TSTP Solution File: GRP123-2.003 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GRP123-2.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n021.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 10:15:59 EDT 2022
% Result : Unsatisfiable 0.19s 0.46s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 31
% Syntax : Number of formulae : 164 ( 101 unt; 8 typ; 0 def)
% Number of atoms : 888 ( 222 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 1621 ( 226 ~; 288 |; 0 &;1107 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 424 ( 0 ^ 424 !; 0 ?; 424 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_e_1,type,
e_1: $i ).
thf(tp_e_2,type,
e_2: $i ).
thf(tp_e_3,type,
e_3: $i ).
thf(tp_equalish,type,
equalish: $i > $i > $o ).
thf(tp_greater,type,
greater: $i > $i > $o ).
thf(tp_group_element,type,
group_element: $i > $o ).
thf(tp_next,type,
next: $i > $i > $o ).
thf(tp_product,type,
product: $i > $i > $i > $o ).
thf(1,axiom,
! [X: $i] : ( product @ X @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_idempotence) ).
thf(2,axiom,
! [W: $i,Y: $i,X: $i,Z: $i] :
( ~ ( product @ W @ Y @ X )
| ~ ( product @ Z @ Y @ X )
| ( equalish @ W @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
thf(3,axiom,
! [X: $i,W: $i,Y: $i,Z: $i] :
( ~ ( product @ X @ W @ Y )
| ~ ( product @ X @ Z @ Y )
| ( equalish @ W @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
thf(4,axiom,
! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( product @ X @ Y @ W )
| ~ ( product @ X @ Y @ Z )
| ( equalish @ W @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function2) ).
thf(5,axiom,
! [X: $i,Y: $i] :
( ~ ( group_element @ X )
| ~ ( group_element @ Y )
| ( product @ X @ Y @ e_1 )
| ( product @ X @ Y @ e_2 )
| ( product @ X @ Y @ e_3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
thf(6,axiom,
~ ( equalish @ e_3 @ e_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
thf(7,axiom,
~ ( equalish @ e_3 @ e_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
thf(8,axiom,
~ ( equalish @ e_2 @ e_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
thf(9,axiom,
~ ( equalish @ e_2 @ e_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
thf(10,axiom,
~ ( equalish @ e_1 @ e_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
thf(11,axiom,
~ ( equalish @ e_1 @ e_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
thf(12,axiom,
group_element @ e_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
thf(13,axiom,
group_element @ e_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
thf(14,axiom,
group_element @ e_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
thf(15,axiom,
! [X: $i,Y: $i,X1: $i] :
( ~ ( product @ X @ e_1 @ Y )
| ~ ( next @ X @ X1 )
| ~ ( greater @ Y @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_redundancy) ).
thf(16,axiom,
greater @ e_3 @ e_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_greater_e_2) ).
thf(17,axiom,
greater @ e_3 @ e_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_greater_e_1) ).
thf(18,axiom,
greater @ e_2 @ e_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_greater_e_1) ).
thf(19,axiom,
next @ e_2 @ e_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_then_e_3) ).
thf(20,axiom,
next @ e_1 @ e_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_then_e_2) ).
thf(21,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(22,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[21]) ).
thf(23,negated_conjecture,
! [X1: $i,Y1: $i,Z1: $i,X2: $i,Y2: $i,Z2: $i] :
( ~ ( product @ X1 @ Y1 @ Z1 )
| ~ ( product @ X2 @ Y2 @ Z1 )
| ~ ( product @ Z2 @ Y1 @ X1 )
| ~ ( product @ Z2 @ Y2 @ X2 )
| ( equalish @ Y1 @ Y2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg1_2) ).
thf(24,negated_conjecture,
! [X1: $i,Y1: $i,Z1: $i,X2: $i,Y2: $i,Z2: $i] :
( ~ ( product @ X1 @ Y1 @ Z1 )
| ~ ( product @ X2 @ Y2 @ Z1 )
| ~ ( product @ Z2 @ Y1 @ X1 )
| ~ ( product @ Z2 @ Y2 @ X2 )
| ( equalish @ X1 @ X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg1_1) ).
thf(25,plain,
$false = $false,
inference(unfold_def,[status(thm)],[22]) ).
thf(26,plain,
( ( ! [X: $i] : ( product @ X @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(27,plain,
( ( ! [W: $i,Y: $i,X: $i,Z: $i] :
( ~ ( product @ W @ Y @ X )
| ~ ( product @ Z @ Y @ X )
| ( equalish @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(28,plain,
( ( ! [X: $i,W: $i,Y: $i,Z: $i] :
( ~ ( product @ X @ W @ Y )
| ~ ( product @ X @ Z @ Y )
| ( equalish @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(29,plain,
( ( ! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( product @ X @ Y @ W )
| ~ ( product @ X @ Y @ Z )
| ( equalish @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(30,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( group_element @ X )
| ~ ( group_element @ Y )
| ( product @ X @ Y @ e_1 )
| ( product @ X @ Y @ e_2 )
| ( product @ X @ Y @ e_3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(31,plain,
( ( ~ ( equalish @ e_3 @ e_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(32,plain,
( ( ~ ( equalish @ e_3 @ e_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(33,plain,
( ( ~ ( equalish @ e_2 @ e_3 ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(34,plain,
( ( ~ ( equalish @ e_2 @ e_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(35,plain,
( ( ~ ( equalish @ e_1 @ e_3 ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(36,plain,
( ( ~ ( equalish @ e_1 @ e_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(37,plain,
( ( group_element @ e_3 )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(38,plain,
( ( group_element @ e_2 )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(39,plain,
( ( group_element @ e_1 )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(40,plain,
( ( ! [X: $i,Y: $i,X1: $i] :
( ~ ( product @ X @ e_1 @ Y )
| ~ ( next @ X @ X1 )
| ~ ( greater @ Y @ X1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(41,plain,
( ( greater @ e_3 @ e_2 )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(42,plain,
( ( greater @ e_3 @ e_1 )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(43,plain,
( ( greater @ e_2 @ e_1 )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(44,plain,
( ( next @ e_2 @ e_3 )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(45,plain,
( ( next @ e_1 @ e_2 )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(46,plain,
( ( ! [X1: $i,Y1: $i,Z1: $i,X2: $i,Y2: $i,Z2: $i] :
( ~ ( product @ X1 @ Y1 @ Z1 )
| ~ ( product @ X2 @ Y2 @ Z1 )
| ~ ( product @ Z2 @ Y1 @ X1 )
| ~ ( product @ Z2 @ Y2 @ X2 )
| ( equalish @ Y1 @ Y2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(47,plain,
( ( ! [X1: $i,Y1: $i,Z1: $i,X2: $i,Y2: $i,Z2: $i] :
( ~ ( product @ X1 @ Y1 @ Z1 )
| ~ ( product @ X2 @ Y2 @ Z1 )
| ~ ( product @ Z2 @ Y1 @ X1 )
| ~ ( product @ Z2 @ Y2 @ X2 )
| ( equalish @ X1 @ X2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(48,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[25]) ).
thf(49,plain,
( ( ! [W: $i,Y: $i,X: $i] :
( ~ ( product @ W @ Y @ X )
| ! [Z: $i] :
( ~ ( product @ Z @ Y @ X )
| ( equalish @ W @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(50,plain,
( ( ! [X: $i,W: $i,Y: $i] :
( ~ ( product @ X @ W @ Y )
| ! [Z: $i] :
( ~ ( product @ X @ Z @ Y )
| ( equalish @ W @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(51,plain,
( ( ! [X: $i,Y: $i,W: $i] :
( ~ ( product @ X @ Y @ W )
| ! [Z: $i] :
( ~ ( product @ X @ Y @ Z )
| ( equalish @ W @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[29]) ).
thf(52,plain,
( ( ! [X: $i] :
( ~ ( group_element @ X )
| ! [Y: $i] :
( ~ ( group_element @ Y )
| ( product @ X @ Y @ e_1 )
| ( product @ X @ Y @ e_2 )
| ( product @ X @ Y @ e_3 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[30]) ).
thf(53,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( product @ X @ e_1 @ Y )
| ! [X1: $i] :
( ~ ( next @ X @ X1 )
| ~ ( greater @ Y @ X1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[40]) ).
thf(54,plain,
( ( ! [X1: $i,Y1: $i,Z1: $i,X2: $i] :
( ~ ( product @ X1 @ Y1 @ Z1 )
| ! [Y2: $i] :
( ~ ( product @ X2 @ Y2 @ Z1 )
| ! [Z2: $i] :
( ~ ( product @ Z2 @ Y1 @ X1 )
| ~ ( product @ Z2 @ Y2 @ X2 )
| ( equalish @ Y1 @ Y2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[46]) ).
thf(55,plain,
( ( ! [X1: $i,Y1: $i,Z1: $i,X2: $i] :
( ~ ( product @ X1 @ Y1 @ Z1 )
| ! [Y2: $i] :
( ~ ( product @ X2 @ Y2 @ Z1 )
| ! [Z2: $i] :
( ~ ( product @ Z2 @ Y1 @ X1 )
| ~ ( product @ Z2 @ Y2 @ X2 )
| ( equalish @ X1 @ X2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[47]) ).
thf(56,plain,
( ( ! [X1: $i,Y1: $i,Z1: $i,X2: $i] :
( ~ ( product @ X1 @ Y1 @ Z1 )
| ! [Y2: $i] :
( ~ ( product @ X2 @ Y2 @ Z1 )
| ! [Z2: $i] :
( ~ ( product @ Z2 @ Y1 @ X1 )
| ~ ( product @ Z2 @ Y2 @ X2 )
| ( equalish @ X1 @ X2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(57,plain,
( ( ! [X1: $i,Y1: $i,Z1: $i,X2: $i] :
( ~ ( product @ X1 @ Y1 @ Z1 )
| ! [Y2: $i] :
( ~ ( product @ X2 @ Y2 @ Z1 )
| ! [Z2: $i] :
( ~ ( product @ Z2 @ Y1 @ X1 )
| ~ ( product @ Z2 @ Y2 @ X2 )
| ( equalish @ Y1 @ Y2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(58,plain,
( ( next @ e_1 @ e_2 )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(59,plain,
( ( next @ e_2 @ e_3 )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(60,plain,
( ( greater @ e_2 @ e_1 )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(61,plain,
( ( greater @ e_3 @ e_1 )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(62,plain,
( ( greater @ e_3 @ e_2 )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(63,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( product @ X @ e_1 @ Y )
| ! [X1: $i] :
( ~ ( next @ X @ X1 )
| ~ ( greater @ Y @ X1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(64,plain,
( ( group_element @ e_1 )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(65,plain,
( ( group_element @ e_2 )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(66,plain,
( ( group_element @ e_3 )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(67,plain,
( ( ~ ( equalish @ e_1 @ e_2 ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(68,plain,
( ( ~ ( equalish @ e_1 @ e_3 ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(69,plain,
( ( ~ ( equalish @ e_2 @ e_1 ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(70,plain,
( ( ~ ( equalish @ e_2 @ e_3 ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(71,plain,
( ( ~ ( equalish @ e_3 @ e_1 ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(72,plain,
( ( ~ ( equalish @ e_3 @ e_2 ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(73,plain,
( ( ! [X: $i] :
( ~ ( group_element @ X )
| ! [Y: $i] :
( ~ ( group_element @ Y )
| ( product @ X @ Y @ e_1 )
| ( product @ X @ Y @ e_2 )
| ( product @ X @ Y @ e_3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(74,plain,
( ( ! [X: $i,Y: $i,W: $i] :
( ~ ( product @ X @ Y @ W )
| ! [Z: $i] :
( ~ ( product @ X @ Y @ Z )
| ( equalish @ W @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(75,plain,
( ( ! [X: $i,W: $i,Y: $i] :
( ~ ( product @ X @ W @ Y )
| ! [Z: $i] :
( ~ ( product @ X @ Z @ Y )
| ( equalish @ W @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(76,plain,
( ( ! [W: $i,Y: $i,X: $i] :
( ~ ( product @ W @ Y @ X )
| ! [Z: $i] :
( ~ ( product @ Z @ Y @ X )
| ( equalish @ W @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(77,plain,
( ( ! [X: $i] : ( product @ X @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(78,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(79,plain,
! [SV1: $i] :
( ( ! [SY30: $i,SY31: $i,SY32: $i] :
( ~ ( product @ SV1 @ SY30 @ SY31 )
| ! [SY33: $i] :
( ~ ( product @ SY32 @ SY33 @ SY31 )
| ! [SY34: $i] :
( ~ ( product @ SY34 @ SY30 @ SV1 )
| ~ ( product @ SY34 @ SY33 @ SY32 )
| ( equalish @ SV1 @ SY32 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(80,plain,
! [SV2: $i] :
( ( ! [SY35: $i,SY36: $i,SY37: $i] :
( ~ ( product @ SV2 @ SY35 @ SY36 )
| ! [SY38: $i] :
( ~ ( product @ SY37 @ SY38 @ SY36 )
| ! [SY39: $i] :
( ~ ( product @ SY39 @ SY35 @ SV2 )
| ~ ( product @ SY39 @ SY38 @ SY37 )
| ( equalish @ SY35 @ SY38 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(81,plain,
! [SV3: $i] :
( ( ! [SY40: $i] :
( ~ ( product @ SV3 @ e_1 @ SY40 )
| ! [SY41: $i] :
( ~ ( next @ SV3 @ SY41 )
| ~ ( greater @ SY40 @ SY41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(82,plain,
( ( equalish @ e_1 @ e_2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(83,plain,
( ( equalish @ e_1 @ e_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(84,plain,
( ( equalish @ e_2 @ e_1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(85,plain,
( ( equalish @ e_2 @ e_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(86,plain,
( ( equalish @ e_3 @ e_1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(87,plain,
( ( equalish @ e_3 @ e_2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(88,plain,
! [SV4: $i] :
( ( ~ ( group_element @ SV4 )
| ! [SY42: $i] :
( ~ ( group_element @ SY42 )
| ( product @ SV4 @ SY42 @ e_1 )
| ( product @ SV4 @ SY42 @ e_2 )
| ( product @ SV4 @ SY42 @ e_3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(89,plain,
! [SV5: $i] :
( ( ! [SY43: $i,SY44: $i] :
( ~ ( product @ SV5 @ SY43 @ SY44 )
| ! [SY45: $i] :
( ~ ( product @ SV5 @ SY43 @ SY45 )
| ( equalish @ SY44 @ SY45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(90,plain,
! [SV6: $i] :
( ( ! [SY46: $i,SY47: $i] :
( ~ ( product @ SV6 @ SY46 @ SY47 )
| ! [SY48: $i] :
( ~ ( product @ SV6 @ SY48 @ SY47 )
| ( equalish @ SY46 @ SY48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(91,plain,
! [SV7: $i] :
( ( ! [SY49: $i,SY50: $i] :
( ~ ( product @ SV7 @ SY49 @ SY50 )
| ! [SY51: $i] :
( ~ ( product @ SY51 @ SY49 @ SY50 )
| ( equalish @ SV7 @ SY51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(92,plain,
! [SV8: $i] :
( ( product @ SV8 @ SV8 @ SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(93,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(94,plain,
! [SV9: $i,SV1: $i] :
( ( ! [SY52: $i,SY53: $i] :
( ~ ( product @ SV1 @ SV9 @ SY52 )
| ! [SY54: $i] :
( ~ ( product @ SY53 @ SY54 @ SY52 )
| ! [SY55: $i] :
( ~ ( product @ SY55 @ SV9 @ SV1 )
| ~ ( product @ SY55 @ SY54 @ SY53 )
| ( equalish @ SV1 @ SY53 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(95,plain,
! [SV10: $i,SV2: $i] :
( ( ! [SY56: $i,SY57: $i] :
( ~ ( product @ SV2 @ SV10 @ SY56 )
| ! [SY58: $i] :
( ~ ( product @ SY57 @ SY58 @ SY56 )
| ! [SY59: $i] :
( ~ ( product @ SY59 @ SV10 @ SV2 )
| ~ ( product @ SY59 @ SY58 @ SY57 )
| ( equalish @ SV10 @ SY58 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(96,plain,
! [SV11: $i,SV3: $i] :
( ( ~ ( product @ SV3 @ e_1 @ SV11 )
| ! [SY60: $i] :
( ~ ( next @ SV3 @ SY60 )
| ~ ( greater @ SV11 @ SY60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(97,plain,
! [SV4: $i] :
( ( ( ~ ( group_element @ SV4 ) )
= $true )
| ( ( ! [SY42: $i] :
( ~ ( group_element @ SY42 )
| ( product @ SV4 @ SY42 @ e_1 )
| ( product @ SV4 @ SY42 @ e_2 )
| ( product @ SV4 @ SY42 @ e_3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(98,plain,
! [SV12: $i,SV5: $i] :
( ( ! [SY61: $i] :
( ~ ( product @ SV5 @ SV12 @ SY61 )
| ! [SY62: $i] :
( ~ ( product @ SV5 @ SV12 @ SY62 )
| ( equalish @ SY61 @ SY62 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(99,plain,
! [SV13: $i,SV6: $i] :
( ( ! [SY63: $i] :
( ~ ( product @ SV6 @ SV13 @ SY63 )
| ! [SY64: $i] :
( ~ ( product @ SV6 @ SY64 @ SY63 )
| ( equalish @ SV13 @ SY64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(100,plain,
! [SV14: $i,SV7: $i] :
( ( ! [SY65: $i] :
( ~ ( product @ SV7 @ SV14 @ SY65 )
| ! [SY66: $i] :
( ~ ( product @ SY66 @ SV14 @ SY65 )
| ( equalish @ SV7 @ SY66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(101,plain,
! [SV15: $i,SV9: $i,SV1: $i] :
( ( ! [SY67: $i] :
( ~ ( product @ SV1 @ SV9 @ SV15 )
| ! [SY68: $i] :
( ~ ( product @ SY67 @ SY68 @ SV15 )
| ! [SY55: $i] :
( ~ ( product @ SY55 @ SV9 @ SV1 )
| ~ ( product @ SY55 @ SY68 @ SY67 )
| ( equalish @ SV1 @ SY67 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(102,plain,
! [SV16: $i,SV10: $i,SV2: $i] :
( ( ! [SY70: $i] :
( ~ ( product @ SV2 @ SV10 @ SV16 )
| ! [SY71: $i] :
( ~ ( product @ SY70 @ SY71 @ SV16 )
| ! [SY59: $i] :
( ~ ( product @ SY59 @ SV10 @ SV2 )
| ~ ( product @ SY59 @ SY71 @ SY70 )
| ( equalish @ SV10 @ SY71 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(103,plain,
! [SV11: $i,SV3: $i] :
( ( ( ~ ( product @ SV3 @ e_1 @ SV11 ) )
= $true )
| ( ( ! [SY60: $i] :
( ~ ( next @ SV3 @ SY60 )
| ~ ( greater @ SV11 @ SY60 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(104,plain,
! [SV4: $i] :
( ( ( group_element @ SV4 )
= $false )
| ( ( ! [SY42: $i] :
( ~ ( group_element @ SY42 )
| ( product @ SV4 @ SY42 @ e_1 )
| ( product @ SV4 @ SY42 @ e_2 )
| ( product @ SV4 @ SY42 @ e_3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(105,plain,
! [SV17: $i,SV12: $i,SV5: $i] :
( ( ~ ( product @ SV5 @ SV12 @ SV17 )
| ! [SY73: $i] :
( ~ ( product @ SV5 @ SV12 @ SY73 )
| ( equalish @ SV17 @ SY73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(106,plain,
! [SV18: $i,SV13: $i,SV6: $i] :
( ( ~ ( product @ SV6 @ SV13 @ SV18 )
| ! [SY74: $i] :
( ~ ( product @ SV6 @ SY74 @ SV18 )
| ( equalish @ SV13 @ SY74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(107,plain,
! [SV19: $i,SV14: $i,SV7: $i] :
( ( ~ ( product @ SV7 @ SV14 @ SV19 )
| ! [SY75: $i] :
( ~ ( product @ SY75 @ SV14 @ SV19 )
| ( equalish @ SV7 @ SY75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(108,plain,
! [SV20: $i,SV15: $i,SV9: $i,SV1: $i] :
( ( ~ ( product @ SV1 @ SV9 @ SV15 )
| ! [SY76: $i] :
( ~ ( product @ SV20 @ SY76 @ SV15 )
| ! [SY77: $i] :
( ~ ( product @ SY77 @ SV9 @ SV1 )
| ~ ( product @ SY77 @ SY76 @ SV20 )
| ( equalish @ SV1 @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(109,plain,
! [SV21: $i,SV16: $i,SV10: $i,SV2: $i] :
( ( ~ ( product @ SV2 @ SV10 @ SV16 )
| ! [SY78: $i] :
( ~ ( product @ SV21 @ SY78 @ SV16 )
| ! [SY79: $i] :
( ~ ( product @ SY79 @ SV10 @ SV2 )
| ~ ( product @ SY79 @ SY78 @ SV21 )
| ( equalish @ SV10 @ SY78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(110,plain,
! [SV11: $i,SV3: $i] :
( ( ( product @ SV3 @ e_1 @ SV11 )
= $false )
| ( ( ! [SY60: $i] :
( ~ ( next @ SV3 @ SY60 )
| ~ ( greater @ SV11 @ SY60 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(111,plain,
! [SV4: $i,SV22: $i] :
( ( ( ~ ( group_element @ SV22 )
| ( product @ SV4 @ SV22 @ e_1 )
| ( product @ SV4 @ SV22 @ e_2 )
| ( product @ SV4 @ SV22 @ e_3 ) )
= $true )
| ( ( group_element @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(112,plain,
! [SV17: $i,SV12: $i,SV5: $i] :
( ( ( ~ ( product @ SV5 @ SV12 @ SV17 ) )
= $true )
| ( ( ! [SY73: $i] :
( ~ ( product @ SV5 @ SV12 @ SY73 )
| ( equalish @ SV17 @ SY73 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(113,plain,
! [SV18: $i,SV13: $i,SV6: $i] :
( ( ( ~ ( product @ SV6 @ SV13 @ SV18 ) )
= $true )
| ( ( ! [SY74: $i] :
( ~ ( product @ SV6 @ SY74 @ SV18 )
| ( equalish @ SV13 @ SY74 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(114,plain,
! [SV19: $i,SV14: $i,SV7: $i] :
( ( ( ~ ( product @ SV7 @ SV14 @ SV19 ) )
= $true )
| ( ( ! [SY75: $i] :
( ~ ( product @ SY75 @ SV14 @ SV19 )
| ( equalish @ SV7 @ SY75 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(115,plain,
! [SV20: $i,SV15: $i,SV9: $i,SV1: $i] :
( ( ( ~ ( product @ SV1 @ SV9 @ SV15 ) )
= $true )
| ( ( ! [SY76: $i] :
( ~ ( product @ SV20 @ SY76 @ SV15 )
| ! [SY77: $i] :
( ~ ( product @ SY77 @ SV9 @ SV1 )
| ~ ( product @ SY77 @ SY76 @ SV20 )
| ( equalish @ SV1 @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(116,plain,
! [SV21: $i,SV16: $i,SV10: $i,SV2: $i] :
( ( ( ~ ( product @ SV2 @ SV10 @ SV16 ) )
= $true )
| ( ( ! [SY78: $i] :
( ~ ( product @ SV21 @ SY78 @ SV16 )
| ! [SY79: $i] :
( ~ ( product @ SY79 @ SV10 @ SV2 )
| ~ ( product @ SY79 @ SY78 @ SV21 )
| ( equalish @ SV10 @ SY78 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(117,plain,
! [SV11: $i,SV23: $i,SV3: $i] :
( ( ( ~ ( next @ SV3 @ SV23 )
| ~ ( greater @ SV11 @ SV23 ) )
= $true )
| ( ( product @ SV3 @ e_1 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(118,plain,
! [SV4: $i,SV22: $i] :
( ( ( ~ ( group_element @ SV22 ) )
= $true )
| ( ( ( product @ SV4 @ SV22 @ e_1 )
| ( product @ SV4 @ SV22 @ e_2 )
| ( product @ SV4 @ SV22 @ e_3 ) )
= $true )
| ( ( group_element @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(119,plain,
! [SV17: $i,SV12: $i,SV5: $i] :
( ( ( product @ SV5 @ SV12 @ SV17 )
= $false )
| ( ( ! [SY73: $i] :
( ~ ( product @ SV5 @ SV12 @ SY73 )
| ( equalish @ SV17 @ SY73 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(120,plain,
! [SV18: $i,SV13: $i,SV6: $i] :
( ( ( product @ SV6 @ SV13 @ SV18 )
= $false )
| ( ( ! [SY74: $i] :
( ~ ( product @ SV6 @ SY74 @ SV18 )
| ( equalish @ SV13 @ SY74 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(121,plain,
! [SV19: $i,SV14: $i,SV7: $i] :
( ( ( product @ SV7 @ SV14 @ SV19 )
= $false )
| ( ( ! [SY75: $i] :
( ~ ( product @ SY75 @ SV14 @ SV19 )
| ( equalish @ SV7 @ SY75 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(122,plain,
! [SV20: $i,SV15: $i,SV9: $i,SV1: $i] :
( ( ( product @ SV1 @ SV9 @ SV15 )
= $false )
| ( ( ! [SY76: $i] :
( ~ ( product @ SV20 @ SY76 @ SV15 )
| ! [SY77: $i] :
( ~ ( product @ SY77 @ SV9 @ SV1 )
| ~ ( product @ SY77 @ SY76 @ SV20 )
| ( equalish @ SV1 @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(123,plain,
! [SV21: $i,SV16: $i,SV10: $i,SV2: $i] :
( ( ( product @ SV2 @ SV10 @ SV16 )
= $false )
| ( ( ! [SY78: $i] :
( ~ ( product @ SV21 @ SY78 @ SV16 )
| ! [SY79: $i] :
( ~ ( product @ SY79 @ SV10 @ SV2 )
| ~ ( product @ SY79 @ SY78 @ SV21 )
| ( equalish @ SV10 @ SY78 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(124,plain,
! [SV11: $i,SV23: $i,SV3: $i] :
( ( ( ~ ( next @ SV3 @ SV23 ) )
= $true )
| ( ( ~ ( greater @ SV11 @ SV23 ) )
= $true )
| ( ( product @ SV3 @ e_1 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(125,plain,
! [SV4: $i,SV22: $i] :
( ( ( group_element @ SV22 )
= $false )
| ( ( ( product @ SV4 @ SV22 @ e_1 )
| ( product @ SV4 @ SV22 @ e_2 )
| ( product @ SV4 @ SV22 @ e_3 ) )
= $true )
| ( ( group_element @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(126,plain,
! [SV17: $i,SV24: $i,SV12: $i,SV5: $i] :
( ( ( ~ ( product @ SV5 @ SV12 @ SV24 )
| ( equalish @ SV17 @ SV24 ) )
= $true )
| ( ( product @ SV5 @ SV12 @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(127,plain,
! [SV13: $i,SV18: $i,SV25: $i,SV6: $i] :
( ( ( ~ ( product @ SV6 @ SV25 @ SV18 )
| ( equalish @ SV13 @ SV25 ) )
= $true )
| ( ( product @ SV6 @ SV13 @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(128,plain,
! [SV7: $i,SV19: $i,SV14: $i,SV26: $i] :
( ( ( ~ ( product @ SV26 @ SV14 @ SV19 )
| ( equalish @ SV7 @ SV26 ) )
= $true )
| ( ( product @ SV7 @ SV14 @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(129,plain,
! [SV1: $i,SV9: $i,SV15: $i,SV27: $i,SV20: $i] :
( ( ( ~ ( product @ SV20 @ SV27 @ SV15 )
| ! [SY80: $i] :
( ~ ( product @ SY80 @ SV9 @ SV1 )
| ~ ( product @ SY80 @ SV27 @ SV20 )
| ( equalish @ SV1 @ SV20 ) ) )
= $true )
| ( ( product @ SV1 @ SV9 @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(130,plain,
! [SV2: $i,SV10: $i,SV16: $i,SV28: $i,SV21: $i] :
( ( ( ~ ( product @ SV21 @ SV28 @ SV16 )
| ! [SY81: $i] :
( ~ ( product @ SY81 @ SV10 @ SV2 )
| ~ ( product @ SY81 @ SV28 @ SV21 )
| ( equalish @ SV10 @ SV28 ) ) )
= $true )
| ( ( product @ SV2 @ SV10 @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(131,plain,
! [SV11: $i,SV23: $i,SV3: $i] :
( ( ( next @ SV3 @ SV23 )
= $false )
| ( ( ~ ( greater @ SV11 @ SV23 ) )
= $true )
| ( ( product @ SV3 @ e_1 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(132,plain,
! [SV22: $i,SV4: $i] :
( ( ( product @ SV4 @ SV22 @ e_1 )
= $true )
| ( ( ( product @ SV4 @ SV22 @ e_2 )
| ( product @ SV4 @ SV22 @ e_3 ) )
= $true )
| ( ( group_element @ SV22 )
= $false )
| ( ( group_element @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(133,plain,
! [SV17: $i,SV24: $i,SV12: $i,SV5: $i] :
( ( ( ~ ( product @ SV5 @ SV12 @ SV24 ) )
= $true )
| ( ( equalish @ SV17 @ SV24 )
= $true )
| ( ( product @ SV5 @ SV12 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(134,plain,
! [SV13: $i,SV18: $i,SV25: $i,SV6: $i] :
( ( ( ~ ( product @ SV6 @ SV25 @ SV18 ) )
= $true )
| ( ( equalish @ SV13 @ SV25 )
= $true )
| ( ( product @ SV6 @ SV13 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(135,plain,
! [SV7: $i,SV19: $i,SV14: $i,SV26: $i] :
( ( ( ~ ( product @ SV26 @ SV14 @ SV19 ) )
= $true )
| ( ( equalish @ SV7 @ SV26 )
= $true )
| ( ( product @ SV7 @ SV14 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(136,plain,
! [SV1: $i,SV9: $i,SV15: $i,SV27: $i,SV20: $i] :
( ( ( ~ ( product @ SV20 @ SV27 @ SV15 ) )
= $true )
| ( ( ! [SY80: $i] :
( ~ ( product @ SY80 @ SV9 @ SV1 )
| ~ ( product @ SY80 @ SV27 @ SV20 )
| ( equalish @ SV1 @ SV20 ) ) )
= $true )
| ( ( product @ SV1 @ SV9 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(137,plain,
! [SV2: $i,SV10: $i,SV16: $i,SV28: $i,SV21: $i] :
( ( ( ~ ( product @ SV21 @ SV28 @ SV16 ) )
= $true )
| ( ( ! [SY81: $i] :
( ~ ( product @ SY81 @ SV10 @ SV2 )
| ~ ( product @ SY81 @ SV28 @ SV21 )
| ( equalish @ SV10 @ SV28 ) ) )
= $true )
| ( ( product @ SV2 @ SV10 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(138,plain,
! [SV3: $i,SV23: $i,SV11: $i] :
( ( ( greater @ SV11 @ SV23 )
= $false )
| ( ( next @ SV3 @ SV23 )
= $false )
| ( ( product @ SV3 @ e_1 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(139,plain,
! [SV22: $i,SV4: $i] :
( ( ( product @ SV4 @ SV22 @ e_2 )
= $true )
| ( ( product @ SV4 @ SV22 @ e_3 )
= $true )
| ( ( product @ SV4 @ SV22 @ e_1 )
= $true )
| ( ( group_element @ SV22 )
= $false )
| ( ( group_element @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(140,plain,
! [SV17: $i,SV24: $i,SV12: $i,SV5: $i] :
( ( ( product @ SV5 @ SV12 @ SV24 )
= $false )
| ( ( equalish @ SV17 @ SV24 )
= $true )
| ( ( product @ SV5 @ SV12 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(141,plain,
! [SV13: $i,SV18: $i,SV25: $i,SV6: $i] :
( ( ( product @ SV6 @ SV25 @ SV18 )
= $false )
| ( ( equalish @ SV13 @ SV25 )
= $true )
| ( ( product @ SV6 @ SV13 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(142,plain,
! [SV7: $i,SV19: $i,SV14: $i,SV26: $i] :
( ( ( product @ SV26 @ SV14 @ SV19 )
= $false )
| ( ( equalish @ SV7 @ SV26 )
= $true )
| ( ( product @ SV7 @ SV14 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(143,plain,
! [SV1: $i,SV9: $i,SV15: $i,SV27: $i,SV20: $i] :
( ( ( product @ SV20 @ SV27 @ SV15 )
= $false )
| ( ( ! [SY80: $i] :
( ~ ( product @ SY80 @ SV9 @ SV1 )
| ~ ( product @ SY80 @ SV27 @ SV20 )
| ( equalish @ SV1 @ SV20 ) ) )
= $true )
| ( ( product @ SV1 @ SV9 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(144,plain,
! [SV2: $i,SV10: $i,SV16: $i,SV28: $i,SV21: $i] :
( ( ( product @ SV21 @ SV28 @ SV16 )
= $false )
| ( ( ! [SY81: $i] :
( ~ ( product @ SY81 @ SV10 @ SV2 )
| ~ ( product @ SY81 @ SV28 @ SV21 )
| ( equalish @ SV10 @ SV28 ) ) )
= $true )
| ( ( product @ SV2 @ SV10 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(145,plain,
! [SV15: $i,SV20: $i,SV27: $i,SV1: $i,SV9: $i,SV29: $i] :
( ( ( ~ ( product @ SV29 @ SV9 @ SV1 )
| ~ ( product @ SV29 @ SV27 @ SV20 )
| ( equalish @ SV1 @ SV20 ) )
= $true )
| ( ( product @ SV20 @ SV27 @ SV15 )
= $false )
| ( ( product @ SV1 @ SV9 @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(146,plain,
! [SV16: $i,SV21: $i,SV28: $i,SV2: $i,SV10: $i,SV30: $i] :
( ( ( ~ ( product @ SV30 @ SV10 @ SV2 )
| ~ ( product @ SV30 @ SV28 @ SV21 )
| ( equalish @ SV10 @ SV28 ) )
= $true )
| ( ( product @ SV21 @ SV28 @ SV16 )
= $false )
| ( ( product @ SV2 @ SV10 @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(147,plain,
! [SV15: $i,SV20: $i,SV27: $i,SV1: $i,SV9: $i,SV29: $i] :
( ( ( ~ ( product @ SV29 @ SV9 @ SV1 ) )
= $true )
| ( ( ~ ( product @ SV29 @ SV27 @ SV20 )
| ( equalish @ SV1 @ SV20 ) )
= $true )
| ( ( product @ SV20 @ SV27 @ SV15 )
= $false )
| ( ( product @ SV1 @ SV9 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(148,plain,
! [SV16: $i,SV21: $i,SV28: $i,SV2: $i,SV10: $i,SV30: $i] :
( ( ( ~ ( product @ SV30 @ SV10 @ SV2 ) )
= $true )
| ( ( ~ ( product @ SV30 @ SV28 @ SV21 )
| ( equalish @ SV10 @ SV28 ) )
= $true )
| ( ( product @ SV21 @ SV28 @ SV16 )
= $false )
| ( ( product @ SV2 @ SV10 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(149,plain,
! [SV15: $i,SV20: $i,SV27: $i,SV1: $i,SV9: $i,SV29: $i] :
( ( ( product @ SV29 @ SV9 @ SV1 )
= $false )
| ( ( ~ ( product @ SV29 @ SV27 @ SV20 )
| ( equalish @ SV1 @ SV20 ) )
= $true )
| ( ( product @ SV20 @ SV27 @ SV15 )
= $false )
| ( ( product @ SV1 @ SV9 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(150,plain,
! [SV16: $i,SV21: $i,SV28: $i,SV2: $i,SV10: $i,SV30: $i] :
( ( ( product @ SV30 @ SV10 @ SV2 )
= $false )
| ( ( ~ ( product @ SV30 @ SV28 @ SV21 )
| ( equalish @ SV10 @ SV28 ) )
= $true )
| ( ( product @ SV21 @ SV28 @ SV16 )
= $false )
| ( ( product @ SV2 @ SV10 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(151,plain,
! [SV15: $i,SV9: $i,SV1: $i,SV20: $i,SV27: $i,SV29: $i] :
( ( ( ~ ( product @ SV29 @ SV27 @ SV20 ) )
= $true )
| ( ( equalish @ SV1 @ SV20 )
= $true )
| ( ( product @ SV29 @ SV9 @ SV1 )
= $false )
| ( ( product @ SV20 @ SV27 @ SV15 )
= $false )
| ( ( product @ SV1 @ SV9 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(152,plain,
! [SV16: $i,SV2: $i,SV10: $i,SV21: $i,SV28: $i,SV30: $i] :
( ( ( ~ ( product @ SV30 @ SV28 @ SV21 ) )
= $true )
| ( ( equalish @ SV10 @ SV28 )
= $true )
| ( ( product @ SV30 @ SV10 @ SV2 )
= $false )
| ( ( product @ SV21 @ SV28 @ SV16 )
= $false )
| ( ( product @ SV2 @ SV10 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(153,plain,
! [SV15: $i,SV9: $i,SV1: $i,SV20: $i,SV27: $i,SV29: $i] :
( ( ( product @ SV29 @ SV27 @ SV20 )
= $false )
| ( ( equalish @ SV1 @ SV20 )
= $true )
| ( ( product @ SV29 @ SV9 @ SV1 )
= $false )
| ( ( product @ SV20 @ SV27 @ SV15 )
= $false )
| ( ( product @ SV1 @ SV9 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(154,plain,
! [SV16: $i,SV2: $i,SV10: $i,SV21: $i,SV28: $i,SV30: $i] :
( ( ( product @ SV30 @ SV28 @ SV21 )
= $false )
| ( ( equalish @ SV10 @ SV28 )
= $true )
| ( ( product @ SV30 @ SV10 @ SV2 )
= $false )
| ( ( product @ SV21 @ SV28 @ SV16 )
= $false )
| ( ( product @ SV2 @ SV10 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(155,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[58,154,153,142,141,140,139,138,93,92,87,86,85,84,83,82,66,65,64,62,61,60,59]) ).
thf(156,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[155]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP123-2.003 : TPTP v8.1.0. Released v1.2.0.
% 0.06/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n021.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 06:37:11 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 22
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 0
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: false
% 0.13/0.36 (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)........
% 0.19/0.46
% 0.19/0.46 ********************************
% 0.19/0.46 * All subproblems solved! *
% 0.19/0.46 ********************************
% 0.19/0.46 % SZS status Unsatisfiable for /export/starexec/sandbox/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:155,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.47
% 0.19/0.47 %**** Beginning of derivation protocol ****
% 0.19/0.47 % SZS output start CNFRefutation
% See solution above
% 0.19/0.47
% 0.19/0.47 %**** End of derivation protocol ****
% 0.19/0.47 %**** no. of clauses in derivation: 156 ****
% 0.19/0.47 %**** clause counter: 155 ****
% 0.19/0.47
% 0.19/0.47 % SZS status Unsatisfiable for /export/starexec/sandbox/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:155,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------