%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GRP039-2 : 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 : n011.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 10:20:08 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.24s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 76 ( 60 unt; 0 typ; 0 def)
% Number of atoms : 311 ( 129 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 383 ( 40 ~; 73 |; 0 &; 270 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 107 ( 0 ^; 107 !; 0 ?; 107 :)
% 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_subgroup_member,type,
subgroup_member: $i > $o ).
thf(1,axiom,
! [X: $i,Y: $i] :
( ( subgroup_member @ X )
| ( subgroup_member @ Y )
| ( ( multiply @ X @ ( element_in_O2 @ X @ Y ) )
= Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_O2) ).
thf(2,axiom,
! [X: $i,Y: $i] :
( ( subgroup_member @ X )
| ( subgroup_member @ Y )
| ( subgroup_member @ ( element_in_O2 @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',an_element_in_O2) ).
thf(3,axiom,
! [X: $i] :
( ( multiply @ X @ ( inverse @ X ) )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
thf(4,axiom,
! [X: $i] :
( ( multiply @ X @ identity )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
thf(5,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( subgroup_member @ X )
| ~ ( subgroup_member @ Y )
| ( ( multiply @ X @ Y )
!= Z )
| ( subgroup_member @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiply) ).
thf(6,axiom,
! [X: $i] :
( ~ ( subgroup_member @ X )
| ( subgroup_member @ ( inverse @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_inverse) ).
thf(7,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Z )
= ( multiply @ X @ ( multiply @ Y @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
thf(8,axiom,
! [X: $i] :
( ( multiply @ ( inverse @ X ) @ X )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(9,axiom,
! [X: $i] :
( ( multiply @ identity @ X )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(10,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(11,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[10]) ).
thf(12,negated_conjecture,
~ ( subgroup_member @ d ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_d_in_O2) ).
thf(13,negated_conjecture,
( ( multiply @ a @ c )
= d ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_c_is_d) ).
thf(14,negated_conjecture,
( ( multiply @ b @ ( inverse @ a ) )
= c ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
thf(15,negated_conjecture,
subgroup_member @ b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_in_O2) ).
thf(16,plain,
$false = $false,
inference(unfold_def,[status(thm)],[11]) ).
thf(17,plain,
( ( ! [X: $i,Y: $i] :
( ( subgroup_member @ X )
| ( subgroup_member @ Y )
| ( ( multiply @ X @ ( element_in_O2 @ X @ Y ) )
= Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(18,plain,
( ( ! [X: $i,Y: $i] :
( ( subgroup_member @ X )
| ( subgroup_member @ Y )
| ( subgroup_member @ ( element_in_O2 @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(19,plain,
( ( ! [X: $i] :
( ( multiply @ X @ ( inverse @ X ) )
= identity ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(20,plain,
( ( ! [X: $i] :
( ( multiply @ X @ identity )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(21,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( subgroup_member @ X )
| ~ ( subgroup_member @ Y )
| ( ( multiply @ X @ Y )
!= Z )
| ( subgroup_member @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(22,plain,
( ( ! [X: $i] :
( ~ ( subgroup_member @ X )
| ( subgroup_member @ ( inverse @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(23,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Z )
= ( multiply @ X @ ( multiply @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(24,plain,
( ( ! [X: $i] :
( ( multiply @ ( inverse @ X ) @ X )
= identity ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(25,plain,
( ( ! [X: $i] :
( ( multiply @ identity @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(26,plain,
( ( ~ ( subgroup_member @ d ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(27,plain,
( ( ( multiply @ a @ c )
= d )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(28,plain,
( ( ( multiply @ b @ ( inverse @ a ) )
= c )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(29,plain,
( ( subgroup_member @ b )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(30,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[16]) ).
thf(31,plain,
( ( subgroup_member @ b )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(32,plain,
( ( ( multiply @ b @ ( inverse @ a ) )
= c )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(33,plain,
( ( ( multiply @ a @ c )
= d )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(34,plain,
( ( ~ ( subgroup_member @ d ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(35,plain,
( ( ! [X: $i] :
( ( multiply @ identity @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(36,plain,
( ( ! [X: $i] :
( ( multiply @ ( inverse @ X ) @ X )
= identity ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(37,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Z )
= ( multiply @ X @ ( multiply @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(38,plain,
( ( ! [X: $i] :
( ~ ( subgroup_member @ X )
| ( subgroup_member @ ( inverse @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(39,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( subgroup_member @ X )
| ~ ( subgroup_member @ Y )
| ( ( multiply @ X @ Y )
!= Z )
| ( subgroup_member @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(40,plain,
( ( ! [X: $i] :
( ( multiply @ X @ identity )
= X ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(41,plain,
( ( ! [X: $i] :
( ( multiply @ X @ ( inverse @ X ) )
= identity ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(42,plain,
( ( ! [X: $i,Y: $i] :
( ( subgroup_member @ X )
| ( subgroup_member @ Y )
| ( subgroup_member @ ( element_in_O2 @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(43,plain,
( ( ! [X: $i,Y: $i] :
( ( subgroup_member @ X )
| ( subgroup_member @ Y )
| ( ( multiply @ X @ ( element_in_O2 @ X @ Y ) )
= Y ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(44,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[30]) ).
thf(45,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subgroup_member @ SX0 )
| ~ ( subgroup_member @ SX1 )
| ( ( multiply @ SX0 @ SX1 )
!= SX2 )
| ( subgroup_member @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(46,plain,
( ( subgroup_member @ d )
= $false ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(47,plain,
! [SV1: $i] :
( ( ( multiply @ identity @ SV1 )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(48,plain,
! [SV2: $i] :
( ( ( multiply @ ( inverse @ SV2 ) @ SV2 )
= identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(49,plain,
! [SV3: $i] :
( ( ! [SY15: $i,SY16: $i] :
( ( multiply @ ( multiply @ SV3 @ SY15 ) @ SY16 )
= ( multiply @ SV3 @ ( multiply @ SY15 @ SY16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(50,plain,
! [SV4: $i] :
( ( ~ ( subgroup_member @ SV4 )
| ( subgroup_member @ ( inverse @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(51,plain,
! [SV5: $i] :
( ( ( multiply @ SV5 @ identity )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(52,plain,
! [SV6: $i] :
( ( ( multiply @ SV6 @ ( inverse @ SV6 ) )
= identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(53,plain,
! [SV7: $i] :
( ( ! [SY17: $i] :
( ( subgroup_member @ SV7 )
| ( subgroup_member @ SY17 )
| ( subgroup_member @ ( element_in_O2 @ SV7 @ SY17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(54,plain,
! [SV8: $i] :
( ( ! [SY18: $i] :
( ( subgroup_member @ SV8 )
| ( subgroup_member @ SY18 )
| ( ( multiply @ SV8 @ ( element_in_O2 @ SV8 @ SY18 ) )
= SY18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(55,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(56,plain,
! [SV9: $i] :
( ( ! [SY19: $i,SY20: $i] :
( ~ ( subgroup_member @ SV9 )
| ~ ( subgroup_member @ SY19 )
| ( ( multiply @ SV9 @ SY19 )
!= SY20 )
| ( subgroup_member @ SY20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(57,plain,
! [SV10: $i,SV3: $i] :
( ( ! [SY21: $i] :
( ( multiply @ ( multiply @ SV3 @ SV10 ) @ SY21 )
= ( multiply @ SV3 @ ( multiply @ SV10 @ SY21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(58,plain,
! [SV4: $i] :
( ( ( ~ ( subgroup_member @ SV4 ) )
= $true )
| ( ( subgroup_member @ ( inverse @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(59,plain,
! [SV11: $i,SV7: $i] :
( ( ( subgroup_member @ SV7 )
| ( subgroup_member @ SV11 )
| ( subgroup_member @ ( element_in_O2 @ SV7 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(60,plain,
! [SV12: $i,SV8: $i] :
( ( ( subgroup_member @ SV8 )
| ( subgroup_member @ SV12 )
| ( ( multiply @ SV8 @ ( element_in_O2 @ SV8 @ SV12 ) )
= SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(61,plain,
! [SV13: $i,SV9: $i] :
( ( ! [SY22: $i] :
( ~ ( subgroup_member @ SV9 )
| ~ ( subgroup_member @ SV13 )
| ( ( multiply @ SV9 @ SV13 )
!= SY22 )
| ( subgroup_member @ SY22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(62,plain,
! [SV14: $i,SV10: $i,SV3: $i] :
( ( ( multiply @ ( multiply @ SV3 @ SV10 ) @ SV14 )
= ( multiply @ SV3 @ ( multiply @ SV10 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(63,plain,
! [SV4: $i] :
( ( ( subgroup_member @ SV4 )
= $false )
| ( ( subgroup_member @ ( inverse @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(64,plain,
! [SV11: $i,SV7: $i] :
( ( ( subgroup_member @ SV7 )
= $true )
| ( ( ( subgroup_member @ SV11 )
| ( subgroup_member @ ( element_in_O2 @ SV7 @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(65,plain,
! [SV12: $i,SV8: $i] :
( ( ( subgroup_member @ SV8 )
= $true )
| ( ( ( subgroup_member @ SV12 )
| ( ( multiply @ SV8 @ ( element_in_O2 @ SV8 @ SV12 ) )
= SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(66,plain,
! [SV15: $i,SV13: $i,SV9: $i] :
( ( ~ ( subgroup_member @ SV9 )
| ~ ( subgroup_member @ SV13 )
| ( ( multiply @ SV9 @ SV13 )
!= SV15 )
| ( subgroup_member @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(67,plain,
! [SV7: $i,SV11: $i] :
( ( ( subgroup_member @ SV11 )
= $true )
| ( ( subgroup_member @ ( element_in_O2 @ SV7 @ SV11 ) )
= $true )
| ( ( subgroup_member @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(68,plain,
! [SV8: $i,SV12: $i] :
( ( ( subgroup_member @ SV12 )
= $true )
| ( ( ( multiply @ SV8 @ ( element_in_O2 @ SV8 @ SV12 ) )
= SV12 )
= $true )
| ( ( subgroup_member @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(69,plain,
! [SV15: $i,SV13: $i,SV9: $i] :
( ( ( ~ ( subgroup_member @ SV9 ) )
= $true )
| ( ( ~ ( subgroup_member @ SV13 )
| ( ( multiply @ SV9 @ SV13 )
!= SV15 )
| ( subgroup_member @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(70,plain,
! [SV15: $i,SV13: $i,SV9: $i] :
( ( ( subgroup_member @ SV9 )
= $false )
| ( ( ~ ( subgroup_member @ SV13 )
| ( ( multiply @ SV9 @ SV13 )
!= SV15 )
| ( subgroup_member @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(71,plain,
! [SV15: $i,SV9: $i,SV13: $i] :
( ( ( ~ ( subgroup_member @ SV13 ) )
= $true )
| ( ( ( ( multiply @ SV9 @ SV13 )
!= SV15 )
| ( subgroup_member @ SV15 ) )
= $true )
| ( ( subgroup_member @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(72,plain,
! [SV15: $i,SV9: $i,SV13: $i] :
( ( ( subgroup_member @ SV13 )
= $false )
| ( ( ( ( multiply @ SV9 @ SV13 )
!= SV15 )
| ( subgroup_member @ SV15 ) )
= $true )
| ( ( subgroup_member @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(73,plain,
! [SV15: $i,SV13: $i,SV9: $i] :
( ( ( ( multiply @ SV9 @ SV13 )
!= SV15 )
= $true )
| ( ( subgroup_member @ SV15 )
= $true )
| ( ( subgroup_member @ SV13 )
= $false )
| ( ( subgroup_member @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(74,plain,
! [SV15: $i,SV13: $i,SV9: $i] :
( ( ( ( multiply @ SV9 @ SV13 )
= SV15 )
= $false )
| ( ( subgroup_member @ SV15 )
= $true )
| ( ( subgroup_member @ SV13 )
= $false )
| ( ( subgroup_member @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(75,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[31,74,68,67,63,62,55,52,51,48,47,46,33,32]) ).
thf(76,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP039-2 : 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
% 0.10/0.17 % Computer : n011.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Oct 6 10:31:51 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.24
% 0.10/0.24 No.of.Axioms: 13
% 0.10/0.24
% 0.10/0.24 Length.of.Defs: 0
% 0.10/0.24
% 0.10/0.24 Contains.Choice.Funs: false
% 0.10/0.24 .
% 0.10/0.24
% 0.10/0.24 ********************************
% 0.10/0.24 * All subproblems solved! *
% 0.10/0.24 ********************************
% 0.10/0.24 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:13,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:75,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.10/0.24
% 0.10/0.24 %**** Beginning of derivation protocol ****
% 0.10/0.24 % SZS output start CNFRefutation
% See solution above
% 0.10/0.24
% 0.10/0.24 %**** End of derivation protocol ****
% 0.10/0.24 %**** no. of clauses in derivation: 76 ****
% 0.10/0.24 %**** clause counter: 75 ****
% 0.10/0.24
% 0.10/0.24 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:13,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:75,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------