TSTP Solution File: GRP034-3 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GRP034-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n015.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 10:15:33 EDT 2022
% Result : Unsatisfiable 0.20s 0.43s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 18
% Syntax : Number of formulae : 99 ( 60 unt; 6 typ; 0 def)
% Number of atoms : 516 ( 144 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 921 ( 123 ~; 159 |; 0 &; 639 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 305 ( 0 ^ 305 !; 0 ?; 305 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $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,C: $i] :
( ~ ( subgroup_member @ A )
| ~ ( subgroup_member @ B )
| ~ ( product @ A @ ( inverse @ B ) @ C )
| ( subgroup_member @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_product_and_inverse) ).
thf(2,axiom,
! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
( ~ ( product @ X @ Y @ U )
| ~ ( product @ Y @ Z @ V )
| ~ ( product @ X @ V @ W )
| ( product @ U @ Z @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity2) ).
thf(3,axiom,
! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
( ~ ( product @ X @ Y @ U )
| ~ ( product @ Y @ Z @ V )
| ~ ( product @ U @ Z @ W )
| ( product @ X @ V @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity1) ).
thf(4,axiom,
! [X: $i,Y: $i,Z: $i,W: $i] :
( ~ ( product @ X @ Y @ Z )
| ~ ( product @ X @ Y @ W )
| ( Z = W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function2) ).
thf(5,axiom,
! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function1) ).
thf(6,axiom,
! [X: $i] : ( product @ X @ ( inverse @ X ) @ identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
thf(7,axiom,
! [X: $i] : ( product @ ( inverse @ X ) @ X @ identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
thf(8,axiom,
! [X: $i] : ( product @ X @ identity @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
thf(9,axiom,
! [X: $i] : ( product @ identity @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
thf(10,axiom,
subgroup_member @ a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_in_subgroup) ).
thf(11,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(12,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[11]) ).
thf(13,negated_conjecture,
~ ( subgroup_member @ ( inverse @ a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_inverse_is_in_subgroup) ).
thf(14,plain,
$false = $false,
inference(unfold_def,[status(thm)],[12]) ).
thf(15,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subgroup_member @ A )
| ~ ( subgroup_member @ B )
| ~ ( product @ A @ ( inverse @ B ) @ C )
| ( subgroup_member @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(16,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
( ~ ( product @ X @ Y @ U )
| ~ ( product @ Y @ Z @ V )
| ~ ( product @ X @ V @ W )
| ( product @ U @ Z @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(17,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
( ~ ( product @ X @ Y @ U )
| ~ ( product @ Y @ Z @ V )
| ~ ( product @ U @ Z @ W )
| ( product @ X @ V @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(18,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)],[4]) ).
thf(19,plain,
( ( ! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(20,plain,
( ( ! [X: $i] : ( product @ X @ ( inverse @ X ) @ identity ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(21,plain,
( ( ! [X: $i] : ( product @ ( inverse @ X ) @ X @ identity ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(22,plain,
( ( ! [X: $i] : ( product @ X @ identity @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(23,plain,
( ( ! [X: $i] : ( product @ identity @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(24,plain,
( ( subgroup_member @ a )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(25,plain,
( ( ~ ( subgroup_member @ ( inverse @ a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(26,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[14]) ).
thf(27,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)],[15]) ).
thf(28,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)],[16]) ).
thf(29,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)],[17]) ).
thf(30,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)],[18]) ).
thf(31,plain,
( ( ~ ( subgroup_member @ ( inverse @ a ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(32,plain,
( ( subgroup_member @ a )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(33,plain,
( ( ! [X: $i] : ( product @ identity @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(34,plain,
( ( ! [X: $i] : ( product @ X @ identity @ X ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(35,plain,
( ( ! [X: $i] : ( product @ ( inverse @ X ) @ X @ identity ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(36,plain,
( ( ! [X: $i] : ( product @ X @ ( inverse @ X ) @ identity ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(37,plain,
( ( ! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(38,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( product @ X @ Y @ Z )
| ! [W: $i] :
( ~ ( product @ X @ Y @ W )
| ( Z = W ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(39,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)],[29]) ).
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(copy,[status(thm)],[28]) ).
thf(41,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)],[27]) ).
thf(42,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(43,plain,
( ( subgroup_member @ ( inverse @ a ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(44,plain,
! [SV1: $i] :
( ( product @ identity @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(45,plain,
! [SV2: $i] :
( ( product @ SV2 @ identity @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(46,plain,
! [SV3: $i] :
( ( product @ ( inverse @ SV3 ) @ SV3 @ identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(47,plain,
! [SV4: $i] :
( ( product @ SV4 @ ( inverse @ SV4 ) @ identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(48,plain,
! [SV5: $i] :
( ( ! [SY25: $i] : ( product @ SV5 @ SY25 @ ( multiply @ SV5 @ SY25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(49,plain,
! [SV6: $i] :
( ( ! [SY26: $i,SY27: $i] :
( ~ ( product @ SV6 @ SY26 @ SY27 )
| ! [SY28: $i] :
( ~ ( product @ SV6 @ SY26 @ SY28 )
| ( SY27 = SY28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(50,plain,
! [SV7: $i] :
( ( ! [SY29: $i,SY30: $i,SY31: $i] :
( ~ ( product @ SV7 @ SY29 @ SY30 )
| ! [SY32: $i] :
( ~ ( product @ SY29 @ SY31 @ SY32 )
| ! [SY33: $i] :
( ~ ( product @ SY30 @ SY31 @ SY33 )
| ( product @ SV7 @ SY32 @ SY33 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(51,plain,
! [SV8: $i] :
( ( ! [SY34: $i,SY35: $i,SY36: $i] :
( ~ ( product @ SV8 @ SY34 @ SY35 )
| ! [SY37: $i] :
( ~ ( product @ SY34 @ SY36 @ SY37 )
| ! [SY38: $i] :
( ~ ( product @ SV8 @ SY37 @ SY38 )
| ( product @ SY35 @ SY36 @ SY38 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(52,plain,
! [SV9: $i] :
( ( ~ ( subgroup_member @ SV9 )
| ! [SY39: $i] :
( ~ ( subgroup_member @ SY39 )
| ! [SY40: $i] :
( ~ ( product @ SV9 @ ( inverse @ SY39 ) @ SY40 )
| ( subgroup_member @ SY40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(53,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(54,plain,
! [SV10: $i,SV5: $i] :
( ( product @ SV5 @ SV10 @ ( multiply @ SV5 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(55,plain,
! [SV11: $i,SV6: $i] :
( ( ! [SY41: $i] :
( ~ ( product @ SV6 @ SV11 @ SY41 )
| ! [SY42: $i] :
( ~ ( product @ SV6 @ SV11 @ SY42 )
| ( SY41 = SY42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(56,plain,
! [SV12: $i,SV7: $i] :
( ( ! [SY43: $i,SY44: $i] :
( ~ ( product @ SV7 @ SV12 @ SY43 )
| ! [SY45: $i] :
( ~ ( product @ SV12 @ SY44 @ SY45 )
| ! [SY33: $i] :
( ~ ( product @ SY43 @ SY44 @ SY33 )
| ( product @ SV7 @ SY45 @ SY33 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(57,plain,
! [SV13: $i,SV8: $i] :
( ( ! [SY47: $i,SY48: $i] :
( ~ ( product @ SV8 @ SV13 @ SY47 )
| ! [SY49: $i] :
( ~ ( product @ SV13 @ SY48 @ SY49 )
| ! [SY38: $i] :
( ~ ( product @ SV8 @ SY49 @ SY38 )
| ( product @ SY47 @ SY48 @ SY38 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(58,plain,
! [SV9: $i] :
( ( ( ~ ( subgroup_member @ SV9 ) )
= $true )
| ( ( ! [SY39: $i] :
( ~ ( subgroup_member @ SY39 )
| ! [SY40: $i] :
( ~ ( product @ SV9 @ ( inverse @ SY39 ) @ SY40 )
| ( subgroup_member @ SY40 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(59,plain,
! [SV14: $i,SV11: $i,SV6: $i] :
( ( ~ ( product @ SV6 @ SV11 @ SV14 )
| ! [SY51: $i] :
( ~ ( product @ SV6 @ SV11 @ SY51 )
| ( SV14 = SY51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(60,plain,
! [SV15: $i,SV12: $i,SV7: $i] :
( ( ! [SY52: $i] :
( ~ ( product @ SV7 @ SV12 @ SV15 )
| ! [SY53: $i] :
( ~ ( product @ SV12 @ SY52 @ SY53 )
| ! [SY54: $i] :
( ~ ( product @ SV15 @ SY52 @ SY54 )
| ( product @ SV7 @ SY53 @ SY54 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(61,plain,
! [SV16: $i,SV13: $i,SV8: $i] :
( ( ! [SY55: $i] :
( ~ ( product @ SV8 @ SV13 @ SV16 )
| ! [SY56: $i] :
( ~ ( product @ SV13 @ SY55 @ SY56 )
| ! [SY57: $i] :
( ~ ( product @ SV8 @ SY56 @ SY57 )
| ( product @ SV16 @ SY55 @ SY57 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(62,plain,
! [SV9: $i] :
( ( ( subgroup_member @ SV9 )
= $false )
| ( ( ! [SY39: $i] :
( ~ ( subgroup_member @ SY39 )
| ! [SY40: $i] :
( ~ ( product @ SV9 @ ( inverse @ SY39 ) @ SY40 )
| ( subgroup_member @ SY40 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(63,plain,
! [SV14: $i,SV11: $i,SV6: $i] :
( ( ( ~ ( product @ SV6 @ SV11 @ SV14 ) )
= $true )
| ( ( ! [SY51: $i] :
( ~ ( product @ SV6 @ SV11 @ SY51 )
| ( SV14 = SY51 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(64,plain,
! [SV17: $i,SV15: $i,SV12: $i,SV7: $i] :
( ( ~ ( product @ SV7 @ SV12 @ SV15 )
| ! [SY58: $i] :
( ~ ( product @ SV12 @ SV17 @ SY58 )
| ! [SY59: $i] :
( ~ ( product @ SV15 @ SV17 @ SY59 )
| ( product @ SV7 @ SY58 @ SY59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(65,plain,
! [SV18: $i,SV16: $i,SV13: $i,SV8: $i] :
( ( ~ ( product @ SV8 @ SV13 @ SV16 )
| ! [SY60: $i] :
( ~ ( product @ SV13 @ SV18 @ SY60 )
| ! [SY61: $i] :
( ~ ( product @ SV8 @ SY60 @ SY61 )
| ( product @ SV16 @ SV18 @ SY61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(66,plain,
! [SV9: $i,SV19: $i] :
( ( ( ~ ( subgroup_member @ SV19 )
| ! [SY62: $i] :
( ~ ( product @ SV9 @ ( inverse @ SV19 ) @ SY62 )
| ( subgroup_member @ SY62 ) ) )
= $true )
| ( ( subgroup_member @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(67,plain,
! [SV14: $i,SV11: $i,SV6: $i] :
( ( ( product @ SV6 @ SV11 @ SV14 )
= $false )
| ( ( ! [SY51: $i] :
( ~ ( product @ SV6 @ SV11 @ SY51 )
| ( SV14 = SY51 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(68,plain,
! [SV17: $i,SV15: $i,SV12: $i,SV7: $i] :
( ( ( ~ ( product @ SV7 @ SV12 @ SV15 ) )
= $true )
| ( ( ! [SY58: $i] :
( ~ ( product @ SV12 @ SV17 @ SY58 )
| ! [SY59: $i] :
( ~ ( product @ SV15 @ SV17 @ SY59 )
| ( product @ SV7 @ SY58 @ SY59 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(69,plain,
! [SV18: $i,SV16: $i,SV13: $i,SV8: $i] :
( ( ( ~ ( product @ SV8 @ SV13 @ SV16 ) )
= $true )
| ( ( ! [SY60: $i] :
( ~ ( product @ SV13 @ SV18 @ SY60 )
| ! [SY61: $i] :
( ~ ( product @ SV8 @ SY60 @ SY61 )
| ( product @ SV16 @ SV18 @ SY61 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(70,plain,
! [SV9: $i,SV19: $i] :
( ( ( ~ ( subgroup_member @ SV19 ) )
= $true )
| ( ( ! [SY62: $i] :
( ~ ( product @ SV9 @ ( inverse @ SV19 ) @ SY62 )
| ( subgroup_member @ SY62 ) ) )
= $true )
| ( ( subgroup_member @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(71,plain,
! [SV14: $i,SV20: $i,SV11: $i,SV6: $i] :
( ( ( ~ ( product @ SV6 @ SV11 @ SV20 )
| ( SV14 = SV20 ) )
= $true )
| ( ( product @ SV6 @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(72,plain,
! [SV17: $i,SV15: $i,SV12: $i,SV7: $i] :
( ( ( product @ SV7 @ SV12 @ SV15 )
= $false )
| ( ( ! [SY58: $i] :
( ~ ( product @ SV12 @ SV17 @ SY58 )
| ! [SY59: $i] :
( ~ ( product @ SV15 @ SV17 @ SY59 )
| ( product @ SV7 @ SY58 @ SY59 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(73,plain,
! [SV18: $i,SV16: $i,SV13: $i,SV8: $i] :
( ( ( product @ SV8 @ SV13 @ SV16 )
= $false )
| ( ( ! [SY60: $i] :
( ~ ( product @ SV13 @ SV18 @ SY60 )
| ! [SY61: $i] :
( ~ ( product @ SV8 @ SY60 @ SY61 )
| ( product @ SV16 @ SV18 @ SY61 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(74,plain,
! [SV9: $i,SV19: $i] :
( ( ( subgroup_member @ SV19 )
= $false )
| ( ( ! [SY62: $i] :
( ~ ( product @ SV9 @ ( inverse @ SV19 ) @ SY62 )
| ( subgroup_member @ SY62 ) ) )
= $true )
| ( ( subgroup_member @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(75,plain,
! [SV14: $i,SV20: $i,SV11: $i,SV6: $i] :
( ( ( ~ ( product @ SV6 @ SV11 @ SV20 ) )
= $true )
| ( ( SV14 = SV20 )
= $true )
| ( ( product @ SV6 @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(76,plain,
! [SV7: $i,SV15: $i,SV21: $i,SV17: $i,SV12: $i] :
( ( ( ~ ( product @ SV12 @ SV17 @ SV21 )
| ! [SY63: $i] :
( ~ ( product @ SV15 @ SV17 @ SY63 )
| ( product @ SV7 @ SV21 @ SY63 ) ) )
= $true )
| ( ( product @ SV7 @ SV12 @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(77,plain,
! [SV16: $i,SV8: $i,SV22: $i,SV18: $i,SV13: $i] :
( ( ( ~ ( product @ SV13 @ SV18 @ SV22 )
| ! [SY64: $i] :
( ~ ( product @ SV8 @ SV22 @ SY64 )
| ( product @ SV16 @ SV18 @ SY64 ) ) )
= $true )
| ( ( product @ SV8 @ SV13 @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(78,plain,
! [SV23: $i,SV19: $i,SV9: $i] :
( ( ( ~ ( product @ SV9 @ ( inverse @ SV19 ) @ SV23 )
| ( subgroup_member @ SV23 ) )
= $true )
| ( ( subgroup_member @ SV19 )
= $false )
| ( ( subgroup_member @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(79,plain,
! [SV14: $i,SV20: $i,SV11: $i,SV6: $i] :
( ( ( product @ SV6 @ SV11 @ SV20 )
= $false )
| ( ( SV14 = SV20 )
= $true )
| ( ( product @ SV6 @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(80,plain,
! [SV7: $i,SV15: $i,SV21: $i,SV17: $i,SV12: $i] :
( ( ( ~ ( product @ SV12 @ SV17 @ SV21 ) )
= $true )
| ( ( ! [SY63: $i] :
( ~ ( product @ SV15 @ SV17 @ SY63 )
| ( product @ SV7 @ SV21 @ SY63 ) ) )
= $true )
| ( ( product @ SV7 @ SV12 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(81,plain,
! [SV16: $i,SV8: $i,SV22: $i,SV18: $i,SV13: $i] :
( ( ( ~ ( product @ SV13 @ SV18 @ SV22 ) )
= $true )
| ( ( ! [SY64: $i] :
( ~ ( product @ SV8 @ SV22 @ SY64 )
| ( product @ SV16 @ SV18 @ SY64 ) ) )
= $true )
| ( ( product @ SV8 @ SV13 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(82,plain,
! [SV23: $i,SV19: $i,SV9: $i] :
( ( ( ~ ( product @ SV9 @ ( inverse @ SV19 ) @ SV23 ) )
= $true )
| ( ( subgroup_member @ SV23 )
= $true )
| ( ( subgroup_member @ SV19 )
= $false )
| ( ( subgroup_member @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(83,plain,
! [SV7: $i,SV15: $i,SV21: $i,SV17: $i,SV12: $i] :
( ( ( product @ SV12 @ SV17 @ SV21 )
= $false )
| ( ( ! [SY63: $i] :
( ~ ( product @ SV15 @ SV17 @ SY63 )
| ( product @ SV7 @ SV21 @ SY63 ) ) )
= $true )
| ( ( product @ SV7 @ SV12 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(84,plain,
! [SV16: $i,SV8: $i,SV22: $i,SV18: $i,SV13: $i] :
( ( ( product @ SV13 @ SV18 @ SV22 )
= $false )
| ( ( ! [SY64: $i] :
( ~ ( product @ SV8 @ SV22 @ SY64 )
| ( product @ SV16 @ SV18 @ SY64 ) ) )
= $true )
| ( ( product @ SV8 @ SV13 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(85,plain,
! [SV23: $i,SV19: $i,SV9: $i] :
( ( ( product @ SV9 @ ( inverse @ SV19 ) @ SV23 )
= $false )
| ( ( subgroup_member @ SV23 )
= $true )
| ( ( subgroup_member @ SV19 )
= $false )
| ( ( subgroup_member @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(86,plain,
! [SV12: $i,SV21: $i,SV7: $i,SV24: $i,SV17: $i,SV15: $i] :
( ( ( ~ ( product @ SV15 @ SV17 @ SV24 )
| ( product @ SV7 @ SV21 @ SV24 ) )
= $true )
| ( ( product @ SV12 @ SV17 @ SV21 )
= $false )
| ( ( product @ SV7 @ SV12 @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(87,plain,
! [SV13: $i,SV18: $i,SV16: $i,SV25: $i,SV22: $i,SV8: $i] :
( ( ( ~ ( product @ SV8 @ SV22 @ SV25 )
| ( product @ SV16 @ SV18 @ SV25 ) )
= $true )
| ( ( product @ SV13 @ SV18 @ SV22 )
= $false )
| ( ( product @ SV8 @ SV13 @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(88,plain,
! [SV12: $i,SV21: $i,SV7: $i,SV24: $i,SV17: $i,SV15: $i] :
( ( ( ~ ( product @ SV15 @ SV17 @ SV24 ) )
= $true )
| ( ( product @ SV7 @ SV21 @ SV24 )
= $true )
| ( ( product @ SV12 @ SV17 @ SV21 )
= $false )
| ( ( product @ SV7 @ SV12 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(89,plain,
! [SV13: $i,SV18: $i,SV16: $i,SV25: $i,SV22: $i,SV8: $i] :
( ( ( ~ ( product @ SV8 @ SV22 @ SV25 ) )
= $true )
| ( ( product @ SV16 @ SV18 @ SV25 )
= $true )
| ( ( product @ SV13 @ SV18 @ SV22 )
= $false )
| ( ( product @ SV8 @ SV13 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(90,plain,
! [SV12: $i,SV21: $i,SV7: $i,SV24: $i,SV17: $i,SV15: $i] :
( ( ( product @ SV15 @ SV17 @ SV24 )
= $false )
| ( ( product @ SV7 @ SV21 @ SV24 )
= $true )
| ( ( product @ SV12 @ SV17 @ SV21 )
= $false )
| ( ( product @ SV7 @ SV12 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(91,plain,
! [SV13: $i,SV18: $i,SV16: $i,SV25: $i,SV22: $i,SV8: $i] :
( ( ( product @ SV8 @ SV22 @ SV25 )
= $false )
| ( ( product @ SV16 @ SV18 @ SV25 )
= $true )
| ( ( product @ SV13 @ SV18 @ SV22 )
= $false )
| ( ( product @ SV8 @ SV13 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(92,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[32,91,90,85,79,54,53,47,46,45,44,43]) ).
thf(93,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP034-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 01:42:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.36
% 0.20/0.36 No.of.Axioms: 11
% 0.20/0.36
% 0.20/0.36 Length.of.Defs: 0
% 0.20/0.36
% 0.20/0.36 Contains.Choice.Funs: false
% 0.20/0.36 (rf:0,axioms:11,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:13,loop_count:0,foatp_calls:0,translation:fof_full)......
% 0.20/0.43
% 0.20/0.43 ********************************
% 0.20/0.43 * All subproblems solved! *
% 0.20/0.43 ********************************
% 0.20/0.43 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:11,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:92,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.43
% 0.20/0.43 %**** Beginning of derivation protocol ****
% 0.20/0.43 % SZS output start CNFRefutation
% See solution above
% 0.20/0.43
% 0.20/0.43 %**** End of derivation protocol ****
% 0.20/0.43 %**** no. of clauses in derivation: 93 ****
% 0.20/0.43 %**** clause counter: 92 ****
% 0.20/0.43
% 0.20/0.43 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:11,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:92,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------