%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : HEN009-3 : 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 10:22:06 AM UTC 2026
% Result : Unsatisfiable 1.13s 0.45s
% Output : CNFRefutation 1.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 70 ( 59 unt; 0 typ; 0 def)
% Number of atoms : 235 ( 109 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 332 ( 37 ~; 33 |; 0 &; 262 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 8 con; 0-2 aty)
% Number of variables : 84 ( 0 ^; 84 !; 0 ?; 84 :)
% 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_divide,type,
divide: $i > $i > $i ).
thf(tp_identity,type,
identity: $i ).
thf(tp_less_equal,type,
less_equal: $i > $i > $o ).
thf(tp_zero,type,
zero: $i ).
thf(1,axiom,
! [X: $i] : ( less_equal @ X @ identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_is_largest) ).
thf(2,axiom,
! [X: $i,Y: $i] :
( ~ ( less_equal @ X @ Y )
| ~ ( less_equal @ Y @ X )
| ( X = Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_equal_and_equal) ).
thf(3,axiom,
! [X: $i] : ( less_equal @ zero @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_is_smallest) ).
thf(4,axiom,
! [X: $i,Z: $i,Y: $i] : ( less_equal @ ( divide @ ( divide @ X @ Z ) @ ( divide @ Y @ Z ) ) @ ( divide @ ( divide @ X @ Y ) @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_property) ).
thf(5,axiom,
! [X: $i,Y: $i] : ( less_equal @ ( divide @ X @ Y ) @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_smaller_than_numerator) ).
thf(6,axiom,
! [X: $i,Y: $i] :
( ( ( divide @ X @ Y )
!= zero )
| ( less_equal @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_less_equal2) ).
thf(7,axiom,
! [X: $i,Y: $i] :
( ~ ( less_equal @ X @ Y )
| ( ( divide @ X @ Y )
= zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_less_equal1) ).
thf(8,axiom,
( ( divide @ identity @ c )
= d ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id_divide_c_is_d) ).
thf(9,axiom,
( ( divide @ identity @ b )
= c ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id_divide_b_is_c) ).
thf(10,axiom,
( ( divide @ identity @ a )
= b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id_divide_a_is_b) ).
thf(11,axiom,
( ( divide @ identity @ a )
!= ( divide @ identity @ ( divide @ identity @ ( divide @ identity @ a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',part_of_theorem) ).
thf(12,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(13,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[12]) ).
thf(14,negated_conjecture,
b != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_b_equals_d) ).
thf(15,plain,
$false = $false,
inference(unfold_def,[status(thm)],[13]) ).
thf(16,plain,
( ( ! [X: $i] : ( less_equal @ X @ identity ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(17,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( less_equal @ X @ Y )
| ~ ( less_equal @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(18,plain,
( ( ! [X: $i] : ( less_equal @ zero @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(19,plain,
( ( ! [X: $i,Z: $i,Y: $i] : ( less_equal @ ( divide @ ( divide @ X @ Z ) @ ( divide @ Y @ Z ) ) @ ( divide @ ( divide @ X @ Y ) @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(20,plain,
( ( ! [X: $i,Y: $i] : ( less_equal @ ( divide @ X @ Y ) @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(21,plain,
( ( ! [X: $i,Y: $i] :
( ( ( divide @ X @ Y )
!= zero )
| ( less_equal @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(22,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( less_equal @ X @ Y )
| ( ( divide @ X @ Y )
= zero ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(23,plain,
( ( ( divide @ identity @ c )
= d )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(24,plain,
( ( ( divide @ identity @ b )
= c )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(25,plain,
( ( ( divide @ identity @ a )
= b )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(26,plain,
( ( ( divide @ identity @ a )
!= ( divide @ identity @ ( divide @ identity @ ( divide @ identity @ a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(27,plain,
( ( b != d )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(28,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[15]) ).
thf(29,plain,
( ( b != d )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(30,plain,
( ( ( divide @ identity @ a )
!= ( divide @ identity @ ( divide @ identity @ ( divide @ identity @ a ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(31,plain,
( ( ( divide @ identity @ a )
= b )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(32,plain,
( ( ( divide @ identity @ b )
= c )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(33,plain,
( ( ( divide @ identity @ c )
= d )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(34,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( less_equal @ X @ Y )
| ( ( divide @ X @ Y )
= zero ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(35,plain,
( ( ! [X: $i,Y: $i] :
( ( ( divide @ X @ Y )
!= zero )
| ( less_equal @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(36,plain,
( ( ! [X: $i,Y: $i] : ( less_equal @ ( divide @ X @ Y ) @ X ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(37,plain,
( ( ! [X: $i,Z: $i,Y: $i] : ( less_equal @ ( divide @ ( divide @ X @ Z ) @ ( divide @ Y @ Z ) ) @ ( divide @ ( divide @ X @ Y ) @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(38,plain,
( ( ! [X: $i] : ( less_equal @ zero @ X ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(39,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( less_equal @ X @ Y )
| ~ ( less_equal @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(40,plain,
( ( ! [X: $i] : ( less_equal @ X @ identity ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(41,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[28]) ).
thf(42,plain,
( ( b != d )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(43,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( divide @ SX0 @ SX1 )
!= zero )
| ( less_equal @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(44,plain,
( ( ( divide @ identity @ a )
!= ( divide @ identity @ ( divide @ identity @ ( divide @ identity @ a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(45,plain,
! [SV1: $i] :
( ( ! [SY13: $i] :
( ~ ( less_equal @ SV1 @ SY13 )
| ( ( divide @ SV1 @ SY13 )
= zero ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(46,plain,
! [SV2: $i] :
( ( ! [SY14: $i] : ( less_equal @ ( divide @ SV2 @ SY14 ) @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(47,plain,
! [SV3: $i] :
( ( ! [SY15: $i,SY16: $i] : ( less_equal @ ( divide @ ( divide @ SV3 @ SY15 ) @ ( divide @ SY16 @ SY15 ) ) @ ( divide @ ( divide @ SV3 @ SY16 ) @ SY15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(48,plain,
! [SV4: $i] :
( ( less_equal @ zero @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(49,plain,
! [SV5: $i] :
( ( ! [SY17: $i] :
( ~ ( less_equal @ SV5 @ SY17 )
| ~ ( less_equal @ SY17 @ SV5 )
| ( SV5 = SY17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(50,plain,
! [SV6: $i] :
( ( less_equal @ SV6 @ identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(51,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(52,plain,
( ( b = d )
= $false ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(53,plain,
! [SV7: $i] :
( ( ! [SY18: $i] :
( ( ( divide @ SV7 @ SY18 )
!= zero )
| ( less_equal @ SV7 @ SY18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(54,plain,
( ( ( divide @ identity @ a )
= ( divide @ identity @ ( divide @ identity @ ( divide @ identity @ a ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(55,plain,
! [SV8: $i,SV1: $i] :
( ( ~ ( less_equal @ SV1 @ SV8 )
| ( ( divide @ SV1 @ SV8 )
= zero ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(56,plain,
! [SV9: $i,SV2: $i] :
( ( less_equal @ ( divide @ SV2 @ SV9 ) @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(57,plain,
! [SV10: $i,SV3: $i] :
( ( ! [SY19: $i] : ( less_equal @ ( divide @ ( divide @ SV3 @ SV10 ) @ ( divide @ SY19 @ SV10 ) ) @ ( divide @ ( divide @ SV3 @ SY19 ) @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(58,plain,
! [SV11: $i,SV5: $i] :
( ( ~ ( less_equal @ SV5 @ SV11 )
| ~ ( less_equal @ SV11 @ SV5 )
| ( SV5 = SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(59,plain,
! [SV12: $i,SV7: $i] :
( ( ( ( divide @ SV7 @ SV12 )
!= zero )
| ( less_equal @ SV7 @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(60,plain,
! [SV8: $i,SV1: $i] :
( ( ( ~ ( less_equal @ SV1 @ SV8 ) )
= $true )
| ( ( ( divide @ SV1 @ SV8 )
= zero )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(61,plain,
! [SV13: $i,SV10: $i,SV3: $i] :
( ( less_equal @ ( divide @ ( divide @ SV3 @ SV10 ) @ ( divide @ SV13 @ SV10 ) ) @ ( divide @ ( divide @ SV3 @ SV13 ) @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(62,plain,
! [SV11: $i,SV5: $i] :
( ( ( ~ ( less_equal @ SV5 @ SV11 ) )
= $true )
| ( ( ~ ( less_equal @ SV11 @ SV5 )
| ( SV5 = SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(63,plain,
! [SV12: $i,SV7: $i] :
( ( ( ( divide @ SV7 @ SV12 )
!= zero )
= $true )
| ( ( less_equal @ SV7 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(64,plain,
! [SV8: $i,SV1: $i] :
( ( ( less_equal @ SV1 @ SV8 )
= $false )
| ( ( ( divide @ SV1 @ SV8 )
= zero )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(65,plain,
! [SV11: $i,SV5: $i] :
( ( ( less_equal @ SV5 @ SV11 )
= $false )
| ( ( ~ ( less_equal @ SV11 @ SV5 )
| ( SV5 = SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(66,plain,
! [SV12: $i,SV7: $i] :
( ( ( ( divide @ SV7 @ SV12 )
= zero )
= $false )
| ( ( less_equal @ SV7 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(67,plain,
! [SV5: $i,SV11: $i] :
( ( ( ~ ( less_equal @ SV11 @ SV5 ) )
= $true )
| ( ( SV5 = SV11 )
= $true )
| ( ( less_equal @ SV5 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(68,plain,
! [SV5: $i,SV11: $i] :
( ( ( less_equal @ SV11 @ SV5 )
= $false )
| ( ( SV5 = SV11 )
= $true )
| ( ( less_equal @ SV5 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(69,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[31,68,66,64,61,56,54,52,51,50,48,33,32]) ).
thf(70,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN009-3 : 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 10:56:47 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
% 1.13/0.45
% 1.13/0.45 No.of.Axioms: 12
% 1.13/0.45
% 1.13/0.45 Length.of.Defs: 0
% 1.13/0.45
% 1.13/0.45 Contains.Choice.Funs: false
% 1.13/0.45 .
% 1.13/0.45
% 1.13/0.45 ********************************
% 1.13/0.45 * All subproblems solved! *
% 1.13/0.45 ********************************
% 1.13/0.45 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:12,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:69,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.13/0.45
% 1.13/0.45 %**** Beginning of derivation protocol ****
% 1.13/0.45 % SZS output start CNFRefutation
% See solution above
% 1.13/0.45
% 1.13/0.45 %**** End of derivation protocol ****
% 1.13/0.45 %**** no. of clauses in derivation: 70 ****
% 1.13/0.45 %**** clause counter: 69 ****
% 1.13/0.45
% 1.13/0.45 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:12,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:69,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------