%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GRP034-4 : 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 : n020.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 10:20:07 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.22s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 74 ( 53 unt; 0 typ; 0 def)
% Number of atoms : 398 ( 99 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 750 ( 104 ~; 126 |; 0 &; 520 @)
% ( 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 : 9 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 238 ( 0 ^; 238 !; 0 ?; 238 :)
% 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 @ B @ ( inverse @ A ) @ C )
| ( subgroup_member @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_subgroup) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',associativity1) ).
thf(4,axiom,
! [X: $i] : ( product @ X @ ( inverse @ X ) @ identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
thf(5,axiom,
! [X: $i] : ( product @ X @ identity @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
thf(6,axiom,
! [X: $i] : ( product @ identity @ X @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(7,axiom,
! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure) ).
thf(8,axiom,
subgroup_member @ a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_in_subgroup) ).
thf(9,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(10,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[9]) ).
thf(11,negated_conjecture,
~ ( subgroup_member @ ( inverse @ a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_inverse_is_in_subgroup) ).
thf(12,plain,
$false = $false,
inference(unfold_def,[status(thm)],[10]) ).
thf(13,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subgroup_member @ A )
| ~ ( subgroup_member @ B )
| ~ ( product @ B @ ( inverse @ A ) @ C )
| ( subgroup_member @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(14,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(15,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(16,plain,
( ( ! [X: $i] : ( product @ X @ ( inverse @ X ) @ identity ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(17,plain,
( ( ! [X: $i] : ( product @ X @ identity @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(18,plain,
( ( ! [X: $i] : ( product @ identity @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(19,plain,
( ( ! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(20,plain,
( ( subgroup_member @ a )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(21,plain,
( ( ~ ( subgroup_member @ ( inverse @ a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(22,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[12]) ).
thf(23,plain,
( ( ~ ( subgroup_member @ ( inverse @ a ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(24,plain,
( ( subgroup_member @ a )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(25,plain,
( ( ! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(26,plain,
( ( ! [X: $i] : ( product @ identity @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(27,plain,
( ( ! [X: $i] : ( product @ X @ identity @ X ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(28,plain,
( ( ! [X: $i] : ( product @ X @ ( inverse @ X ) @ identity ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(29,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
( ~ ( product @ X @ Y @ U )
| ~ ( product @ Y @ Z @ V )
| ~ ( product @ U @ Z @ W )
| ( product @ X @ V @ W ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(30,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
( ~ ( product @ X @ Y @ U )
| ~ ( product @ Y @ Z @ V )
| ~ ( product @ X @ V @ W )
| ( product @ U @ Z @ W ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(31,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subgroup_member @ A )
| ~ ( subgroup_member @ B )
| ~ ( product @ B @ ( inverse @ A ) @ C )
| ( subgroup_member @ C ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(32,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[22]) ).
thf(33,plain,
( ( subgroup_member @ ( inverse @ a ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(34,plain,
! [SV1: $i] :
( ( ! [SY20: $i] : ( product @ SV1 @ SY20 @ ( multiply @ SV1 @ SY20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(35,plain,
! [SV2: $i] :
( ( product @ identity @ SV2 @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(36,plain,
! [SV3: $i] :
( ( product @ SV3 @ identity @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(37,plain,
! [SV4: $i] :
( ( product @ SV4 @ ( inverse @ SV4 ) @ identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(38,plain,
! [SV5: $i] :
( ( ! [SY21: $i,SY22: $i,SY23: $i,SY24: $i,SY25: $i] :
( ~ ( product @ SV5 @ SY21 @ SY22 )
| ~ ( product @ SY21 @ SY23 @ SY24 )
| ~ ( product @ SY22 @ SY23 @ SY25 )
| ( product @ SV5 @ SY24 @ SY25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(39,plain,
! [SV6: $i] :
( ( ! [SY26: $i,SY27: $i,SY28: $i,SY29: $i,SY30: $i] :
( ~ ( product @ SV6 @ SY26 @ SY27 )
| ~ ( product @ SY26 @ SY28 @ SY29 )
| ~ ( product @ SV6 @ SY29 @ SY30 )
| ( product @ SY27 @ SY28 @ SY30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(40,plain,
! [SV7: $i] :
( ( ! [SY31: $i,SY32: $i] :
( ~ ( subgroup_member @ SV7 )
| ~ ( subgroup_member @ SY31 )
| ~ ( product @ SY31 @ ( inverse @ SV7 ) @ SY32 )
| ( subgroup_member @ SY32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(41,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(42,plain,
! [SV8: $i,SV1: $i] :
( ( product @ SV1 @ SV8 @ ( multiply @ SV1 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(43,plain,
! [SV9: $i,SV5: $i] :
( ( ! [SY33: $i,SY34: $i,SY35: $i,SY36: $i] :
( ~ ( product @ SV5 @ SV9 @ SY33 )
| ~ ( product @ SV9 @ SY34 @ SY35 )
| ~ ( product @ SY33 @ SY34 @ SY36 )
| ( product @ SV5 @ SY35 @ SY36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(44,plain,
! [SV10: $i,SV6: $i] :
( ( ! [SY37: $i,SY38: $i,SY39: $i,SY40: $i] :
( ~ ( product @ SV6 @ SV10 @ SY37 )
| ~ ( product @ SV10 @ SY38 @ SY39 )
| ~ ( product @ SV6 @ SY39 @ SY40 )
| ( product @ SY37 @ SY38 @ SY40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(45,plain,
! [SV11: $i,SV7: $i] :
( ( ! [SY41: $i] :
( ~ ( subgroup_member @ SV7 )
| ~ ( subgroup_member @ SV11 )
| ~ ( product @ SV11 @ ( inverse @ SV7 ) @ SY41 )
| ( subgroup_member @ SY41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(46,plain,
! [SV12: $i,SV9: $i,SV5: $i] :
( ( ! [SY42: $i,SY43: $i,SY44: $i] :
( ~ ( product @ SV5 @ SV9 @ SV12 )
| ~ ( product @ SV9 @ SY42 @ SY43 )
| ~ ( product @ SV12 @ SY42 @ SY44 )
| ( product @ SV5 @ SY43 @ SY44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(47,plain,
! [SV13: $i,SV10: $i,SV6: $i] :
( ( ! [SY45: $i,SY46: $i,SY47: $i] :
( ~ ( product @ SV6 @ SV10 @ SV13 )
| ~ ( product @ SV10 @ SY45 @ SY46 )
| ~ ( product @ SV6 @ SY46 @ SY47 )
| ( product @ SV13 @ SY45 @ SY47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(48,plain,
! [SV14: $i,SV11: $i,SV7: $i] :
( ( ~ ( subgroup_member @ SV7 )
| ~ ( subgroup_member @ SV11 )
| ~ ( product @ SV11 @ ( inverse @ SV7 ) @ SV14 )
| ( subgroup_member @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(49,plain,
! [SV15: $i,SV12: $i,SV9: $i,SV5: $i] :
( ( ! [SY48: $i,SY49: $i] :
( ~ ( product @ SV5 @ SV9 @ SV12 )
| ~ ( product @ SV9 @ SV15 @ SY48 )
| ~ ( product @ SV12 @ SV15 @ SY49 )
| ( product @ SV5 @ SY48 @ SY49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(50,plain,
! [SV16: $i,SV13: $i,SV10: $i,SV6: $i] :
( ( ! [SY50: $i,SY51: $i] :
( ~ ( product @ SV6 @ SV10 @ SV13 )
| ~ ( product @ SV10 @ SV16 @ SY50 )
| ~ ( product @ SV6 @ SY50 @ SY51 )
| ( product @ SV13 @ SV16 @ SY51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(51,plain,
! [SV14: $i,SV11: $i,SV7: $i] :
( ( ( ~ ( subgroup_member @ SV7 ) )
= $true )
| ( ( ~ ( subgroup_member @ SV11 )
| ~ ( product @ SV11 @ ( inverse @ SV7 ) @ SV14 )
| ( subgroup_member @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(52,plain,
! [SV17: $i,SV15: $i,SV12: $i,SV9: $i,SV5: $i] :
( ( ! [SY52: $i] :
( ~ ( product @ SV5 @ SV9 @ SV12 )
| ~ ( product @ SV9 @ SV15 @ SV17 )
| ~ ( product @ SV12 @ SV15 @ SY52 )
| ( product @ SV5 @ SV17 @ SY52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(53,plain,
! [SV18: $i,SV16: $i,SV13: $i,SV10: $i,SV6: $i] :
( ( ! [SY53: $i] :
( ~ ( product @ SV6 @ SV10 @ SV13 )
| ~ ( product @ SV10 @ SV16 @ SV18 )
| ~ ( product @ SV6 @ SV18 @ SY53 )
| ( product @ SV13 @ SV16 @ SY53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(54,plain,
! [SV14: $i,SV11: $i,SV7: $i] :
( ( ( subgroup_member @ SV7 )
= $false )
| ( ( ~ ( subgroup_member @ SV11 )
| ~ ( product @ SV11 @ ( inverse @ SV7 ) @ SV14 )
| ( subgroup_member @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(55,plain,
! [SV19: $i,SV17: $i,SV15: $i,SV12: $i,SV9: $i,SV5: $i] :
( ( ~ ( product @ SV5 @ SV9 @ SV12 )
| ~ ( product @ SV9 @ SV15 @ SV17 )
| ~ ( product @ SV12 @ SV15 @ SV19 )
| ( product @ SV5 @ SV17 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(56,plain,
! [SV20: $i,SV18: $i,SV16: $i,SV13: $i,SV10: $i,SV6: $i] :
( ( ~ ( product @ SV6 @ SV10 @ SV13 )
| ~ ( product @ SV10 @ SV16 @ SV18 )
| ~ ( product @ SV6 @ SV18 @ SV20 )
| ( product @ SV13 @ SV16 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(57,plain,
! [SV14: $i,SV7: $i,SV11: $i] :
( ( ( ~ ( subgroup_member @ SV11 ) )
= $true )
| ( ( ~ ( product @ SV11 @ ( inverse @ SV7 ) @ SV14 )
| ( subgroup_member @ SV14 ) )
= $true )
| ( ( subgroup_member @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[54]) ).
thf(58,plain,
! [SV19: $i,SV17: $i,SV15: $i,SV12: $i,SV9: $i,SV5: $i] :
( ( ( ~ ( product @ SV5 @ SV9 @ SV12 ) )
= $true )
| ( ( ~ ( product @ SV9 @ SV15 @ SV17 )
| ~ ( product @ SV12 @ SV15 @ SV19 )
| ( product @ SV5 @ SV17 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(59,plain,
! [SV20: $i,SV18: $i,SV16: $i,SV13: $i,SV10: $i,SV6: $i] :
( ( ( ~ ( product @ SV6 @ SV10 @ SV13 ) )
= $true )
| ( ( ~ ( product @ SV10 @ SV16 @ SV18 )
| ~ ( product @ SV6 @ SV18 @ SV20 )
| ( product @ SV13 @ SV16 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(60,plain,
! [SV14: $i,SV7: $i,SV11: $i] :
( ( ( subgroup_member @ SV11 )
= $false )
| ( ( ~ ( product @ SV11 @ ( inverse @ SV7 ) @ SV14 )
| ( subgroup_member @ SV14 ) )
= $true )
| ( ( subgroup_member @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(61,plain,
! [SV19: $i,SV17: $i,SV15: $i,SV12: $i,SV9: $i,SV5: $i] :
( ( ( product @ SV5 @ SV9 @ SV12 )
= $false )
| ( ( ~ ( product @ SV9 @ SV15 @ SV17 )
| ~ ( product @ SV12 @ SV15 @ SV19 )
| ( product @ SV5 @ SV17 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(62,plain,
! [SV20: $i,SV18: $i,SV16: $i,SV13: $i,SV10: $i,SV6: $i] :
( ( ( product @ SV6 @ SV10 @ SV13 )
= $false )
| ( ( ~ ( product @ SV10 @ SV16 @ SV18 )
| ~ ( product @ SV6 @ SV18 @ SV20 )
| ( product @ SV13 @ SV16 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(63,plain,
! [SV14: $i,SV7: $i,SV11: $i] :
( ( ( ~ ( product @ SV11 @ ( inverse @ SV7 ) @ SV14 ) )
= $true )
| ( ( subgroup_member @ SV14 )
= $true )
| ( ( subgroup_member @ SV11 )
= $false )
| ( ( subgroup_member @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(64,plain,
! [SV5: $i,SV19: $i,SV12: $i,SV17: $i,SV15: $i,SV9: $i] :
( ( ( ~ ( product @ SV9 @ SV15 @ SV17 ) )
= $true )
| ( ( ~ ( product @ SV12 @ SV15 @ SV19 )
| ( product @ SV5 @ SV17 @ SV19 ) )
= $true )
| ( ( product @ SV5 @ SV9 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(65,plain,
! [SV13: $i,SV20: $i,SV6: $i,SV18: $i,SV16: $i,SV10: $i] :
( ( ( ~ ( product @ SV10 @ SV16 @ SV18 ) )
= $true )
| ( ( ~ ( product @ SV6 @ SV18 @ SV20 )
| ( product @ SV13 @ SV16 @ SV20 ) )
= $true )
| ( ( product @ SV6 @ SV10 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(66,plain,
! [SV14: $i,SV7: $i,SV11: $i] :
( ( ( product @ SV11 @ ( inverse @ SV7 ) @ SV14 )
= $false )
| ( ( subgroup_member @ SV14 )
= $true )
| ( ( subgroup_member @ SV11 )
= $false )
| ( ( subgroup_member @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(67,plain,
! [SV5: $i,SV19: $i,SV12: $i,SV17: $i,SV15: $i,SV9: $i] :
( ( ( product @ SV9 @ SV15 @ SV17 )
= $false )
| ( ( ~ ( product @ SV12 @ SV15 @ SV19 )
| ( product @ SV5 @ SV17 @ SV19 ) )
= $true )
| ( ( product @ SV5 @ SV9 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(68,plain,
! [SV13: $i,SV20: $i,SV6: $i,SV18: $i,SV16: $i,SV10: $i] :
( ( ( product @ SV10 @ SV16 @ SV18 )
= $false )
| ( ( ~ ( product @ SV6 @ SV18 @ SV20 )
| ( product @ SV13 @ SV16 @ SV20 ) )
= $true )
| ( ( product @ SV6 @ SV10 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(69,plain,
! [SV9: $i,SV17: $i,SV5: $i,SV19: $i,SV15: $i,SV12: $i] :
( ( ( ~ ( product @ SV12 @ SV15 @ SV19 ) )
= $true )
| ( ( product @ SV5 @ SV17 @ SV19 )
= $true )
| ( ( product @ SV9 @ SV15 @ SV17 )
= $false )
| ( ( product @ SV5 @ SV9 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[67]) ).
thf(70,plain,
! [SV10: $i,SV16: $i,SV13: $i,SV20: $i,SV18: $i,SV6: $i] :
( ( ( ~ ( product @ SV6 @ SV18 @ SV20 ) )
= $true )
| ( ( product @ SV13 @ SV16 @ SV20 )
= $true )
| ( ( product @ SV10 @ SV16 @ SV18 )
= $false )
| ( ( product @ SV6 @ SV10 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(71,plain,
! [SV9: $i,SV17: $i,SV5: $i,SV19: $i,SV15: $i,SV12: $i] :
( ( ( product @ SV12 @ SV15 @ SV19 )
= $false )
| ( ( product @ SV5 @ SV17 @ SV19 )
= $true )
| ( ( product @ SV9 @ SV15 @ SV17 )
= $false )
| ( ( product @ SV5 @ SV9 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(72,plain,
! [SV10: $i,SV16: $i,SV13: $i,SV20: $i,SV18: $i,SV6: $i] :
( ( ( product @ SV6 @ SV18 @ SV20 )
= $false )
| ( ( product @ SV13 @ SV16 @ SV20 )
= $true )
| ( ( product @ SV10 @ SV16 @ SV18 )
= $false )
| ( ( product @ SV6 @ SV10 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(73,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[24,72,71,66,42,41,37,36,35,33]) ).
thf(74,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP034-4 : 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
% 0.12/0.17 % Computer : n020.cluster.edu
% 0.12/0.17 % Model : x86_64 x86_64
% 0.12/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.17 % Memory : 8046.5625MB
% 0.12/0.17 % OS : Linux 6.8.0-71-generic
% 0.12/0.17 % CPULimit : 300
% 0.12/0.17 % WCLimit : 300
% 0.12/0.17 % DateTime : Tue Oct 6 10:32:36 UTC 2026
% 0.12/0.17 % CPUTime :
% 0.12/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.22
% 0.12/0.22 No.of.Axioms: 9
% 0.12/0.22
% 0.12/0.22 Length.of.Defs: 0
% 0.12/0.22
% 0.12/0.22 Contains.Choice.Funs: false
% 0.12/0.22 .
% 0.12/0.22
% 0.12/0.22 ********************************
% 0.12/0.22 * All subproblems solved! *
% 0.12/0.22 ********************************
% 0.12/0.22 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:9,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:73,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.12/0.22
% 0.12/0.22 %**** Beginning of derivation protocol ****
% 0.12/0.22 % SZS output start CNFRefutation
% See solution above
% 0.12/0.22
% 0.12/0.22 %**** End of derivation protocol ****
% 0.12/0.22 %**** no. of clauses in derivation: 74 ****
% 0.12/0.22 %**** clause counter: 73 ****
% 0.12/0.22
% 0.12/0.22 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:9,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:73,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------