%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GRP129-2.004 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 10:20:25 AM UTC 2026
% Result : Unsatisfiable 10.24s 2.01s
% Output : CNFRefutation 10.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 32
% Syntax : Number of formulae : 162 ( 128 unt; 0 typ; 0 def)
% Number of atoms : 690 ( 179 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 1090 ( 150 ~; 170 |; 0 &; 770 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 6 con; 0-3 aty)
% Number of variables : 233 ( 0 ^; 233 !; 0 ?; 233 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_e_1,type,
e_1: $i ).
thf(tp_e_2,type,
e_2: $i ).
thf(tp_e_3,type,
e_3: $i ).
thf(tp_e_4,type,
e_4: $i ).
thf(tp_equalish,type,
equalish: $i > $i > $o ).
thf(tp_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,
! [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(2,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(3,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(4,axiom,
! [X: $i,Y: $i] :
( ~ ( group_element @ X )
| ~ ( group_element @ Y )
| ( product @ X @ Y @ e_1 )
| ( product @ X @ Y @ e_2 )
| ( product @ X @ Y @ e_3 )
| ( product @ X @ Y @ e_4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
thf(5,axiom,
~ ( equalish @ e_4 @ e_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_3) ).
thf(6,axiom,
~ ( equalish @ e_4 @ e_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_2) ).
thf(7,axiom,
~ ( equalish @ e_4 @ e_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_1) ).
thf(8,axiom,
~ ( equalish @ e_3 @ e_4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
thf(9,axiom,
~ ( equalish @ e_3 @ e_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
thf(10,axiom,
~ ( equalish @ e_3 @ e_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
thf(11,axiom,
~ ( equalish @ e_2 @ e_4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_4) ).
thf(12,axiom,
~ ( equalish @ e_2 @ e_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
thf(13,axiom,
~ ( equalish @ e_2 @ e_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
thf(14,axiom,
~ ( equalish @ e_1 @ e_4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_4) ).
thf(15,axiom,
~ ( equalish @ e_1 @ e_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
thf(16,axiom,
~ ( equalish @ e_1 @ e_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
thf(17,axiom,
group_element @ e_4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_4) ).
thf(18,axiom,
group_element @ e_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
thf(19,axiom,
group_element @ e_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
thf(20,axiom,
group_element @ e_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
thf(21,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(22,axiom,
greater @ e_4 @ e_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_greater_e_3) ).
thf(23,axiom,
greater @ e_4 @ e_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_greater_e_2) ).
thf(24,axiom,
greater @ e_3 @ e_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_greater_e_2) ).
thf(25,axiom,
greater @ e_4 @ e_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_greater_e_1) ).
thf(26,axiom,
greater @ e_3 @ e_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_greater_e_1) ).
thf(27,axiom,
greater @ e_2 @ e_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_greater_e_1) ).
thf(28,axiom,
next @ e_3 @ e_4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_then_e_4) ).
thf(29,axiom,
next @ e_2 @ e_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_then_e_3) ).
thf(30,axiom,
next @ e_1 @ e_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_then_e_2) ).
thf(31,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(32,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[31]) ).
thf(33,negated_conjecture,
! [Y: $i,X: $i,Z1: $i,Z2: $i] :
( ~ ( product @ Y @ X @ Z1 )
| ~ ( product @ X @ Z1 @ Z2 )
| ( product @ Z1 @ Y @ Z2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).
thf(34,plain,
$false = $false,
inference(unfold_def,[status(thm)],[32]) ).
thf(35,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)],[1]) ).
thf(36,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)],[2]) ).
thf(37,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)],[3]) ).
thf(38,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( group_element @ X )
| ~ ( group_element @ Y )
| ( product @ X @ Y @ e_1 )
| ( product @ X @ Y @ e_2 )
| ( product @ X @ Y @ e_3 )
| ( product @ X @ Y @ e_4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(39,plain,
( ( ~ ( equalish @ e_4 @ e_3 ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(40,plain,
( ( ~ ( equalish @ e_4 @ e_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(41,plain,
( ( ~ ( equalish @ e_4 @ e_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(42,plain,
( ( ~ ( equalish @ e_3 @ e_4 ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(43,plain,
( ( ~ ( equalish @ e_3 @ e_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(44,plain,
( ( ~ ( equalish @ e_3 @ e_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(45,plain,
( ( ~ ( equalish @ e_2 @ e_4 ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(46,plain,
( ( ~ ( equalish @ e_2 @ e_3 ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(47,plain,
( ( ~ ( equalish @ e_2 @ e_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(48,plain,
( ( ~ ( equalish @ e_1 @ e_4 ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(49,plain,
( ( ~ ( equalish @ e_1 @ e_3 ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(50,plain,
( ( ~ ( equalish @ e_1 @ e_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(51,plain,
( ( group_element @ e_4 )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(52,plain,
( ( group_element @ e_3 )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(53,plain,
( ( group_element @ e_2 )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(54,plain,
( ( group_element @ e_1 )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(55,plain,
( ( ! [X: $i,Y: $i,X1: $i] :
( ~ ( product @ X @ e_1 @ Y )
| ~ ( next @ X @ X1 )
| ~ ( greater @ Y @ X1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(56,plain,
( ( greater @ e_4 @ e_3 )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(57,plain,
( ( greater @ e_4 @ e_2 )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(58,plain,
( ( greater @ e_3 @ e_2 )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(59,plain,
( ( greater @ e_4 @ e_1 )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(60,plain,
( ( greater @ e_3 @ e_1 )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(61,plain,
( ( greater @ e_2 @ e_1 )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(62,plain,
( ( next @ e_3 @ e_4 )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(63,plain,
( ( next @ e_2 @ e_3 )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(64,plain,
( ( next @ e_1 @ e_2 )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(65,plain,
( ( ! [Y: $i,X: $i,Z1: $i,Z2: $i] :
( ~ ( product @ Y @ X @ Z1 )
| ~ ( product @ X @ Z1 @ Z2 )
| ( product @ Z1 @ Y @ Z2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(66,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[34]) ).
thf(67,plain,
( ( ! [Y: $i,X: $i,Z1: $i,Z2: $i] :
( ~ ( product @ Y @ X @ Z1 )
| ~ ( product @ X @ Z1 @ Z2 )
| ( product @ Z1 @ Y @ Z2 ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(68,plain,
( ( next @ e_1 @ e_2 )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(69,plain,
( ( next @ e_2 @ e_3 )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(70,plain,
( ( next @ e_3 @ e_4 )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(71,plain,
( ( greater @ e_2 @ e_1 )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(72,plain,
( ( greater @ e_3 @ e_1 )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(73,plain,
( ( greater @ e_4 @ e_1 )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(74,plain,
( ( greater @ e_3 @ e_2 )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(75,plain,
( ( greater @ e_4 @ e_2 )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(76,plain,
( ( greater @ e_4 @ e_3 )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(77,plain,
( ( ! [X: $i,Y: $i,X1: $i] :
( ~ ( product @ X @ e_1 @ Y )
| ~ ( next @ X @ X1 )
| ~ ( greater @ Y @ X1 ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(78,plain,
( ( group_element @ e_1 )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(79,plain,
( ( group_element @ e_2 )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(80,plain,
( ( group_element @ e_3 )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(81,plain,
( ( group_element @ e_4 )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(82,plain,
( ( ~ ( equalish @ e_1 @ e_2 ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(83,plain,
( ( ~ ( equalish @ e_1 @ e_3 ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(84,plain,
( ( ~ ( equalish @ e_1 @ e_4 ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(85,plain,
( ( ~ ( equalish @ e_2 @ e_1 ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(86,plain,
( ( ~ ( equalish @ e_2 @ e_3 ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(87,plain,
( ( ~ ( equalish @ e_2 @ e_4 ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(88,plain,
( ( ~ ( equalish @ e_3 @ e_1 ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(89,plain,
( ( ~ ( equalish @ e_3 @ e_2 ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(90,plain,
( ( ~ ( equalish @ e_3 @ e_4 ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(91,plain,
( ( ~ ( equalish @ e_4 @ e_1 ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(92,plain,
( ( ~ ( equalish @ e_4 @ e_2 ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(93,plain,
( ( ~ ( equalish @ e_4 @ e_3 ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(94,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( group_element @ X )
| ~ ( group_element @ Y )
| ( product @ X @ Y @ e_1 )
| ( product @ X @ Y @ e_2 )
| ( product @ X @ Y @ e_3 )
| ( product @ X @ Y @ e_4 ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(95,plain,
( ( ! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( product @ X @ Y @ W )
| ~ ( product @ X @ Y @ Z )
| ( equalish @ W @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(96,plain,
( ( ! [X: $i,W: $i,Y: $i,Z: $i] :
( ~ ( product @ X @ W @ Y )
| ~ ( product @ X @ Z @ Y )
| ( equalish @ W @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(97,plain,
( ( ! [W: $i,Y: $i,X: $i,Z: $i] :
( ~ ( product @ W @ Y @ X )
| ~ ( product @ Z @ Y @ X )
| ( equalish @ W @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(98,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[66]) ).
thf(99,plain,
! [SV1: $i] :
( ( ! [SY21: $i,SY22: $i,SY23: $i] :
( ~ ( product @ SV1 @ SY21 @ SY22 )
| ~ ( product @ SY21 @ SY22 @ SY23 )
| ( product @ SY22 @ SV1 @ SY23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(100,plain,
! [SV2: $i] :
( ( ! [SY24: $i,SY25: $i] :
( ~ ( product @ SV2 @ e_1 @ SY24 )
| ~ ( next @ SV2 @ SY25 )
| ~ ( greater @ SY24 @ SY25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(101,plain,
( ( equalish @ e_1 @ e_2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(102,plain,
( ( equalish @ e_1 @ e_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(103,plain,
( ( equalish @ e_1 @ e_4 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(104,plain,
( ( equalish @ e_2 @ e_1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(105,plain,
( ( equalish @ e_2 @ e_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(106,plain,
( ( equalish @ e_2 @ e_4 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(107,plain,
( ( equalish @ e_3 @ e_1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(108,plain,
( ( equalish @ e_3 @ e_2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(109,plain,
( ( equalish @ e_3 @ e_4 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(110,plain,
( ( equalish @ e_4 @ e_1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(111,plain,
( ( equalish @ e_4 @ e_2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(112,plain,
( ( equalish @ e_4 @ e_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(113,plain,
! [SV3: $i] :
( ( ! [SY26: $i] :
( ~ ( group_element @ SV3 )
| ~ ( group_element @ SY26 )
| ( product @ SV3 @ SY26 @ e_1 )
| ( product @ SV3 @ SY26 @ e_2 )
| ( product @ SV3 @ SY26 @ e_3 )
| ( product @ SV3 @ SY26 @ e_4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(114,plain,
! [SV4: $i] :
( ( ! [SY27: $i,SY28: $i,SY29: $i] :
( ~ ( product @ SV4 @ SY27 @ SY28 )
| ~ ( product @ SV4 @ SY27 @ SY29 )
| ( equalish @ SY28 @ SY29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(115,plain,
! [SV5: $i] :
( ( ! [SY30: $i,SY31: $i,SY32: $i] :
( ~ ( product @ SV5 @ SY30 @ SY31 )
| ~ ( product @ SV5 @ SY32 @ SY31 )
| ( equalish @ SY30 @ SY32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(116,plain,
! [SV6: $i] :
( ( ! [SY33: $i,SY34: $i,SY35: $i] :
( ~ ( product @ SV6 @ SY33 @ SY34 )
| ~ ( product @ SY35 @ SY33 @ SY34 )
| ( equalish @ SV6 @ SY35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(117,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(118,plain,
! [SV7: $i,SV1: $i] :
( ( ! [SY36: $i,SY37: $i] :
( ~ ( product @ SV1 @ SV7 @ SY36 )
| ~ ( product @ SV7 @ SY36 @ SY37 )
| ( product @ SY36 @ SV1 @ SY37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(119,plain,
! [SV8: $i,SV2: $i] :
( ( ! [SY38: $i] :
( ~ ( product @ SV2 @ e_1 @ SV8 )
| ~ ( next @ SV2 @ SY38 )
| ~ ( greater @ SV8 @ SY38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(120,plain,
! [SV9: $i,SV3: $i] :
( ( ~ ( group_element @ SV3 )
| ~ ( group_element @ SV9 )
| ( product @ SV3 @ SV9 @ e_1 )
| ( product @ SV3 @ SV9 @ e_2 )
| ( product @ SV3 @ SV9 @ e_3 )
| ( product @ SV3 @ SV9 @ e_4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(121,plain,
! [SV10: $i,SV4: $i] :
( ( ! [SY39: $i,SY40: $i] :
( ~ ( product @ SV4 @ SV10 @ SY39 )
| ~ ( product @ SV4 @ SV10 @ SY40 )
| ( equalish @ SY39 @ SY40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(122,plain,
! [SV11: $i,SV5: $i] :
( ( ! [SY41: $i,SY42: $i] :
( ~ ( product @ SV5 @ SV11 @ SY41 )
| ~ ( product @ SV5 @ SY42 @ SY41 )
| ( equalish @ SV11 @ SY42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(123,plain,
! [SV12: $i,SV6: $i] :
( ( ! [SY43: $i,SY44: $i] :
( ~ ( product @ SV6 @ SV12 @ SY43 )
| ~ ( product @ SY44 @ SV12 @ SY43 )
| ( equalish @ SV6 @ SY44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(124,plain,
! [SV13: $i,SV7: $i,SV1: $i] :
( ( ! [SY45: $i] :
( ~ ( product @ SV1 @ SV7 @ SV13 )
| ~ ( product @ SV7 @ SV13 @ SY45 )
| ( product @ SV13 @ SV1 @ SY45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(125,plain,
! [SV14: $i,SV8: $i,SV2: $i] :
( ( ~ ( product @ SV2 @ e_1 @ SV8 )
| ~ ( next @ SV2 @ SV14 )
| ~ ( greater @ SV8 @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(126,plain,
! [SV9: $i,SV3: $i] :
( ( ( ~ ( group_element @ SV3 ) )
= $true )
| ( ( ~ ( group_element @ SV9 )
| ( product @ SV3 @ SV9 @ e_1 )
| ( product @ SV3 @ SV9 @ e_2 )
| ( product @ SV3 @ SV9 @ e_3 )
| ( product @ SV3 @ SV9 @ e_4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(127,plain,
! [SV15: $i,SV10: $i,SV4: $i] :
( ( ! [SY46: $i] :
( ~ ( product @ SV4 @ SV10 @ SV15 )
| ~ ( product @ SV4 @ SV10 @ SY46 )
| ( equalish @ SV15 @ SY46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(128,plain,
! [SV16: $i,SV11: $i,SV5: $i] :
( ( ! [SY47: $i] :
( ~ ( product @ SV5 @ SV11 @ SV16 )
| ~ ( product @ SV5 @ SY47 @ SV16 )
| ( equalish @ SV11 @ SY47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(129,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ! [SY48: $i] :
( ~ ( product @ SV6 @ SV12 @ SV17 )
| ~ ( product @ SY48 @ SV12 @ SV17 )
| ( equalish @ SV6 @ SY48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(130,plain,
! [SV18: $i,SV13: $i,SV7: $i,SV1: $i] :
( ( ~ ( product @ SV1 @ SV7 @ SV13 )
| ~ ( product @ SV7 @ SV13 @ SV18 )
| ( product @ SV13 @ SV1 @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(131,plain,
! [SV14: $i,SV8: $i,SV2: $i] :
( ( ( ~ ( product @ SV2 @ e_1 @ SV8 ) )
= $true )
| ( ( ~ ( next @ SV2 @ SV14 )
| ~ ( greater @ SV8 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(132,plain,
! [SV9: $i,SV3: $i] :
( ( ( group_element @ SV3 )
= $false )
| ( ( ~ ( group_element @ SV9 )
| ( product @ SV3 @ SV9 @ e_1 )
| ( product @ SV3 @ SV9 @ e_2 )
| ( product @ SV3 @ SV9 @ e_3 )
| ( product @ SV3 @ SV9 @ e_4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(133,plain,
! [SV19: $i,SV15: $i,SV10: $i,SV4: $i] :
( ( ~ ( product @ SV4 @ SV10 @ SV15 )
| ~ ( product @ SV4 @ SV10 @ SV19 )
| ( equalish @ SV15 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(134,plain,
! [SV20: $i,SV16: $i,SV11: $i,SV5: $i] :
( ( ~ ( product @ SV5 @ SV11 @ SV16 )
| ~ ( product @ SV5 @ SV20 @ SV16 )
| ( equalish @ SV11 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(135,plain,
! [SV21: $i,SV17: $i,SV12: $i,SV6: $i] :
( ( ~ ( product @ SV6 @ SV12 @ SV17 )
| ~ ( product @ SV21 @ SV12 @ SV17 )
| ( equalish @ SV6 @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(136,plain,
! [SV18: $i,SV13: $i,SV7: $i,SV1: $i] :
( ( ( ~ ( product @ SV1 @ SV7 @ SV13 ) )
= $true )
| ( ( ~ ( product @ SV7 @ SV13 @ SV18 )
| ( product @ SV13 @ SV1 @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(137,plain,
! [SV14: $i,SV8: $i,SV2: $i] :
( ( ( product @ SV2 @ e_1 @ SV8 )
= $false )
| ( ( ~ ( next @ SV2 @ SV14 )
| ~ ( greater @ SV8 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(138,plain,
! [SV3: $i,SV9: $i] :
( ( ( ~ ( group_element @ SV9 ) )
= $true )
| ( ( ( product @ SV3 @ SV9 @ e_1 )
| ( product @ SV3 @ SV9 @ e_2 )
| ( product @ SV3 @ SV9 @ e_3 )
| ( product @ SV3 @ SV9 @ e_4 ) )
= $true )
| ( ( group_element @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(139,plain,
! [SV19: $i,SV15: $i,SV10: $i,SV4: $i] :
( ( ( ~ ( product @ SV4 @ SV10 @ SV15 ) )
= $true )
| ( ( ~ ( product @ SV4 @ SV10 @ SV19 )
| ( equalish @ SV15 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(140,plain,
! [SV20: $i,SV16: $i,SV11: $i,SV5: $i] :
( ( ( ~ ( product @ SV5 @ SV11 @ SV16 ) )
= $true )
| ( ( ~ ( product @ SV5 @ SV20 @ SV16 )
| ( equalish @ SV11 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(141,plain,
! [SV21: $i,SV17: $i,SV12: $i,SV6: $i] :
( ( ( ~ ( product @ SV6 @ SV12 @ SV17 ) )
= $true )
| ( ( ~ ( product @ SV21 @ SV12 @ SV17 )
| ( equalish @ SV6 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(142,plain,
! [SV18: $i,SV13: $i,SV7: $i,SV1: $i] :
( ( ( product @ SV1 @ SV7 @ SV13 )
= $false )
| ( ( ~ ( product @ SV7 @ SV13 @ SV18 )
| ( product @ SV13 @ SV1 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(143,plain,
! [SV8: $i,SV14: $i,SV2: $i] :
( ( ( ~ ( next @ SV2 @ SV14 ) )
= $true )
| ( ( ~ ( greater @ SV8 @ SV14 ) )
= $true )
| ( ( product @ SV2 @ e_1 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(144,plain,
! [SV3: $i,SV9: $i] :
( ( ( group_element @ SV9 )
= $false )
| ( ( ( product @ SV3 @ SV9 @ e_1 )
| ( product @ SV3 @ SV9 @ e_2 )
| ( product @ SV3 @ SV9 @ e_3 )
| ( product @ SV3 @ SV9 @ e_4 ) )
= $true )
| ( ( group_element @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(145,plain,
! [SV19: $i,SV15: $i,SV10: $i,SV4: $i] :
( ( ( product @ SV4 @ SV10 @ SV15 )
= $false )
| ( ( ~ ( product @ SV4 @ SV10 @ SV19 )
| ( equalish @ SV15 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(146,plain,
! [SV20: $i,SV16: $i,SV11: $i,SV5: $i] :
( ( ( product @ SV5 @ SV11 @ SV16 )
= $false )
| ( ( ~ ( product @ SV5 @ SV20 @ SV16 )
| ( equalish @ SV11 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(147,plain,
! [SV21: $i,SV17: $i,SV12: $i,SV6: $i] :
( ( ( product @ SV6 @ SV12 @ SV17 )
= $false )
| ( ( ~ ( product @ SV21 @ SV12 @ SV17 )
| ( equalish @ SV6 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(148,plain,
! [SV1: $i,SV18: $i,SV13: $i,SV7: $i] :
( ( ( ~ ( product @ SV7 @ SV13 @ SV18 ) )
= $true )
| ( ( product @ SV13 @ SV1 @ SV18 )
= $true )
| ( ( product @ SV1 @ SV7 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(149,plain,
! [SV8: $i,SV14: $i,SV2: $i] :
( ( ( next @ SV2 @ SV14 )
= $false )
| ( ( ~ ( greater @ SV8 @ SV14 ) )
= $true )
| ( ( product @ SV2 @ e_1 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(150,plain,
! [SV9: $i,SV3: $i] :
( ( ( product @ SV3 @ SV9 @ e_1 )
= $true )
| ( ( ( product @ SV3 @ SV9 @ e_2 )
| ( product @ SV3 @ SV9 @ e_3 )
| ( product @ SV3 @ SV9 @ e_4 ) )
= $true )
| ( ( group_element @ SV9 )
= $false )
| ( ( group_element @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(151,plain,
! [SV15: $i,SV19: $i,SV10: $i,SV4: $i] :
( ( ( ~ ( product @ SV4 @ SV10 @ SV19 ) )
= $true )
| ( ( equalish @ SV15 @ SV19 )
= $true )
| ( ( product @ SV4 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(152,plain,
! [SV11: $i,SV16: $i,SV20: $i,SV5: $i] :
( ( ( ~ ( product @ SV5 @ SV20 @ SV16 ) )
= $true )
| ( ( equalish @ SV11 @ SV20 )
= $true )
| ( ( product @ SV5 @ SV11 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(153,plain,
! [SV6: $i,SV17: $i,SV12: $i,SV21: $i] :
( ( ( ~ ( product @ SV21 @ SV12 @ SV17 ) )
= $true )
| ( ( equalish @ SV6 @ SV21 )
= $true )
| ( ( product @ SV6 @ SV12 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(154,plain,
! [SV1: $i,SV18: $i,SV13: $i,SV7: $i] :
( ( ( product @ SV7 @ SV13 @ SV18 )
= $false )
| ( ( product @ SV13 @ SV1 @ SV18 )
= $true )
| ( ( product @ SV1 @ SV7 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(155,plain,
! [SV2: $i,SV14: $i,SV8: $i] :
( ( ( greater @ SV8 @ SV14 )
= $false )
| ( ( next @ SV2 @ SV14 )
= $false )
| ( ( product @ SV2 @ e_1 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(156,plain,
! [SV9: $i,SV3: $i] :
( ( ( product @ SV3 @ SV9 @ e_2 )
= $true )
| ( ( ( product @ SV3 @ SV9 @ e_3 )
| ( product @ SV3 @ SV9 @ e_4 ) )
= $true )
| ( ( product @ SV3 @ SV9 @ e_1 )
= $true )
| ( ( group_element @ SV9 )
= $false )
| ( ( group_element @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(157,plain,
! [SV15: $i,SV19: $i,SV10: $i,SV4: $i] :
( ( ( product @ SV4 @ SV10 @ SV19 )
= $false )
| ( ( equalish @ SV15 @ SV19 )
= $true )
| ( ( product @ SV4 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(158,plain,
! [SV11: $i,SV16: $i,SV20: $i,SV5: $i] :
( ( ( product @ SV5 @ SV20 @ SV16 )
= $false )
| ( ( equalish @ SV11 @ SV20 )
= $true )
| ( ( product @ SV5 @ SV11 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(159,plain,
! [SV6: $i,SV17: $i,SV12: $i,SV21: $i] :
( ( ( product @ SV21 @ SV12 @ SV17 )
= $false )
| ( ( equalish @ SV6 @ SV21 )
= $true )
| ( ( product @ SV6 @ SV12 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(160,plain,
! [SV9: $i,SV3: $i] :
( ( ( product @ SV3 @ SV9 @ e_3 )
= $true )
| ( ( product @ SV3 @ SV9 @ e_4 )
= $true )
| ( ( product @ SV3 @ SV9 @ e_2 )
= $true )
| ( ( product @ SV3 @ SV9 @ e_1 )
= $true )
| ( ( group_element @ SV9 )
= $false )
| ( ( group_element @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(161,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[68,160,159,158,157,155,154,117,112,111,110,109,108,107,106,105,104,103,102,101,81,80,79,78,76,75,74,73,72,71,70,69]) ).
thf(162,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[161]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP129-2.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.14 % Computer : n019.cluster.edu
% 0.09/0.14 % Model : x86_64 x86_64
% 0.09/0.14 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.14 % Memory : 8046.5625MB
% 0.09/0.14 % OS : Linux 6.8.0-71-generic
% 0.09/0.14 % CPULimit : 300
% 0.09/0.14 % WCLimit : 300
% 0.09/0.14 % DateTime : Tue Oct 6 10:35:46 UTC 2026
% 0.09/0.14 % CPUTime :
% 0.09/0.14 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.24/2.01
% 10.24/2.01 No.of.Axioms: 31
% 10.24/2.01
% 10.24/2.01 Length.of.Defs: 0
% 10.24/2.01
% 10.24/2.01 Contains.Choice.Funs: false
% 10.24/2.01 ..
% 10.24/2.01
% 10.24/2.01 ********************************
% 10.24/2.01 * All subproblems solved! *
% 10.24/2.01 ********************************
% 10.24/2.01 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:31,ps:0,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:161,loop_count:0,foatp_calls:1,translation:fof_full)
% 10.24/2.01
% 10.24/2.01 %**** Beginning of derivation protocol ****
% 10.24/2.01 % SZS output start CNFRefutation
% See solution above
% 10.24/2.01
% 10.24/2.01 %**** End of derivation protocol ****
% 10.24/2.01 %**** no. of clauses in derivation: 162 ****
% 10.24/2.01 %**** clause counter: 161 ****
% 10.24/2.01
% 10.24/2.01 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:31,ps:0,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:161,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------