%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : HEN006-5 : 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 : n004.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 10:22:03 AM UTC 2026
% Result : Unsatisfiable 0.26s 0.28s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 49 ( 44 unt; 0 typ; 0 def)
% Number of atoms : 159 ( 106 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 230 ( 22 ~; 20 |; 0 &; 188 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 7 con; 0-2 aty)
% Number of variables : 60 ( 0 ^; 60 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_b,type,
b: $i ).
thf(tp_d,type,
d: $i ).
thf(tp_divide,type,
divide: $i > $i > $i ).
thf(tp_identity,type,
identity: $i ).
thf(tp_zero,type,
zero: $i ).
thf(1,axiom,
! [X: $i] :
( ( divide @ X @ zero )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_divide_zero_is_x) ).
thf(2,axiom,
! [X: $i] :
( ( divide @ X @ identity )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_is_largest) ).
thf(3,axiom,
! [X: $i,Y: $i] :
( ( ( divide @ X @ Y )
!= zero )
| ( ( divide @ Y @ X )
!= zero )
| ( X = Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',divide_and_equal) ).
thf(4,axiom,
! [X: $i] :
( ( divide @ zero @ X )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_is_smallest) ).
thf(5,axiom,
! [X: $i,Z: $i,Y: $i] :
( ( divide @ ( divide @ ( divide @ X @ Z ) @ ( divide @ Y @ Z ) ) @ ( divide @ ( divide @ X @ Y ) @ Z ) )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_property) ).
thf(6,axiom,
! [X: $i,Y: $i] :
( ( divide @ ( divide @ X @ Y ) @ X )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_smaller_than_numerator) ).
thf(7,axiom,
( ( divide @ ( divide @ a @ b ) @ d )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_divide_b_divide_d_is_zero) ).
thf(8,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(9,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[8]) ).
thf(10,negated_conjecture,
( ( divide @ ( divide @ a @ d ) @ b )
!= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_property_of_divide1) ).
thf(11,plain,
$false = $false,
inference(unfold_def,[status(thm)],[9]) ).
thf(12,plain,
( ( ! [X: $i] :
( ( divide @ X @ zero )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(13,plain,
( ( ! [X: $i] :
( ( divide @ X @ identity )
= zero ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(14,plain,
( ( ! [X: $i,Y: $i] :
( ( ( divide @ X @ Y )
!= zero )
| ( ( divide @ Y @ X )
!= zero )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(15,plain,
( ( ! [X: $i] :
( ( divide @ zero @ X )
= zero ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(16,plain,
( ( ! [X: $i,Z: $i,Y: $i] :
( ( divide @ ( divide @ ( divide @ X @ Z ) @ ( divide @ Y @ Z ) ) @ ( divide @ ( divide @ X @ Y ) @ Z ) )
= zero ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(17,plain,
( ( ! [X: $i,Y: $i] :
( ( divide @ ( divide @ X @ Y ) @ X )
= zero ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(18,plain,
( ( ( divide @ ( divide @ a @ b ) @ d )
= zero )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(19,plain,
( ( ( divide @ ( divide @ a @ d ) @ b )
!= zero )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(20,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(21,plain,
( ( ! [X: $i,Y: $i] :
( ( ( divide @ X @ Y )
!= zero )
| ( ( divide @ Y @ X )
!= zero )
| ( X = Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(22,plain,
( ( ( divide @ ( divide @ a @ d ) @ b )
!= zero )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(23,plain,
( ( ( divide @ ( divide @ a @ d ) @ b )
!= zero )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(24,plain,
( ( ( divide @ ( divide @ a @ b ) @ d )
= zero )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(25,plain,
( ( ! [X: $i,Y: $i] :
( ( divide @ ( divide @ X @ Y ) @ X )
= zero ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(26,plain,
( ( ! [X: $i,Z: $i,Y: $i] :
( ( divide @ ( divide @ ( divide @ X @ Z ) @ ( divide @ Y @ Z ) ) @ ( divide @ ( divide @ X @ Y ) @ Z ) )
= zero ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(27,plain,
( ( ! [X: $i] :
( ( divide @ zero @ X )
= zero ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(28,plain,
( ( ! [X: $i,Y: $i] :
( ( ( divide @ X @ Y )
!= zero )
| ( ( divide @ Y @ X )
!= zero )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(29,plain,
( ( ! [X: $i] :
( ( divide @ X @ identity )
= zero ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(30,plain,
( ( ! [X: $i] :
( ( divide @ X @ zero )
= X ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(31,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[20]) ).
thf(32,plain,
( ( ( divide @ ( divide @ a @ d ) @ b )
= zero )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(33,plain,
! [SV1: $i] :
( ( ! [SY10: $i] :
( ( divide @ ( divide @ SV1 @ SY10 ) @ SV1 )
= zero ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(34,plain,
! [SV2: $i] :
( ( ! [SY11: $i,SY12: $i] :
( ( divide @ ( divide @ ( divide @ SV2 @ SY11 ) @ ( divide @ SY12 @ SY11 ) ) @ ( divide @ ( divide @ SV2 @ SY12 ) @ SY11 ) )
= zero ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(35,plain,
! [SV3: $i] :
( ( ( divide @ zero @ SV3 )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(36,plain,
! [SV4: $i] :
( ( ! [SY13: $i] :
( ( ( divide @ SV4 @ SY13 )
!= zero )
| ( ( divide @ SY13 @ SV4 )
!= zero )
| ( SV4 = SY13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(37,plain,
! [SV5: $i] :
( ( ( divide @ SV5 @ identity )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(38,plain,
! [SV6: $i] :
( ( ( divide @ SV6 @ zero )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(39,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(40,plain,
! [SV7: $i,SV1: $i] :
( ( ( divide @ ( divide @ SV1 @ SV7 ) @ SV1 )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(41,plain,
! [SV8: $i,SV2: $i] :
( ( ! [SY14: $i] :
( ( divide @ ( divide @ ( divide @ SV2 @ SV8 ) @ ( divide @ SY14 @ SV8 ) ) @ ( divide @ ( divide @ SV2 @ SY14 ) @ SV8 ) )
= zero ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(42,plain,
! [SV9: $i,SV4: $i] :
( ( ( ( divide @ SV4 @ SV9 )
!= zero )
| ( ( divide @ SV9 @ SV4 )
!= zero )
| ( SV4 = SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(43,plain,
! [SV10: $i,SV8: $i,SV2: $i] :
( ( ( divide @ ( divide @ ( divide @ SV2 @ SV8 ) @ ( divide @ SV10 @ SV8 ) ) @ ( divide @ ( divide @ SV2 @ SV10 ) @ SV8 ) )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(44,plain,
! [SV9: $i,SV4: $i] :
( ( ( ( divide @ SV4 @ SV9 )
!= zero )
= $true )
| ( ( ( ( divide @ SV9 @ SV4 )
!= zero )
| ( SV4 = SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(45,plain,
! [SV9: $i,SV4: $i] :
( ( ( ( divide @ SV4 @ SV9 )
= zero )
= $false )
| ( ( ( ( divide @ SV9 @ SV4 )
!= zero )
| ( SV4 = SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(46,plain,
! [SV4: $i,SV9: $i] :
( ( ( ( divide @ SV9 @ SV4 )
!= zero )
= $true )
| ( ( SV4 = SV9 )
= $true )
| ( ( ( divide @ SV4 @ SV9 )
= zero )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(47,plain,
! [SV4: $i,SV9: $i] :
( ( ( ( divide @ SV9 @ SV4 )
= zero )
= $false )
| ( ( SV4 = SV9 )
= $true )
| ( ( ( divide @ SV4 @ SV9 )
= zero )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(48,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[24,47,43,40,39,38,37,35,32]) ).
thf(49,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : HEN006-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.20 % Computer : n004.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Oct 6 10:56:24 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.26/0.28
% 0.26/0.28 No.of.Axioms: 8
% 0.26/0.28
% 0.26/0.28 Length.of.Defs: 0
% 0.26/0.28
% 0.26/0.28 Contains.Choice.Funs: false
% 0.26/0.28 .
% 0.26/0.28
% 0.26/0.28 ********************************
% 0.26/0.28 * All subproblems solved! *
% 0.26/0.28 ********************************
% 0.26/0.28 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:8,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:5,ordering:none,proof_output:1,protocol_output:false,clause_count:48,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.26/0.28
% 0.26/0.28 %**** Beginning of derivation protocol ****
% 0.26/0.28 % SZS output start CNFRefutation
% See solution above
% 0.26/0.28
% 0.26/0.28 %**** End of derivation protocol ****
% 0.26/0.28 %**** no. of clauses in derivation: 49 ****
% 0.26/0.28 %**** clause counter: 48 ****
% 0.26/0.28
% 0.26/0.28 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:8,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:5,ordering:none,proof_output:1,protocol_output:false,clause_count:48,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------