%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GRP039-6 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:20:09 AM UTC 2026
% Result : Unsatisfiable 3.86s 0.96s
% Output : CNFRefutation 3.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 23
% Syntax : Number of formulae : 171 ( 110 unt; 0 typ; 0 def)
% Number of atoms : 903 ( 225 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 1628 ( 209 ~; 282 |; 0 &;1137 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 7 con; 0-3 aty)
% Number of variables : 508 ( 0 ^; 508 !; 0 ?; 508 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_b,type,
b: $i ).
thf(tp_c,type,
c: $i ).
thf(tp_d,type,
d: $i ).
thf(tp_element_in_O2,type,
element_in_O2: $i > $i > $i ).
thf(tp_equalish,type,
equalish: $i > $i > $o ).
thf(tp_identity,type,
identity: $i ).
thf(tp_inverse,type,
inverse: $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] :
( ( product @ A @ ( element_in_O2 @ A @ B ) @ B )
| ( subgroup_member @ B )
| ( subgroup_member @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_O2) ).
thf(2,axiom,
! [A: $i,B: $i] :
( ( subgroup_member @ ( element_in_O2 @ A @ B ) )
| ( subgroup_member @ B )
| ( subgroup_member @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',an_element_in_O2) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ D @ B @ C )
| ( equalish @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ A @ D @ C )
| ( equalish @ D @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
thf(5,axiom,
subgroup_member @ identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_is_in_subgroup) ).
thf(6,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',well_defined) ).
thf(7,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(8,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(9,axiom,
! [X: $i] : ( product @ X @ ( inverse @ X ) @ identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
thf(10,axiom,
! [X: $i] : ( product @ ( inverse @ X ) @ X @ identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(11,axiom,
! [X: $i] : ( product @ X @ identity @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
thf(12,axiom,
! [X: $i] : ( product @ identity @ X @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( subgroup_member @ A )
| ~ ( subgroup_member @ B )
| ~ ( product @ A @ B @ C )
| ( subgroup_member @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_product) ).
thf(14,axiom,
! [X: $i] :
( ~ ( subgroup_member @ X )
| ( subgroup_member @ ( inverse @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_inverse) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ ( element_in_O2 @ A @ C ) @ ( element_in_O2 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_in_O2_substitution2) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ ( element_in_O2 @ C @ A ) @ ( element_in_O2 @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_in_O2_substitution1) ).
thf(17,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(18,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(19,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(20,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[19]) ).
thf(21,negated_conjecture,
~ ( subgroup_member @ d ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_d_is_in_subgroup) ).
thf(22,negated_conjecture,
product @ a @ c @ d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_c_is_d) ).
thf(23,negated_conjecture,
product @ b @ ( inverse @ a ) @ c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
thf(24,negated_conjecture,
subgroup_member @ b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_in_subgroup) ).
thf(25,plain,
$false = $false,
inference(unfold_def,[status(thm)],[20]) ).
thf(26,plain,
( ( ! [A: $i,B: $i] :
( ( product @ A @ ( element_in_O2 @ A @ B ) @ B )
| ( subgroup_member @ B )
| ( subgroup_member @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(27,plain,
( ( ! [A: $i,B: $i] :
( ( subgroup_member @ ( element_in_O2 @ A @ B ) )
| ( subgroup_member @ B )
| ( subgroup_member @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(28,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ D @ B @ C )
| ( equalish @ D @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(29,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ A @ D @ C )
| ( equalish @ D @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(30,plain,
( ( subgroup_member @ identity )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(31,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)],[6]) ).
thf(32,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)],[7]) ).
thf(33,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)],[8]) ).
thf(34,plain,
( ( ! [X: $i] : ( product @ X @ ( inverse @ X ) @ identity ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(35,plain,
( ( ! [X: $i] : ( product @ ( inverse @ X ) @ X @ identity ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(36,plain,
( ( ! [X: $i] : ( product @ X @ identity @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(37,plain,
( ( ! [X: $i] : ( product @ identity @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(38,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subgroup_member @ A )
| ~ ( subgroup_member @ B )
| ~ ( product @ A @ B @ C )
| ( subgroup_member @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(39,plain,
( ( ! [X: $i] :
( ~ ( subgroup_member @ X )
| ( subgroup_member @ ( inverse @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(40,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ ( element_in_O2 @ A @ C ) @ ( element_in_O2 @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(41,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ ( element_in_O2 @ C @ A ) @ ( element_in_O2 @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(42,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)],[17]) ).
thf(43,plain,
( ( ! [A: $i,B: $i] :
( ~ ( equalish @ A @ B )
| ~ ( subgroup_member @ A )
| ( subgroup_member @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(44,plain,
( ( ~ ( subgroup_member @ d ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(45,plain,
( ( product @ a @ c @ d )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(46,plain,
( ( product @ b @ ( inverse @ a ) @ c )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(47,plain,
( ( subgroup_member @ b )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(48,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[25]) ).
thf(49,plain,
( ( subgroup_member @ b )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(50,plain,
( ( product @ b @ ( inverse @ a ) @ c )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(51,plain,
( ( product @ a @ c @ d )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(52,plain,
( ( ~ ( subgroup_member @ d ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(53,plain,
( ( ! [A: $i,B: $i] :
( ~ ( equalish @ A @ B )
| ~ ( subgroup_member @ A )
| ( subgroup_member @ B ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(54,plain,
( ( ! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( product @ W @ Z @ X )
| ( product @ W @ Z @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(55,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ ( element_in_O2 @ C @ A ) @ ( element_in_O2 @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(56,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ ( element_in_O2 @ A @ C ) @ ( element_in_O2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(57,plain,
( ( ! [X: $i] :
( ~ ( subgroup_member @ X )
| ( subgroup_member @ ( inverse @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(58,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subgroup_member @ A )
| ~ ( subgroup_member @ B )
| ~ ( product @ A @ B @ C )
| ( subgroup_member @ C ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(59,plain,
( ( ! [X: $i] : ( product @ identity @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(60,plain,
( ( ! [X: $i] : ( product @ X @ identity @ X ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(61,plain,
( ( ! [X: $i] : ( product @ ( inverse @ X ) @ X @ identity ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(62,plain,
( ( ! [X: $i] : ( product @ X @ ( inverse @ X ) @ identity ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(63,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(copy,[status(thm)],[33]) ).
thf(64,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(copy,[status(thm)],[32]) ).
thf(65,plain,
( ( ! [X: $i,Y: $i,Z: $i,W: $i] :
( ~ ( product @ X @ Y @ Z )
| ~ ( product @ X @ Y @ W )
| ( equalish @ Z @ W ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(66,plain,
( ( subgroup_member @ identity )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(67,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ A @ D @ C )
| ( equalish @ D @ B ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(68,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ D @ B @ C )
| ( equalish @ D @ A ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(69,plain,
( ( ! [A: $i,B: $i] :
( ( subgroup_member @ ( element_in_O2 @ A @ B ) )
| ( subgroup_member @ B )
| ( subgroup_member @ A ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(70,plain,
( ( ! [A: $i,B: $i] :
( ( product @ A @ ( element_in_O2 @ A @ B ) @ B )
| ( subgroup_member @ B )
| ( subgroup_member @ A ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(71,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[48]) ).
thf(72,plain,
( ( subgroup_member @ d )
= $false ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(73,plain,
! [SV1: $i] :
( ( ! [SY48: $i] :
( ~ ( equalish @ SV1 @ SY48 )
| ~ ( subgroup_member @ SV1 )
| ( subgroup_member @ SY48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(74,plain,
! [SV2: $i] :
( ( ! [SY49: $i,SY50: $i,SY51: $i] :
( ~ ( equalish @ SV2 @ SY49 )
| ~ ( product @ SY50 @ SY51 @ SV2 )
| ( product @ SY50 @ SY51 @ SY49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(75,plain,
! [SV3: $i] :
( ( ! [SY52: $i,SY53: $i] :
( ~ ( equalish @ SV3 @ SY52 )
| ( equalish @ ( element_in_O2 @ SY53 @ SV3 ) @ ( element_in_O2 @ SY53 @ SY52 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(76,plain,
! [SV4: $i] :
( ( ! [SY54: $i,SY55: $i] :
( ~ ( equalish @ SV4 @ SY54 )
| ( equalish @ ( element_in_O2 @ SV4 @ SY55 ) @ ( element_in_O2 @ SY54 @ SY55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(77,plain,
! [SV5: $i] :
( ( ~ ( subgroup_member @ SV5 )
| ( subgroup_member @ ( inverse @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(78,plain,
! [SV6: $i] :
( ( ! [SY56: $i,SY57: $i] :
( ~ ( subgroup_member @ SV6 )
| ~ ( subgroup_member @ SY56 )
| ~ ( product @ SV6 @ SY56 @ SY57 )
| ( subgroup_member @ SY57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(79,plain,
! [SV7: $i] :
( ( product @ identity @ SV7 @ SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(80,plain,
! [SV8: $i] :
( ( product @ SV8 @ identity @ SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(81,plain,
! [SV9: $i] :
( ( product @ ( inverse @ SV9 ) @ SV9 @ identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(82,plain,
! [SV10: $i] :
( ( product @ SV10 @ ( inverse @ SV10 ) @ identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(83,plain,
! [SV11: $i] :
( ( ! [SY58: $i,SY59: $i,SY60: $i,SY61: $i,SY62: $i] :
( ~ ( product @ SV11 @ SY58 @ SY59 )
| ~ ( product @ SY58 @ SY60 @ SY61 )
| ~ ( product @ SY59 @ SY60 @ SY62 )
| ( product @ SV11 @ SY61 @ SY62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(84,plain,
! [SV12: $i] :
( ( ! [SY63: $i,SY64: $i,SY65: $i,SY66: $i,SY67: $i] :
( ~ ( product @ SV12 @ SY63 @ SY64 )
| ~ ( product @ SY63 @ SY65 @ SY66 )
| ~ ( product @ SV12 @ SY66 @ SY67 )
| ( product @ SY64 @ SY65 @ SY67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(85,plain,
! [SV13: $i] :
( ( ! [SY68: $i,SY69: $i,SY70: $i] :
( ~ ( product @ SV13 @ SY68 @ SY69 )
| ~ ( product @ SV13 @ SY68 @ SY70 )
| ( equalish @ SY69 @ SY70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(86,plain,
! [SV14: $i] :
( ( ! [SY71: $i,SY72: $i,SY73: $i] :
( ~ ( product @ SV14 @ SY71 @ SY72 )
| ~ ( product @ SV14 @ SY73 @ SY72 )
| ( equalish @ SY73 @ SY71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(87,plain,
! [SV15: $i] :
( ( ! [SY74: $i,SY75: $i,SY76: $i] :
( ~ ( product @ SV15 @ SY74 @ SY75 )
| ~ ( product @ SY76 @ SY74 @ SY75 )
| ( equalish @ SY76 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(88,plain,
! [SV16: $i] :
( ( ! [SY77: $i] :
( ( subgroup_member @ ( element_in_O2 @ SV16 @ SY77 ) )
| ( subgroup_member @ SY77 )
| ( subgroup_member @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(89,plain,
! [SV17: $i] :
( ( ! [SY78: $i] :
( ( product @ SV17 @ ( element_in_O2 @ SV17 @ SY78 ) @ SY78 )
| ( subgroup_member @ SY78 )
| ( subgroup_member @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(90,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(91,plain,
! [SV18: $i,SV1: $i] :
( ( ~ ( equalish @ SV1 @ SV18 )
| ~ ( subgroup_member @ SV1 )
| ( subgroup_member @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(92,plain,
! [SV19: $i,SV2: $i] :
( ( ! [SY79: $i,SY80: $i] :
( ~ ( equalish @ SV2 @ SV19 )
| ~ ( product @ SY79 @ SY80 @ SV2 )
| ( product @ SY79 @ SY80 @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(93,plain,
! [SV20: $i,SV3: $i] :
( ( ! [SY81: $i] :
( ~ ( equalish @ SV3 @ SV20 )
| ( equalish @ ( element_in_O2 @ SY81 @ SV3 ) @ ( element_in_O2 @ SY81 @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(94,plain,
! [SV21: $i,SV4: $i] :
( ( ! [SY82: $i] :
( ~ ( equalish @ SV4 @ SV21 )
| ( equalish @ ( element_in_O2 @ SV4 @ SY82 ) @ ( element_in_O2 @ SV21 @ SY82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(95,plain,
! [SV5: $i] :
( ( ( ~ ( subgroup_member @ SV5 ) )
= $true )
| ( ( subgroup_member @ ( inverse @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(96,plain,
! [SV22: $i,SV6: $i] :
( ( ! [SY83: $i] :
( ~ ( subgroup_member @ SV6 )
| ~ ( subgroup_member @ SV22 )
| ~ ( product @ SV6 @ SV22 @ SY83 )
| ( subgroup_member @ SY83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(97,plain,
! [SV23: $i,SV11: $i] :
( ( ! [SY84: $i,SY85: $i,SY86: $i,SY87: $i] :
( ~ ( product @ SV11 @ SV23 @ SY84 )
| ~ ( product @ SV23 @ SY85 @ SY86 )
| ~ ( product @ SY84 @ SY85 @ SY87 )
| ( product @ SV11 @ SY86 @ SY87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(98,plain,
! [SV24: $i,SV12: $i] :
( ( ! [SY88: $i,SY89: $i,SY90: $i,SY91: $i] :
( ~ ( product @ SV12 @ SV24 @ SY88 )
| ~ ( product @ SV24 @ SY89 @ SY90 )
| ~ ( product @ SV12 @ SY90 @ SY91 )
| ( product @ SY88 @ SY89 @ SY91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(99,plain,
! [SV25: $i,SV13: $i] :
( ( ! [SY92: $i,SY93: $i] :
( ~ ( product @ SV13 @ SV25 @ SY92 )
| ~ ( product @ SV13 @ SV25 @ SY93 )
| ( equalish @ SY92 @ SY93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(100,plain,
! [SV26: $i,SV14: $i] :
( ( ! [SY94: $i,SY95: $i] :
( ~ ( product @ SV14 @ SV26 @ SY94 )
| ~ ( product @ SV14 @ SY95 @ SY94 )
| ( equalish @ SY95 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(101,plain,
! [SV27: $i,SV15: $i] :
( ( ! [SY96: $i,SY97: $i] :
( ~ ( product @ SV15 @ SV27 @ SY96 )
| ~ ( product @ SY97 @ SV27 @ SY96 )
| ( equalish @ SY97 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(102,plain,
! [SV28: $i,SV16: $i] :
( ( ( subgroup_member @ ( element_in_O2 @ SV16 @ SV28 ) )
| ( subgroup_member @ SV28 )
| ( subgroup_member @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(103,plain,
! [SV29: $i,SV17: $i] :
( ( ( product @ SV17 @ ( element_in_O2 @ SV17 @ SV29 ) @ SV29 )
| ( subgroup_member @ SV29 )
| ( subgroup_member @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(104,plain,
! [SV18: $i,SV1: $i] :
( ( ( ~ ( equalish @ SV1 @ SV18 ) )
= $true )
| ( ( ~ ( subgroup_member @ SV1 )
| ( subgroup_member @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(105,plain,
! [SV30: $i,SV19: $i,SV2: $i] :
( ( ! [SY98: $i] :
( ~ ( equalish @ SV2 @ SV19 )
| ~ ( product @ SV30 @ SY98 @ SV2 )
| ( product @ SV30 @ SY98 @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(106,plain,
! [SV31: $i,SV20: $i,SV3: $i] :
( ( ~ ( equalish @ SV3 @ SV20 )
| ( equalish @ ( element_in_O2 @ SV31 @ SV3 ) @ ( element_in_O2 @ SV31 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(107,plain,
! [SV32: $i,SV21: $i,SV4: $i] :
( ( ~ ( equalish @ SV4 @ SV21 )
| ( equalish @ ( element_in_O2 @ SV4 @ SV32 ) @ ( element_in_O2 @ SV21 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(108,plain,
! [SV5: $i] :
( ( ( subgroup_member @ SV5 )
= $false )
| ( ( subgroup_member @ ( inverse @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(109,plain,
! [SV33: $i,SV22: $i,SV6: $i] :
( ( ~ ( subgroup_member @ SV6 )
| ~ ( subgroup_member @ SV22 )
| ~ ( product @ SV6 @ SV22 @ SV33 )
| ( subgroup_member @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(110,plain,
! [SV34: $i,SV23: $i,SV11: $i] :
( ( ! [SY99: $i,SY100: $i,SY101: $i] :
( ~ ( product @ SV11 @ SV23 @ SV34 )
| ~ ( product @ SV23 @ SY99 @ SY100 )
| ~ ( product @ SV34 @ SY99 @ SY101 )
| ( product @ SV11 @ SY100 @ SY101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(111,plain,
! [SV35: $i,SV24: $i,SV12: $i] :
( ( ! [SY102: $i,SY103: $i,SY104: $i] :
( ~ ( product @ SV12 @ SV24 @ SV35 )
| ~ ( product @ SV24 @ SY102 @ SY103 )
| ~ ( product @ SV12 @ SY103 @ SY104 )
| ( product @ SV35 @ SY102 @ SY104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(112,plain,
! [SV36: $i,SV25: $i,SV13: $i] :
( ( ! [SY105: $i] :
( ~ ( product @ SV13 @ SV25 @ SV36 )
| ~ ( product @ SV13 @ SV25 @ SY105 )
| ( equalish @ SV36 @ SY105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(113,plain,
! [SV37: $i,SV26: $i,SV14: $i] :
( ( ! [SY106: $i] :
( ~ ( product @ SV14 @ SV26 @ SV37 )
| ~ ( product @ SV14 @ SY106 @ SV37 )
| ( equalish @ SY106 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(114,plain,
! [SV38: $i,SV27: $i,SV15: $i] :
( ( ! [SY107: $i] :
( ~ ( product @ SV15 @ SV27 @ SV38 )
| ~ ( product @ SY107 @ SV27 @ SV38 )
| ( equalish @ SY107 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(115,plain,
! [SV28: $i,SV16: $i] :
( ( ( subgroup_member @ ( element_in_O2 @ SV16 @ SV28 ) )
= $true )
| ( ( ( subgroup_member @ SV28 )
| ( subgroup_member @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(116,plain,
! [SV29: $i,SV17: $i] :
( ( ( product @ SV17 @ ( element_in_O2 @ SV17 @ SV29 ) @ SV29 )
= $true )
| ( ( ( subgroup_member @ SV29 )
| ( subgroup_member @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(117,plain,
! [SV18: $i,SV1: $i] :
( ( ( equalish @ SV1 @ SV18 )
= $false )
| ( ( ~ ( subgroup_member @ SV1 )
| ( subgroup_member @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(118,plain,
! [SV39: $i,SV30: $i,SV19: $i,SV2: $i] :
( ( ~ ( equalish @ SV2 @ SV19 )
| ~ ( product @ SV30 @ SV39 @ SV2 )
| ( product @ SV30 @ SV39 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(119,plain,
! [SV31: $i,SV20: $i,SV3: $i] :
( ( ( ~ ( equalish @ SV3 @ SV20 ) )
= $true )
| ( ( equalish @ ( element_in_O2 @ SV31 @ SV3 ) @ ( element_in_O2 @ SV31 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(120,plain,
! [SV32: $i,SV21: $i,SV4: $i] :
( ( ( ~ ( equalish @ SV4 @ SV21 ) )
= $true )
| ( ( equalish @ ( element_in_O2 @ SV4 @ SV32 ) @ ( element_in_O2 @ SV21 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(121,plain,
! [SV33: $i,SV22: $i,SV6: $i] :
( ( ( ~ ( subgroup_member @ SV6 ) )
= $true )
| ( ( ~ ( subgroup_member @ SV22 )
| ~ ( product @ SV6 @ SV22 @ SV33 )
| ( subgroup_member @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(122,plain,
! [SV40: $i,SV34: $i,SV23: $i,SV11: $i] :
( ( ! [SY108: $i,SY109: $i] :
( ~ ( product @ SV11 @ SV23 @ SV34 )
| ~ ( product @ SV23 @ SV40 @ SY108 )
| ~ ( product @ SV34 @ SV40 @ SY109 )
| ( product @ SV11 @ SY108 @ SY109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(123,plain,
! [SV41: $i,SV35: $i,SV24: $i,SV12: $i] :
( ( ! [SY110: $i,SY111: $i] :
( ~ ( product @ SV12 @ SV24 @ SV35 )
| ~ ( product @ SV24 @ SV41 @ SY110 )
| ~ ( product @ SV12 @ SY110 @ SY111 )
| ( product @ SV35 @ SV41 @ SY111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(124,plain,
! [SV42: $i,SV36: $i,SV25: $i,SV13: $i] :
( ( ~ ( product @ SV13 @ SV25 @ SV36 )
| ~ ( product @ SV13 @ SV25 @ SV42 )
| ( equalish @ SV36 @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(125,plain,
! [SV43: $i,SV37: $i,SV26: $i,SV14: $i] :
( ( ~ ( product @ SV14 @ SV26 @ SV37 )
| ~ ( product @ SV14 @ SV43 @ SV37 )
| ( equalish @ SV43 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(126,plain,
! [SV44: $i,SV38: $i,SV27: $i,SV15: $i] :
( ( ~ ( product @ SV15 @ SV27 @ SV38 )
| ~ ( product @ SV44 @ SV27 @ SV38 )
| ( equalish @ SV44 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(127,plain,
! [SV16: $i,SV28: $i] :
( ( ( subgroup_member @ SV28 )
= $true )
| ( ( subgroup_member @ SV16 )
= $true )
| ( ( subgroup_member @ ( element_in_O2 @ SV16 @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(128,plain,
! [SV17: $i,SV29: $i] :
( ( ( subgroup_member @ SV29 )
= $true )
| ( ( subgroup_member @ SV17 )
= $true )
| ( ( product @ SV17 @ ( element_in_O2 @ SV17 @ SV29 ) @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(129,plain,
! [SV18: $i,SV1: $i] :
( ( ( ~ ( subgroup_member @ SV1 ) )
= $true )
| ( ( subgroup_member @ SV18 )
= $true )
| ( ( equalish @ SV1 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(130,plain,
! [SV39: $i,SV30: $i,SV19: $i,SV2: $i] :
( ( ( ~ ( equalish @ SV2 @ SV19 ) )
= $true )
| ( ( ~ ( product @ SV30 @ SV39 @ SV2 )
| ( product @ SV30 @ SV39 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(131,plain,
! [SV31: $i,SV20: $i,SV3: $i] :
( ( ( equalish @ SV3 @ SV20 )
= $false )
| ( ( equalish @ ( element_in_O2 @ SV31 @ SV3 ) @ ( element_in_O2 @ SV31 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(132,plain,
! [SV32: $i,SV21: $i,SV4: $i] :
( ( ( equalish @ SV4 @ SV21 )
= $false )
| ( ( equalish @ ( element_in_O2 @ SV4 @ SV32 ) @ ( element_in_O2 @ SV21 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(133,plain,
! [SV33: $i,SV22: $i,SV6: $i] :
( ( ( subgroup_member @ SV6 )
= $false )
| ( ( ~ ( subgroup_member @ SV22 )
| ~ ( product @ SV6 @ SV22 @ SV33 )
| ( subgroup_member @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(134,plain,
! [SV45: $i,SV40: $i,SV34: $i,SV23: $i,SV11: $i] :
( ( ! [SY112: $i] :
( ~ ( product @ SV11 @ SV23 @ SV34 )
| ~ ( product @ SV23 @ SV40 @ SV45 )
| ~ ( product @ SV34 @ SV40 @ SY112 )
| ( product @ SV11 @ SV45 @ SY112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(135,plain,
! [SV46: $i,SV41: $i,SV35: $i,SV24: $i,SV12: $i] :
( ( ! [SY113: $i] :
( ~ ( product @ SV12 @ SV24 @ SV35 )
| ~ ( product @ SV24 @ SV41 @ SV46 )
| ~ ( product @ SV12 @ SV46 @ SY113 )
| ( product @ SV35 @ SV41 @ SY113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(136,plain,
! [SV42: $i,SV36: $i,SV25: $i,SV13: $i] :
( ( ( ~ ( product @ SV13 @ SV25 @ SV36 ) )
= $true )
| ( ( ~ ( product @ SV13 @ SV25 @ SV42 )
| ( equalish @ SV36 @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(137,plain,
! [SV43: $i,SV37: $i,SV26: $i,SV14: $i] :
( ( ( ~ ( product @ SV14 @ SV26 @ SV37 ) )
= $true )
| ( ( ~ ( product @ SV14 @ SV43 @ SV37 )
| ( equalish @ SV43 @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(138,plain,
! [SV44: $i,SV38: $i,SV27: $i,SV15: $i] :
( ( ( ~ ( product @ SV15 @ SV27 @ SV38 ) )
= $true )
| ( ( ~ ( product @ SV44 @ SV27 @ SV38 )
| ( equalish @ SV44 @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(139,plain,
! [SV18: $i,SV1: $i] :
( ( ( subgroup_member @ SV1 )
= $false )
| ( ( subgroup_member @ SV18 )
= $true )
| ( ( equalish @ SV1 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(140,plain,
! [SV39: $i,SV30: $i,SV19: $i,SV2: $i] :
( ( ( equalish @ SV2 @ SV19 )
= $false )
| ( ( ~ ( product @ SV30 @ SV39 @ SV2 )
| ( product @ SV30 @ SV39 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(141,plain,
! [SV33: $i,SV6: $i,SV22: $i] :
( ( ( ~ ( subgroup_member @ SV22 ) )
= $true )
| ( ( ~ ( product @ SV6 @ SV22 @ SV33 )
| ( subgroup_member @ SV33 ) )
= $true )
| ( ( subgroup_member @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(142,plain,
! [SV47: $i,SV45: $i,SV40: $i,SV34: $i,SV23: $i,SV11: $i] :
( ( ~ ( product @ SV11 @ SV23 @ SV34 )
| ~ ( product @ SV23 @ SV40 @ SV45 )
| ~ ( product @ SV34 @ SV40 @ SV47 )
| ( product @ SV11 @ SV45 @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(143,plain,
! [SV48: $i,SV46: $i,SV41: $i,SV35: $i,SV24: $i,SV12: $i] :
( ( ~ ( product @ SV12 @ SV24 @ SV35 )
| ~ ( product @ SV24 @ SV41 @ SV46 )
| ~ ( product @ SV12 @ SV46 @ SV48 )
| ( product @ SV35 @ SV41 @ SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(144,plain,
! [SV42: $i,SV36: $i,SV25: $i,SV13: $i] :
( ( ( product @ SV13 @ SV25 @ SV36 )
= $false )
| ( ( ~ ( product @ SV13 @ SV25 @ SV42 )
| ( equalish @ SV36 @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(145,plain,
! [SV43: $i,SV37: $i,SV26: $i,SV14: $i] :
( ( ( product @ SV14 @ SV26 @ SV37 )
= $false )
| ( ( ~ ( product @ SV14 @ SV43 @ SV37 )
| ( equalish @ SV43 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(146,plain,
! [SV44: $i,SV38: $i,SV27: $i,SV15: $i] :
( ( ( product @ SV15 @ SV27 @ SV38 )
= $false )
| ( ( ~ ( product @ SV44 @ SV27 @ SV38 )
| ( equalish @ SV44 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(147,plain,
! [SV19: $i,SV2: $i,SV39: $i,SV30: $i] :
( ( ( ~ ( product @ SV30 @ SV39 @ SV2 ) )
= $true )
| ( ( product @ SV30 @ SV39 @ SV19 )
= $true )
| ( ( equalish @ SV2 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(148,plain,
! [SV33: $i,SV6: $i,SV22: $i] :
( ( ( subgroup_member @ SV22 )
= $false )
| ( ( ~ ( product @ SV6 @ SV22 @ SV33 )
| ( subgroup_member @ SV33 ) )
= $true )
| ( ( subgroup_member @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(149,plain,
! [SV47: $i,SV45: $i,SV40: $i,SV34: $i,SV23: $i,SV11: $i] :
( ( ( ~ ( product @ SV11 @ SV23 @ SV34 ) )
= $true )
| ( ( ~ ( product @ SV23 @ SV40 @ SV45 )
| ~ ( product @ SV34 @ SV40 @ SV47 )
| ( product @ SV11 @ SV45 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(150,plain,
! [SV48: $i,SV46: $i,SV41: $i,SV35: $i,SV24: $i,SV12: $i] :
( ( ( ~ ( product @ SV12 @ SV24 @ SV35 ) )
= $true )
| ( ( ~ ( product @ SV24 @ SV41 @ SV46 )
| ~ ( product @ SV12 @ SV46 @ SV48 )
| ( product @ SV35 @ SV41 @ SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(151,plain,
! [SV36: $i,SV42: $i,SV25: $i,SV13: $i] :
( ( ( ~ ( product @ SV13 @ SV25 @ SV42 ) )
= $true )
| ( ( equalish @ SV36 @ SV42 )
= $true )
| ( ( product @ SV13 @ SV25 @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(152,plain,
! [SV26: $i,SV37: $i,SV43: $i,SV14: $i] :
( ( ( ~ ( product @ SV14 @ SV43 @ SV37 ) )
= $true )
| ( ( equalish @ SV43 @ SV26 )
= $true )
| ( ( product @ SV14 @ SV26 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(153,plain,
! [SV15: $i,SV38: $i,SV27: $i,SV44: $i] :
( ( ( ~ ( product @ SV44 @ SV27 @ SV38 ) )
= $true )
| ( ( equalish @ SV44 @ SV15 )
= $true )
| ( ( product @ SV15 @ SV27 @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(154,plain,
! [SV19: $i,SV2: $i,SV39: $i,SV30: $i] :
( ( ( product @ SV30 @ SV39 @ SV2 )
= $false )
| ( ( product @ SV30 @ SV39 @ SV19 )
= $true )
| ( ( equalish @ SV2 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(155,plain,
! [SV33: $i,SV22: $i,SV6: $i] :
( ( ( ~ ( product @ SV6 @ SV22 @ SV33 ) )
= $true )
| ( ( subgroup_member @ SV33 )
= $true )
| ( ( subgroup_member @ SV22 )
= $false )
| ( ( subgroup_member @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(156,plain,
! [SV47: $i,SV45: $i,SV40: $i,SV34: $i,SV23: $i,SV11: $i] :
( ( ( product @ SV11 @ SV23 @ SV34 )
= $false )
| ( ( ~ ( product @ SV23 @ SV40 @ SV45 )
| ~ ( product @ SV34 @ SV40 @ SV47 )
| ( product @ SV11 @ SV45 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(157,plain,
! [SV48: $i,SV46: $i,SV41: $i,SV35: $i,SV24: $i,SV12: $i] :
( ( ( product @ SV12 @ SV24 @ SV35 )
= $false )
| ( ( ~ ( product @ SV24 @ SV41 @ SV46 )
| ~ ( product @ SV12 @ SV46 @ SV48 )
| ( product @ SV35 @ SV41 @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(158,plain,
! [SV36: $i,SV42: $i,SV25: $i,SV13: $i] :
( ( ( product @ SV13 @ SV25 @ SV42 )
= $false )
| ( ( equalish @ SV36 @ SV42 )
= $true )
| ( ( product @ SV13 @ SV25 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(159,plain,
! [SV26: $i,SV37: $i,SV43: $i,SV14: $i] :
( ( ( product @ SV14 @ SV43 @ SV37 )
= $false )
| ( ( equalish @ SV43 @ SV26 )
= $true )
| ( ( product @ SV14 @ SV26 @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(160,plain,
! [SV15: $i,SV38: $i,SV27: $i,SV44: $i] :
( ( ( product @ SV44 @ SV27 @ SV38 )
= $false )
| ( ( equalish @ SV44 @ SV15 )
= $true )
| ( ( product @ SV15 @ SV27 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(161,plain,
! [SV33: $i,SV22: $i,SV6: $i] :
( ( ( product @ SV6 @ SV22 @ SV33 )
= $false )
| ( ( subgroup_member @ SV33 )
= $true )
| ( ( subgroup_member @ SV22 )
= $false )
| ( ( subgroup_member @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(162,plain,
! [SV11: $i,SV47: $i,SV34: $i,SV45: $i,SV40: $i,SV23: $i] :
( ( ( ~ ( product @ SV23 @ SV40 @ SV45 ) )
= $true )
| ( ( ~ ( product @ SV34 @ SV40 @ SV47 )
| ( product @ SV11 @ SV45 @ SV47 ) )
= $true )
| ( ( product @ SV11 @ SV23 @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(163,plain,
! [SV35: $i,SV48: $i,SV12: $i,SV46: $i,SV41: $i,SV24: $i] :
( ( ( ~ ( product @ SV24 @ SV41 @ SV46 ) )
= $true )
| ( ( ~ ( product @ SV12 @ SV46 @ SV48 )
| ( product @ SV35 @ SV41 @ SV48 ) )
= $true )
| ( ( product @ SV12 @ SV24 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(164,plain,
! [SV11: $i,SV47: $i,SV34: $i,SV45: $i,SV40: $i,SV23: $i] :
( ( ( product @ SV23 @ SV40 @ SV45 )
= $false )
| ( ( ~ ( product @ SV34 @ SV40 @ SV47 )
| ( product @ SV11 @ SV45 @ SV47 ) )
= $true )
| ( ( product @ SV11 @ SV23 @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(165,plain,
! [SV35: $i,SV48: $i,SV12: $i,SV46: $i,SV41: $i,SV24: $i] :
( ( ( product @ SV24 @ SV41 @ SV46 )
= $false )
| ( ( ~ ( product @ SV12 @ SV46 @ SV48 )
| ( product @ SV35 @ SV41 @ SV48 ) )
= $true )
| ( ( product @ SV12 @ SV24 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(166,plain,
! [SV23: $i,SV45: $i,SV11: $i,SV47: $i,SV40: $i,SV34: $i] :
( ( ( ~ ( product @ SV34 @ SV40 @ SV47 ) )
= $true )
| ( ( product @ SV11 @ SV45 @ SV47 )
= $true )
| ( ( product @ SV23 @ SV40 @ SV45 )
= $false )
| ( ( product @ SV11 @ SV23 @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(167,plain,
! [SV24: $i,SV41: $i,SV35: $i,SV48: $i,SV46: $i,SV12: $i] :
( ( ( ~ ( product @ SV12 @ SV46 @ SV48 ) )
= $true )
| ( ( product @ SV35 @ SV41 @ SV48 )
= $true )
| ( ( product @ SV24 @ SV41 @ SV46 )
= $false )
| ( ( product @ SV12 @ SV24 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(168,plain,
! [SV23: $i,SV45: $i,SV11: $i,SV47: $i,SV40: $i,SV34: $i] :
( ( ( product @ SV34 @ SV40 @ SV47 )
= $false )
| ( ( product @ SV11 @ SV45 @ SV47 )
= $true )
| ( ( product @ SV23 @ SV40 @ SV45 )
= $false )
| ( ( product @ SV11 @ SV23 @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(169,plain,
! [SV24: $i,SV41: $i,SV35: $i,SV48: $i,SV46: $i,SV12: $i] :
( ( ( product @ SV12 @ SV46 @ SV48 )
= $false )
| ( ( product @ SV35 @ SV41 @ SV48 )
= $true )
| ( ( product @ SV24 @ SV41 @ SV46 )
= $false )
| ( ( product @ SV12 @ SV24 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(170,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[49,169,168,161,160,159,158,154,139,132,131,128,127,108,90,82,81,80,79,72,66,51,50]) ).
thf(171,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[170]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP039-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.22 % Computer : n004.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Oct 6 10:31:39 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.23 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.86/0.96
% 3.86/0.96 No.of.Axioms: 22
% 3.86/0.96
% 3.86/0.96 Length.of.Defs: 0
% 3.86/0.96
% 3.86/0.96 Contains.Choice.Funs: false
% 3.86/0.96 ...
% 3.86/0.96
% 3.86/0.96 ********************************
% 3.86/0.96 * All subproblems solved! *
% 3.86/0.96 ********************************
% 3.86/0.96 % 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:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:170,loop_count:0,foatp_calls:1,translation:fof_full)
% 3.86/0.96
% 3.86/0.96 %**** Beginning of derivation protocol ****
% 3.86/0.96 % SZS output start CNFRefutation
% See solution above
% 3.86/0.96
% 3.86/0.96 %**** End of derivation protocol ****
% 3.86/0.96 %**** no. of clauses in derivation: 171 ****
% 3.86/0.96 %**** clause counter: 170 ****
% 3.86/0.96
% 3.86/0.96 % 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:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:170,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------