%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GRP040-3 : 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 : n009.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 2.95s 0.78s
% Output : CNFRefutation 2.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 18
% Syntax : Number of formulae : 121 ( 82 unt; 0 typ; 0 def)
% Number of atoms : 628 ( 176 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 1065 ( 126 ~; 187 |; 0 &; 752 @)
% ( 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 : 337 ( 0 ^; 337 !; 0 ?; 337 :)
% 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_identity,type,
identity: $i ).
thf(tp_inverse,type,
inverse: $i > $i ).
thf(tp_multiply,type,
multiply: $i > $i > $i ).
thf(tp_product,type,
product: $i > $i > $i > $o ).
thf(tp_subgroup_member,type,
subgroup_member: $i > $o ).
thf(1,axiom,
! [A: $i,B: $i] :
( ( 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] :
( ~ ( subgroup_member @ A )
| ~ ( subgroup_member @ B )
| ~ ( product @ A @ ( inverse @ B ) @ C )
| ( subgroup_member @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_product_and_inverse) ).
thf(4,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(5,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(6,axiom,
! [X: $i,Y: $i,Z: $i,W: $i] :
( ~ ( product @ X @ Y @ Z )
| ~ ( product @ X @ Y @ W )
| ( Z = W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function2) ).
thf(7,axiom,
! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function1) ).
thf(8,axiom,
! [X: $i] : ( product @ X @ ( inverse @ X ) @ identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
thf(9,axiom,
! [X: $i] : ( product @ ( inverse @ X ) @ X @ identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(10,axiom,
! [X: $i] : ( product @ X @ identity @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
thf(11,axiom,
! [X: $i] : ( product @ identity @ X @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(12,axiom,
product @ a @ c @ d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_c_is_d) ).
thf(13,axiom,
product @ b @ ( inverse @ a ) @ c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
thf(14,axiom,
~ ( subgroup_member @ d ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_in_subgroup) ).
thf(15,axiom,
subgroup_member @ b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_in_subgroup) ).
thf(16,axiom,
~ ( subgroup_member @ a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_in_subgroup) ).
thf(17,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(18,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[17]) ).
thf(19,negated_conjecture,
! [A: $i] :
( ( inverse @ ( inverse @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_inverse_is_self_cancelling) ).
thf(20,plain,
$false = $false,
inference(unfold_def,[status(thm)],[18]) ).
thf(21,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(22,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(23,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subgroup_member @ A )
| ~ ( subgroup_member @ B )
| ~ ( product @ A @ ( inverse @ B ) @ C )
| ( subgroup_member @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(24,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)],[4]) ).
thf(25,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)],[5]) ).
thf(26,plain,
( ( ! [X: $i,Y: $i,Z: $i,W: $i] :
( ~ ( product @ X @ Y @ Z )
| ~ ( product @ X @ Y @ W )
| ( Z = W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(27,plain,
( ( ! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(28,plain,
( ( ! [X: $i] : ( product @ X @ ( inverse @ X ) @ identity ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(29,plain,
( ( ! [X: $i] : ( product @ ( inverse @ X ) @ X @ identity ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(30,plain,
( ( ! [X: $i] : ( product @ X @ identity @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(31,plain,
( ( ! [X: $i] : ( product @ identity @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(32,plain,
( ( product @ a @ c @ d )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(33,plain,
( ( product @ b @ ( inverse @ a ) @ c )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(34,plain,
( ( ~ ( subgroup_member @ d ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(35,plain,
( ( subgroup_member @ b )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(36,plain,
( ( ~ ( subgroup_member @ a ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(37,plain,
( ( ! [A: $i] :
( ( inverse @ ( inverse @ A ) )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(38,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[20]) ).
thf(39,plain,
( ( ! [A: $i] :
( ~ ( subgroup_member @ A )
| ! [B: $i] :
( ~ ( subgroup_member @ B )
| ! [C: $i] :
( ~ ( product @ A @ ( inverse @ B ) @ C )
| ( subgroup_member @ C ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(40,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i] :
( ~ ( product @ X @ Y @ U )
| ! [V: $i] :
( ~ ( product @ Y @ Z @ V )
| ! [W: $i] :
( ~ ( product @ X @ V @ W )
| ( product @ U @ Z @ W ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(41,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i] :
( ~ ( product @ X @ Y @ U )
| ! [V: $i] :
( ~ ( product @ Y @ Z @ V )
| ! [W: $i] :
( ~ ( product @ U @ Z @ W )
| ( product @ X @ V @ W ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(42,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( product @ X @ Y @ Z )
| ! [W: $i] :
( ~ ( product @ X @ Y @ W )
| ( Z = W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(43,plain,
( ( ! [A: $i] :
( ( inverse @ ( inverse @ A ) )
= A ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(44,plain,
( ( ~ ( subgroup_member @ a ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(45,plain,
( ( subgroup_member @ b )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(46,plain,
( ( ~ ( subgroup_member @ d ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(47,plain,
( ( product @ b @ ( inverse @ a ) @ c )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(48,plain,
( ( product @ a @ c @ d )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(49,plain,
( ( ! [X: $i] : ( product @ identity @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(50,plain,
( ( ! [X: $i] : ( product @ X @ identity @ X ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(51,plain,
( ( ! [X: $i] : ( product @ ( inverse @ X ) @ X @ identity ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(52,plain,
( ( ! [X: $i] : ( product @ X @ ( inverse @ X ) @ identity ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(53,plain,
( ( ! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(54,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( product @ X @ Y @ Z )
| ! [W: $i] :
( ~ ( product @ X @ Y @ W )
| ( Z = W ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(55,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i] :
( ~ ( product @ X @ Y @ U )
| ! [V: $i] :
( ~ ( product @ Y @ Z @ V )
| ! [W: $i] :
( ~ ( product @ U @ Z @ W )
| ( product @ X @ V @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(56,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i] :
( ~ ( product @ X @ Y @ U )
| ! [V: $i] :
( ~ ( product @ Y @ Z @ V )
| ! [W: $i] :
( ~ ( product @ X @ V @ W )
| ( product @ U @ Z @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(57,plain,
( ( ! [A: $i] :
( ~ ( subgroup_member @ A )
| ! [B: $i] :
( ~ ( subgroup_member @ B )
| ! [C: $i] :
( ~ ( product @ A @ ( inverse @ B ) @ C )
| ( subgroup_member @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(58,plain,
( ( ! [A: $i,B: $i] :
( ( subgroup_member @ ( element_in_O2 @ A @ B ) )
| ( subgroup_member @ B )
| ( subgroup_member @ A ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(59,plain,
( ( ! [A: $i,B: $i] :
( ( product @ A @ ( element_in_O2 @ A @ B ) @ B )
| ( subgroup_member @ B )
| ( subgroup_member @ A ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(60,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[38]) ).
thf(61,plain,
! [SV1: $i] :
( ( ( inverse @ ( inverse @ SV1 ) )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(62,plain,
( ( subgroup_member @ a )
= $false ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(63,plain,
( ( subgroup_member @ d )
= $false ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(64,plain,
! [SV2: $i] :
( ( product @ identity @ SV2 @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(65,plain,
! [SV3: $i] :
( ( product @ SV3 @ identity @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(66,plain,
! [SV4: $i] :
( ( product @ ( inverse @ SV4 ) @ SV4 @ identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(67,plain,
! [SV5: $i] :
( ( product @ SV5 @ ( inverse @ SV5 ) @ identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(68,plain,
! [SV6: $i] :
( ( ! [SY30: $i] : ( product @ SV6 @ SY30 @ ( multiply @ SV6 @ SY30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(69,plain,
! [SV7: $i] :
( ( ! [SY31: $i,SY32: $i] :
( ~ ( product @ SV7 @ SY31 @ SY32 )
| ! [SY33: $i] :
( ~ ( product @ SV7 @ SY31 @ SY33 )
| ( SY32 = SY33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(70,plain,
! [SV8: $i] :
( ( ! [SY34: $i,SY35: $i,SY36: $i] :
( ~ ( product @ SV8 @ SY34 @ SY35 )
| ! [SY37: $i] :
( ~ ( product @ SY34 @ SY36 @ SY37 )
| ! [SY38: $i] :
( ~ ( product @ SY35 @ SY36 @ SY38 )
| ( product @ SV8 @ SY37 @ SY38 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(71,plain,
! [SV9: $i] :
( ( ! [SY39: $i,SY40: $i,SY41: $i] :
( ~ ( product @ SV9 @ SY39 @ SY40 )
| ! [SY42: $i] :
( ~ ( product @ SY39 @ SY41 @ SY42 )
| ! [SY43: $i] :
( ~ ( product @ SV9 @ SY42 @ SY43 )
| ( product @ SY40 @ SY41 @ SY43 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(72,plain,
! [SV10: $i] :
( ( ~ ( subgroup_member @ SV10 )
| ! [SY44: $i] :
( ~ ( subgroup_member @ SY44 )
| ! [SY45: $i] :
( ~ ( product @ SV10 @ ( inverse @ SY44 ) @ SY45 )
| ( subgroup_member @ SY45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(73,plain,
! [SV11: $i] :
( ( ! [SY46: $i] :
( ( subgroup_member @ ( element_in_O2 @ SV11 @ SY46 ) )
| ( subgroup_member @ SY46 )
| ( subgroup_member @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(74,plain,
! [SV12: $i] :
( ( ! [SY47: $i] :
( ( product @ SV12 @ ( element_in_O2 @ SV12 @ SY47 ) @ SY47 )
| ( subgroup_member @ SY47 )
| ( subgroup_member @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(75,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(76,plain,
! [SV13: $i,SV6: $i] :
( ( product @ SV6 @ SV13 @ ( multiply @ SV6 @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(77,plain,
! [SV14: $i,SV7: $i] :
( ( ! [SY48: $i] :
( ~ ( product @ SV7 @ SV14 @ SY48 )
| ! [SY49: $i] :
( ~ ( product @ SV7 @ SV14 @ SY49 )
| ( SY48 = SY49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(78,plain,
! [SV15: $i,SV8: $i] :
( ( ! [SY50: $i,SY51: $i] :
( ~ ( product @ SV8 @ SV15 @ SY50 )
| ! [SY52: $i] :
( ~ ( product @ SV15 @ SY51 @ SY52 )
| ! [SY38: $i] :
( ~ ( product @ SY50 @ SY51 @ SY38 )
| ( product @ SV8 @ SY52 @ SY38 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(79,plain,
! [SV16: $i,SV9: $i] :
( ( ! [SY54: $i,SY55: $i] :
( ~ ( product @ SV9 @ SV16 @ SY54 )
| ! [SY56: $i] :
( ~ ( product @ SV16 @ SY55 @ SY56 )
| ! [SY43: $i] :
( ~ ( product @ SV9 @ SY56 @ SY43 )
| ( product @ SY54 @ SY55 @ SY43 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(80,plain,
! [SV10: $i] :
( ( ( ~ ( subgroup_member @ SV10 ) )
= $true )
| ( ( ! [SY44: $i] :
( ~ ( subgroup_member @ SY44 )
| ! [SY45: $i] :
( ~ ( product @ SV10 @ ( inverse @ SY44 ) @ SY45 )
| ( subgroup_member @ SY45 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(81,plain,
! [SV17: $i,SV11: $i] :
( ( ( subgroup_member @ ( element_in_O2 @ SV11 @ SV17 ) )
| ( subgroup_member @ SV17 )
| ( subgroup_member @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(82,plain,
! [SV18: $i,SV12: $i] :
( ( ( product @ SV12 @ ( element_in_O2 @ SV12 @ SV18 ) @ SV18 )
| ( subgroup_member @ SV18 )
| ( subgroup_member @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(83,plain,
! [SV19: $i,SV14: $i,SV7: $i] :
( ( ~ ( product @ SV7 @ SV14 @ SV19 )
| ! [SY58: $i] :
( ~ ( product @ SV7 @ SV14 @ SY58 )
| ( SV19 = SY58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(84,plain,
! [SV20: $i,SV15: $i,SV8: $i] :
( ( ! [SY59: $i] :
( ~ ( product @ SV8 @ SV15 @ SV20 )
| ! [SY60: $i] :
( ~ ( product @ SV15 @ SY59 @ SY60 )
| ! [SY61: $i] :
( ~ ( product @ SV20 @ SY59 @ SY61 )
| ( product @ SV8 @ SY60 @ SY61 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(85,plain,
! [SV21: $i,SV16: $i,SV9: $i] :
( ( ! [SY62: $i] :
( ~ ( product @ SV9 @ SV16 @ SV21 )
| ! [SY63: $i] :
( ~ ( product @ SV16 @ SY62 @ SY63 )
| ! [SY64: $i] :
( ~ ( product @ SV9 @ SY63 @ SY64 )
| ( product @ SV21 @ SY62 @ SY64 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(86,plain,
! [SV10: $i] :
( ( ( subgroup_member @ SV10 )
= $false )
| ( ( ! [SY44: $i] :
( ~ ( subgroup_member @ SY44 )
| ! [SY45: $i] :
( ~ ( product @ SV10 @ ( inverse @ SY44 ) @ SY45 )
| ( subgroup_member @ SY45 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(87,plain,
! [SV17: $i,SV11: $i] :
( ( ( subgroup_member @ ( element_in_O2 @ SV11 @ SV17 ) )
= $true )
| ( ( ( subgroup_member @ SV17 )
| ( subgroup_member @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(88,plain,
! [SV18: $i,SV12: $i] :
( ( ( product @ SV12 @ ( element_in_O2 @ SV12 @ SV18 ) @ SV18 )
= $true )
| ( ( ( subgroup_member @ SV18 )
| ( subgroup_member @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(89,plain,
! [SV19: $i,SV14: $i,SV7: $i] :
( ( ( ~ ( product @ SV7 @ SV14 @ SV19 ) )
= $true )
| ( ( ! [SY58: $i] :
( ~ ( product @ SV7 @ SV14 @ SY58 )
| ( SV19 = SY58 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(90,plain,
! [SV22: $i,SV20: $i,SV15: $i,SV8: $i] :
( ( ~ ( product @ SV8 @ SV15 @ SV20 )
| ! [SY65: $i] :
( ~ ( product @ SV15 @ SV22 @ SY65 )
| ! [SY66: $i] :
( ~ ( product @ SV20 @ SV22 @ SY66 )
| ( product @ SV8 @ SY65 @ SY66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(91,plain,
! [SV23: $i,SV21: $i,SV16: $i,SV9: $i] :
( ( ~ ( product @ SV9 @ SV16 @ SV21 )
| ! [SY67: $i] :
( ~ ( product @ SV16 @ SV23 @ SY67 )
| ! [SY68: $i] :
( ~ ( product @ SV9 @ SY67 @ SY68 )
| ( product @ SV21 @ SV23 @ SY68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(92,plain,
! [SV10: $i,SV24: $i] :
( ( ( ~ ( subgroup_member @ SV24 )
| ! [SY69: $i] :
( ~ ( product @ SV10 @ ( inverse @ SV24 ) @ SY69 )
| ( subgroup_member @ SY69 ) ) )
= $true )
| ( ( subgroup_member @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(93,plain,
! [SV11: $i,SV17: $i] :
( ( ( subgroup_member @ SV17 )
= $true )
| ( ( subgroup_member @ SV11 )
= $true )
| ( ( subgroup_member @ ( element_in_O2 @ SV11 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(94,plain,
! [SV12: $i,SV18: $i] :
( ( ( subgroup_member @ SV18 )
= $true )
| ( ( subgroup_member @ SV12 )
= $true )
| ( ( product @ SV12 @ ( element_in_O2 @ SV12 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(95,plain,
! [SV19: $i,SV14: $i,SV7: $i] :
( ( ( product @ SV7 @ SV14 @ SV19 )
= $false )
| ( ( ! [SY58: $i] :
( ~ ( product @ SV7 @ SV14 @ SY58 )
| ( SV19 = SY58 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(96,plain,
! [SV22: $i,SV20: $i,SV15: $i,SV8: $i] :
( ( ( ~ ( product @ SV8 @ SV15 @ SV20 ) )
= $true )
| ( ( ! [SY65: $i] :
( ~ ( product @ SV15 @ SV22 @ SY65 )
| ! [SY66: $i] :
( ~ ( product @ SV20 @ SV22 @ SY66 )
| ( product @ SV8 @ SY65 @ SY66 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(97,plain,
! [SV23: $i,SV21: $i,SV16: $i,SV9: $i] :
( ( ( ~ ( product @ SV9 @ SV16 @ SV21 ) )
= $true )
| ( ( ! [SY67: $i] :
( ~ ( product @ SV16 @ SV23 @ SY67 )
| ! [SY68: $i] :
( ~ ( product @ SV9 @ SY67 @ SY68 )
| ( product @ SV21 @ SV23 @ SY68 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(98,plain,
! [SV10: $i,SV24: $i] :
( ( ( ~ ( subgroup_member @ SV24 ) )
= $true )
| ( ( ! [SY69: $i] :
( ~ ( product @ SV10 @ ( inverse @ SV24 ) @ SY69 )
| ( subgroup_member @ SY69 ) ) )
= $true )
| ( ( subgroup_member @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(99,plain,
! [SV19: $i,SV25: $i,SV14: $i,SV7: $i] :
( ( ( ~ ( product @ SV7 @ SV14 @ SV25 )
| ( SV19 = SV25 ) )
= $true )
| ( ( product @ SV7 @ SV14 @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(100,plain,
! [SV22: $i,SV20: $i,SV15: $i,SV8: $i] :
( ( ( product @ SV8 @ SV15 @ SV20 )
= $false )
| ( ( ! [SY65: $i] :
( ~ ( product @ SV15 @ SV22 @ SY65 )
| ! [SY66: $i] :
( ~ ( product @ SV20 @ SV22 @ SY66 )
| ( product @ SV8 @ SY65 @ SY66 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(101,plain,
! [SV23: $i,SV21: $i,SV16: $i,SV9: $i] :
( ( ( product @ SV9 @ SV16 @ SV21 )
= $false )
| ( ( ! [SY67: $i] :
( ~ ( product @ SV16 @ SV23 @ SY67 )
| ! [SY68: $i] :
( ~ ( product @ SV9 @ SY67 @ SY68 )
| ( product @ SV21 @ SV23 @ SY68 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(102,plain,
! [SV10: $i,SV24: $i] :
( ( ( subgroup_member @ SV24 )
= $false )
| ( ( ! [SY69: $i] :
( ~ ( product @ SV10 @ ( inverse @ SV24 ) @ SY69 )
| ( subgroup_member @ SY69 ) ) )
= $true )
| ( ( subgroup_member @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(103,plain,
! [SV19: $i,SV25: $i,SV14: $i,SV7: $i] :
( ( ( ~ ( product @ SV7 @ SV14 @ SV25 ) )
= $true )
| ( ( SV19 = SV25 )
= $true )
| ( ( product @ SV7 @ SV14 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(104,plain,
! [SV8: $i,SV20: $i,SV26: $i,SV22: $i,SV15: $i] :
( ( ( ~ ( product @ SV15 @ SV22 @ SV26 )
| ! [SY70: $i] :
( ~ ( product @ SV20 @ SV22 @ SY70 )
| ( product @ SV8 @ SV26 @ SY70 ) ) )
= $true )
| ( ( product @ SV8 @ SV15 @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(105,plain,
! [SV21: $i,SV9: $i,SV27: $i,SV23: $i,SV16: $i] :
( ( ( ~ ( product @ SV16 @ SV23 @ SV27 )
| ! [SY71: $i] :
( ~ ( product @ SV9 @ SV27 @ SY71 )
| ( product @ SV21 @ SV23 @ SY71 ) ) )
= $true )
| ( ( product @ SV9 @ SV16 @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(106,plain,
! [SV28: $i,SV24: $i,SV10: $i] :
( ( ( ~ ( product @ SV10 @ ( inverse @ SV24 ) @ SV28 )
| ( subgroup_member @ SV28 ) )
= $true )
| ( ( subgroup_member @ SV24 )
= $false )
| ( ( subgroup_member @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(107,plain,
! [SV19: $i,SV25: $i,SV14: $i,SV7: $i] :
( ( ( product @ SV7 @ SV14 @ SV25 )
= $false )
| ( ( SV19 = SV25 )
= $true )
| ( ( product @ SV7 @ SV14 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(108,plain,
! [SV8: $i,SV20: $i,SV26: $i,SV22: $i,SV15: $i] :
( ( ( ~ ( product @ SV15 @ SV22 @ SV26 ) )
= $true )
| ( ( ! [SY70: $i] :
( ~ ( product @ SV20 @ SV22 @ SY70 )
| ( product @ SV8 @ SV26 @ SY70 ) ) )
= $true )
| ( ( product @ SV8 @ SV15 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(109,plain,
! [SV21: $i,SV9: $i,SV27: $i,SV23: $i,SV16: $i] :
( ( ( ~ ( product @ SV16 @ SV23 @ SV27 ) )
= $true )
| ( ( ! [SY71: $i] :
( ~ ( product @ SV9 @ SV27 @ SY71 )
| ( product @ SV21 @ SV23 @ SY71 ) ) )
= $true )
| ( ( product @ SV9 @ SV16 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(110,plain,
! [SV28: $i,SV24: $i,SV10: $i] :
( ( ( ~ ( product @ SV10 @ ( inverse @ SV24 ) @ SV28 ) )
= $true )
| ( ( subgroup_member @ SV28 )
= $true )
| ( ( subgroup_member @ SV24 )
= $false )
| ( ( subgroup_member @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(111,plain,
! [SV8: $i,SV20: $i,SV26: $i,SV22: $i,SV15: $i] :
( ( ( product @ SV15 @ SV22 @ SV26 )
= $false )
| ( ( ! [SY70: $i] :
( ~ ( product @ SV20 @ SV22 @ SY70 )
| ( product @ SV8 @ SV26 @ SY70 ) ) )
= $true )
| ( ( product @ SV8 @ SV15 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(112,plain,
! [SV21: $i,SV9: $i,SV27: $i,SV23: $i,SV16: $i] :
( ( ( product @ SV16 @ SV23 @ SV27 )
= $false )
| ( ( ! [SY71: $i] :
( ~ ( product @ SV9 @ SV27 @ SY71 )
| ( product @ SV21 @ SV23 @ SY71 ) ) )
= $true )
| ( ( product @ SV9 @ SV16 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(113,plain,
! [SV28: $i,SV24: $i,SV10: $i] :
( ( ( product @ SV10 @ ( inverse @ SV24 ) @ SV28 )
= $false )
| ( ( subgroup_member @ SV28 )
= $true )
| ( ( subgroup_member @ SV24 )
= $false )
| ( ( subgroup_member @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(114,plain,
! [SV15: $i,SV26: $i,SV8: $i,SV29: $i,SV22: $i,SV20: $i] :
( ( ( ~ ( product @ SV20 @ SV22 @ SV29 )
| ( product @ SV8 @ SV26 @ SV29 ) )
= $true )
| ( ( product @ SV15 @ SV22 @ SV26 )
= $false )
| ( ( product @ SV8 @ SV15 @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(115,plain,
! [SV16: $i,SV23: $i,SV21: $i,SV30: $i,SV27: $i,SV9: $i] :
( ( ( ~ ( product @ SV9 @ SV27 @ SV30 )
| ( product @ SV21 @ SV23 @ SV30 ) )
= $true )
| ( ( product @ SV16 @ SV23 @ SV27 )
= $false )
| ( ( product @ SV9 @ SV16 @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(116,plain,
! [SV15: $i,SV26: $i,SV8: $i,SV29: $i,SV22: $i,SV20: $i] :
( ( ( ~ ( product @ SV20 @ SV22 @ SV29 ) )
= $true )
| ( ( product @ SV8 @ SV26 @ SV29 )
= $true )
| ( ( product @ SV15 @ SV22 @ SV26 )
= $false )
| ( ( product @ SV8 @ SV15 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(117,plain,
! [SV16: $i,SV23: $i,SV21: $i,SV30: $i,SV27: $i,SV9: $i] :
( ( ( ~ ( product @ SV9 @ SV27 @ SV30 ) )
= $true )
| ( ( product @ SV21 @ SV23 @ SV30 )
= $true )
| ( ( product @ SV16 @ SV23 @ SV27 )
= $false )
| ( ( product @ SV9 @ SV16 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(118,plain,
! [SV15: $i,SV26: $i,SV8: $i,SV29: $i,SV22: $i,SV20: $i] :
( ( ( product @ SV20 @ SV22 @ SV29 )
= $false )
| ( ( product @ SV8 @ SV26 @ SV29 )
= $true )
| ( ( product @ SV15 @ SV22 @ SV26 )
= $false )
| ( ( product @ SV8 @ SV15 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(119,plain,
! [SV16: $i,SV23: $i,SV21: $i,SV30: $i,SV27: $i,SV9: $i] :
( ( ( product @ SV9 @ SV27 @ SV30 )
= $false )
| ( ( product @ SV21 @ SV23 @ SV30 )
= $true )
| ( ( product @ SV16 @ SV23 @ SV27 )
= $false )
| ( ( product @ SV9 @ SV16 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(120,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[45,119,118,113,107,94,93,76,75,67,66,65,64,63,62,61,48,47]) ).
thf(121,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP040-3 : 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
% 0.08/0.19 % Computer : n009.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Oct 6 10:31:47 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.95/0.78
% 2.95/0.78 No.of.Axioms: 17
% 2.95/0.78
% 2.95/0.78 Length.of.Defs: 0
% 2.95/0.78
% 2.95/0.78 Contains.Choice.Funs: false
% 2.95/0.78 ...
% 2.95/0.78
% 2.95/0.78 ********************************
% 2.95/0.78 * All subproblems solved! *
% 2.95/0.78 ********************************
% 2.95/0.78 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:17,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:120,loop_count:0,foatp_calls:1,translation:fof_full)
% 2.95/0.78
% 2.95/0.78 %**** Beginning of derivation protocol ****
% 2.95/0.78 % SZS output start CNFRefutation
% See solution above
% 2.95/0.78
% 2.95/0.78 %**** End of derivation protocol ****
% 2.95/0.78 %**** no. of clauses in derivation: 121 ****
% 2.95/0.78 %**** clause counter: 120 ****
% 2.95/0.78
% 2.95/0.78 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:17,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:120,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------