SV1 ) @ SV1 @ ( j @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(162,plain,
! [SV5: $i,SV41: $i,SV23: $i] :
( ( ( ~ ( equalish @ SV23 @ SV41 ) )
= $true )
| ( ( equalish @ SV5 @ SV41 )
= $true )
| ( ( equalish @ SV5 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(163,plain,
! [SV27: $i,SV47: $i,SV44: $i,SV9: $i] :
( ( ( ~ ( product @ SV9 @ SV44 @ SV47 )
| ( product @ SV27 @ SV44 @ SV47 ) )
= $true )
| ( ( equalish @ SV9 @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(164,plain,
! [SV28: $i,SV48: $i,SV10: $i,SV45: $i] :
( ( ( ~ ( product @ SV45 @ SV10 @ SV48 )
| ( product @ SV45 @ SV28 @ SV48 ) )
= $true )
| ( ( equalish @ SV10 @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(165,plain,
! [SV29: $i,SV11: $i,SV49: $i,SV46: $i] :
( ( ( ~ ( product @ SV46 @ SV49 @ SV11 )
| ( product @ SV46 @ SV49 @ SV29 ) )
= $true )
| ( ( equalish @ SV11 @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(166,plain,
! [SV30: $i,SV12: $i] :
( ( ( subgroup_member @ SV12 )
= $false )
| ( ( subgroup_member @ SV30 )
= $true )
| ( ( equalish @ SV12 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(167,plain,
! [SV35: $i,SV50: $i,SV32: $i,SV18: $i] :
( ( ( ~ ( product @ SV18 @ SV32 @ SV50 )
| ( equalish @ SV35 @ SV50 ) )
= $true )
| ( ( product @ SV18 @ SV32 @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(168,plain,
! [SV38: $i,SV36: $i,SV33: $i,SV19: $i] :
( ( ( product @ SV19 @ SV33 @ SV36 )
= $false )
| ( ( ! [SY115: $i] :
( ~ ( product @ SV33 @ SV38 @ SY115 )
| ! [SY116: $i] :
( ~ ( product @ SV36 @ SV38 @ SY116 )
| ( product @ SV19 @ SY115 @ SY116 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(169,plain,
! [SV39: $i,SV37: $i,SV34: $i,SV20: $i] :
( ( ( product @ SV20 @ SV34 @ SV37 )
= $false )
| ( ( ! [SY117: $i] :
( ~ ( product @ SV34 @ SV39 @ SY117 )
| ! [SY118: $i] :
( ~ ( product @ SV20 @ SY117 @ SY118 )
| ( product @ SV37 @ SV39 @ SY118 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(170,plain,
! [SV21: $i,SV40: $i] :
( ( ( subgroup_member @ SV40 )
= $false )
| ( ( ! [SY119: $i] :
( ~ ( product @ SV21 @ ( inverse @ SV40 ) @ SY119 )
| ( subgroup_member @ SY119 ) ) )
= $true )
| ( ( subgroup_member @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(171,plain,
! [SV5: $i,SV41: $i,SV23: $i] :
( ( ( equalish @ SV23 @ SV41 )
= $false )
| ( ( equalish @ SV5 @ SV41 )
= $true )
| ( ( equalish @ SV5 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(172,plain,
! [SV27: $i,SV47: $i,SV44: $i,SV9: $i] :
( ( ( ~ ( product @ SV9 @ SV44 @ SV47 ) )
= $true )
| ( ( product @ SV27 @ SV44 @ SV47 )
= $true )
| ( ( equalish @ SV9 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(173,plain,
! [SV28: $i,SV48: $i,SV10: $i,SV45: $i] :
( ( ( ~ ( product @ SV45 @ SV10 @ SV48 ) )
= $true )
| ( ( product @ SV45 @ SV28 @ SV48 )
= $true )
| ( ( equalish @ SV10 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(174,plain,
! [SV29: $i,SV11: $i,SV49: $i,SV46: $i] :
( ( ( ~ ( product @ SV46 @ SV49 @ SV11 ) )
= $true )
| ( ( product @ SV46 @ SV49 @ SV29 )
= $true )
| ( ( equalish @ SV11 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(175,plain,
! [SV35: $i,SV50: $i,SV32: $i,SV18: $i] :
( ( ( ~ ( product @ SV18 @ SV32 @ SV50 ) )
= $true )
| ( ( equalish @ SV35 @ SV50 )
= $true )
| ( ( product @ SV18 @ SV32 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(176,plain,
! [SV19: $i,SV36: $i,SV51: $i,SV38: $i,SV33: $i] :
( ( ( ~ ( product @ SV33 @ SV38 @ SV51 )
| ! [SY123: $i] :
( ~ ( product @ SV36 @ SV38 @ SY123 )
| ( product @ SV19 @ SV51 @ SY123 ) ) )
= $true )
| ( ( product @ SV19 @ SV33 @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(177,plain,
! [SV37: $i,SV20: $i,SV52: $i,SV39: $i,SV34: $i] :
( ( ( ~ ( product @ SV34 @ SV39 @ SV52 )
| ! [SY124: $i] :
( ~ ( product @ SV20 @ SV52 @ SY124 )
| ( product @ SV37 @ SV39 @ SY124 ) ) )
= $true )
| ( ( product @ SV20 @ SV34 @ SV37 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(178,plain,
! [SV53: $i,SV40: $i,SV21: $i] :
( ( ( ~ ( product @ SV21 @ ( inverse @ SV40 ) @ SV53 )
| ( subgroup_member @ SV53 ) )
= $true )
| ( ( subgroup_member @ SV40 )
= $false )
| ( ( subgroup_member @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(179,plain,
! [SV27: $i,SV47: $i,SV44: $i,SV9: $i] :
( ( ( product @ SV9 @ SV44 @ SV47 )
= $false )
| ( ( product @ SV27 @ SV44 @ SV47 )
= $true )
| ( ( equalish @ SV9 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(180,plain,
! [SV28: $i,SV48: $i,SV10: $i,SV45: $i] :
( ( ( product @ SV45 @ SV10 @ SV48 )
= $false )
| ( ( product @ SV45 @ SV28 @ SV48 )
= $true )
| ( ( equalish @ SV10 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(181,plain,
! [SV29: $i,SV11: $i,SV49: $i,SV46: $i] :
( ( ( product @ SV46 @ SV49 @ SV11 )
= $false )
| ( ( product @ SV46 @ SV49 @ SV29 )
= $true )
| ( ( equalish @ SV11 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(182,plain,
! [SV35: $i,SV50: $i,SV32: $i,SV18: $i] :
( ( ( product @ SV18 @ SV32 @ SV50 )
= $false )
| ( ( equalish @ SV35 @ SV50 )
= $true )
| ( ( product @ SV18 @ SV32 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(183,plain,
! [SV19: $i,SV36: $i,SV51: $i,SV38: $i,SV33: $i] :
( ( ( ~ ( product @ SV33 @ SV38 @ SV51 ) )
= $true )
| ( ( ! [SY123: $i] :
( ~ ( product @ SV36 @ SV38 @ SY123 )
| ( product @ SV19 @ SV51 @ SY123 ) ) )
= $true )
| ( ( product @ SV19 @ SV33 @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(184,plain,
! [SV37: $i,SV20: $i,SV52: $i,SV39: $i,SV34: $i] :
( ( ( ~ ( product @ SV34 @ SV39 @ SV52 ) )
= $true )
| ( ( ! [SY124: $i] :
( ~ ( product @ SV20 @ SV52 @ SY124 )
| ( product @ SV37 @ SV39 @ SY124 ) ) )
= $true )
| ( ( product @ SV20 @ SV34 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(185,plain,
! [SV53: $i,SV40: $i,SV21: $i] :
( ( ( ~ ( product @ SV21 @ ( inverse @ SV40 ) @ SV53 ) )
= $true )
| ( ( subgroup_member @ SV53 )
= $true )
| ( ( subgroup_member @ SV40 )
= $false )
| ( ( subgroup_member @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(186,plain,
! [SV19: $i,SV36: $i,SV51: $i,SV38: $i,SV33: $i] :
( ( ( product @ SV33 @ SV38 @ SV51 )
= $false )
| ( ( ! [SY123: $i] :
( ~ ( product @ SV36 @ SV38 @ SY123 )
| ( product @ SV19 @ SV51 @ SY123 ) ) )
= $true )
| ( ( product @ SV19 @ SV33 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(187,plain,
! [SV37: $i,SV20: $i,SV52: $i,SV39: $i,SV34: $i] :
( ( ( product @ SV34 @ SV39 @ SV52 )
= $false )
| ( ( ! [SY124: $i] :
( ~ ( product @ SV20 @ SV52 @ SY124 )
| ( product @ SV37 @ SV39 @ SY124 ) ) )
= $true )
| ( ( product @ SV20 @ SV34 @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(188,plain,
! [SV53: $i,SV40: $i,SV21: $i] :
( ( ( product @ SV21 @ ( inverse @ SV40 ) @ SV53 )
= $false )
| ( ( subgroup_member @ SV53 )
= $true )
| ( ( subgroup_member @ SV40 )
= $false )
| ( ( subgroup_member @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(189,plain,
! [SV33: $i,SV51: $i,SV19: $i,SV54: $i,SV38: $i,SV36: $i] :
( ( ( ~ ( product @ SV36 @ SV38 @ SV54 )
| ( product @ SV19 @ SV51 @ SV54 ) )
= $true )
| ( ( product @ SV33 @ SV38 @ SV51 )
= $false )
| ( ( product @ SV19 @ SV33 @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(190,plain,
! [SV34: $i,SV39: $i,SV37: $i,SV55: $i,SV52: $i,SV20: $i] :
( ( ( ~ ( product @ SV20 @ SV52 @ SV55 )
| ( product @ SV37 @ SV39 @ SV55 ) )
= $true )
| ( ( product @ SV34 @ SV39 @ SV52 )
= $false )
| ( ( product @ SV20 @ SV34 @ SV37 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(191,plain,
! [SV33: $i,SV51: $i,SV19: $i,SV54: $i,SV38: $i,SV36: $i] :
( ( ( ~ ( product @ SV36 @ SV38 @ SV54 ) )
= $true )
| ( ( product @ SV19 @ SV51 @ SV54 )
= $true )
| ( ( product @ SV33 @ SV38 @ SV51 )
= $false )
| ( ( product @ SV19 @ SV33 @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(192,plain,
! [SV34: $i,SV39: $i,SV37: $i,SV55: $i,SV52: $i,SV20: $i] :
( ( ( ~ ( product @ SV20 @ SV52 @ SV55 ) )
= $true )
| ( ( product @ SV37 @ SV39 @ SV55 )
= $true )
| ( ( product @ SV34 @ SV39 @ SV52 )
= $false )
| ( ( product @ SV20 @ SV34 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(193,plain,
! [SV33: $i,SV51: $i,SV19: $i,SV54: $i,SV38: $i,SV36: $i] :
( ( ( product @ SV36 @ SV38 @ SV54 )
= $false )
| ( ( product @ SV19 @ SV51 @ SV54 )
= $true )
| ( ( product @ SV33 @ SV38 @ SV51 )
= $false )
| ( ( product @ SV19 @ SV33 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(194,plain,
! [SV34: $i,SV39: $i,SV37: $i,SV55: $i,SV52: $i,SV20: $i] :
( ( ( product @ SV20 @ SV52 @ SV55 )
= $false )
| ( ( product @ SV37 @ SV39 @ SV55 )
= $true )
| ( ( product @ SV34 @ SV39 @ SV52 )
= $false )
| ( ( product @ SV20 @ SV34 @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(195,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[60,194,193,188,182,181,180,179,171,166,161,152,151,138,136,121,115,103,97,96,95,94,84]) ).
thf(196,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[195]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP033-3 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.12/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n014.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 13 06:33:52 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.18/0.35
% 0.18/0.35 No.of.Axioms: 22
% 0.18/0.35
% 0.18/0.35 Length.of.Defs: 0
% 0.18/0.35
% 0.18/0.35 Contains.Choice.Funs: false
% 0.18/0.37 .
% 0.18/0.37 (rf:0,axioms:22,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:24,loop_count:0,foatp_calls:0,translation:fof_full)...........
% 0.18/0.46
% 0.18/0.46 ********************************
% 0.18/0.46 * All subproblems solved! *
% 0.18/0.46 ********************************
% 0.18/0.46 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:22,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:195,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.18/0.47
% 0.18/0.47 %**** Beginning of derivation protocol ****
% 0.18/0.47 % SZS output start CNFRefutation
% See solution above
% 0.18/0.47
% 0.18/0.47 %**** End of derivation protocol ****
% 0.18/0.47 %**** no. of clauses in derivation: 196 ****
% 0.18/0.47 %**** clause counter: 195 ****
% 0.18/0.47
% 0.18/0.47 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:22,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:195,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------