TSTP Solution File: HEN003-5 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : HEN003-5 : 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 : n004.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 12:57:14 EDT 2022
% Result : Unsatisfiable 0.18s 0.38s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 46 ( 37 unt; 4 typ; 0 def)
% Number of atoms : 142 ( 94 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 200 ( 22 ~; 20 |; 0 &; 158 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 5 con; 0-2 aty)
% Number of variables : 56 ( 0 ^ 56 !; 0 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $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 @ identity )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_is_largest) ).
thf(2,axiom,
! [X: $i,Y: $i] :
( ( ( divide @ X @ Y )
!= zero )
| ( ( divide @ Y @ X )
!= zero )
| ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divide_and_equal) ).
thf(3,axiom,
! [X: $i] :
( ( divide @ zero @ X )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_is_smallest) ).
thf(4,axiom,
! [X: $i,Z: $i,Y: $i] :
( ( divide @ ( divide @ ( divide @ X @ Z ) @ ( divide @ Y @ Z ) ) @ ( divide @ ( divide @ X @ Y ) @ Z ) )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_property) ).
thf(5,axiom,
! [X: $i,Y: $i] :
( ( divide @ ( divide @ X @ Y ) @ X )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_smaller_than_numerator) ).
thf(6,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(7,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,negated_conjecture,
( divide @ a @ a )
!= zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_x_divide_x_is_zero) ).
thf(9,plain,
$false = $false,
inference(unfold_def,[status(thm)],[7]) ).
thf(10,plain,
( ( ! [X: $i] :
( ( divide @ X @ identity )
= zero ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(11,plain,
( ( ! [X: $i,Y: $i] :
( ( ( divide @ X @ Y )
!= zero )
| ( ( divide @ Y @ X )
!= zero )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(12,plain,
( ( ! [X: $i] :
( ( divide @ zero @ X )
= zero ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(13,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)],[4]) ).
thf(14,plain,
( ( ! [X: $i,Y: $i] :
( ( divide @ ( divide @ X @ Y ) @ X )
= zero ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(15,plain,
( ( ( ( divide @ a @ a )
!= zero ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(16,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(17,plain,
( ( ! [X: $i,Y: $i] :
( ( ( divide @ X @ Y )
!= zero )
| ( ( divide @ Y @ X )
!= zero )
| ( X = Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(18,plain,
( ( ( ( divide @ a @ a )
!= zero ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(19,plain,
( ( ( ( divide @ a @ a )
!= zero ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(20,plain,
( ( ! [X: $i,Y: $i] :
( ( divide @ ( divide @ X @ Y ) @ X )
= zero ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(21,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)],[13]) ).
thf(22,plain,
( ( ! [X: $i] :
( ( divide @ zero @ X )
= zero ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(23,plain,
( ( ! [X: $i,Y: $i] :
( ( ( divide @ X @ Y )
!= zero )
| ( ( divide @ Y @ X )
!= zero )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(24,plain,
( ( ! [X: $i] :
( ( divide @ X @ identity )
= zero ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(25,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(26,plain,
( ( ( divide @ a @ a )
= zero )
= $false ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(27,plain,
! [SV1: $i] :
( ( ! [SY9: $i] :
( ( divide @ ( divide @ SV1 @ SY9 ) @ SV1 )
= zero ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(28,plain,
! [SV2: $i] :
( ( ! [SY10: $i,SY11: $i] :
( ( divide @ ( divide @ ( divide @ SV2 @ SY10 ) @ ( divide @ SY11 @ SY10 ) ) @ ( divide @ ( divide @ SV2 @ SY11 ) @ SY10 ) )
= zero ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(29,plain,
! [SV3: $i] :
( ( ( divide @ zero @ SV3 )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(30,plain,
! [SV4: $i] :
( ( ! [SY12: $i] :
( ( ( divide @ SV4 @ SY12 )
!= zero )
| ( ( divide @ SY12 @ SV4 )
!= zero )
| ( SV4 = SY12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(31,plain,
! [SV5: $i] :
( ( ( divide @ SV5 @ identity )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(32,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(33,plain,
! [SV6: $i,SV1: $i] :
( ( ( divide @ ( divide @ SV1 @ SV6 ) @ SV1 )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(34,plain,
! [SV7: $i,SV2: $i] :
( ( ! [SY13: $i] :
( ( divide @ ( divide @ ( divide @ SV2 @ SV7 ) @ ( divide @ SY13 @ SV7 ) ) @ ( divide @ ( divide @ SV2 @ SY13 ) @ SV7 ) )
= zero ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(35,plain,
! [SV8: $i,SV4: $i] :
( ( ( ( divide @ SV4 @ SV8 )
!= zero )
| ( ( divide @ SV8 @ SV4 )
!= zero )
| ( SV4 = SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(36,plain,
! [SV9: $i,SV7: $i,SV2: $i] :
( ( ( divide @ ( divide @ ( divide @ SV2 @ SV7 ) @ ( divide @ SV9 @ SV7 ) ) @ ( divide @ ( divide @ SV2 @ SV9 ) @ SV7 ) )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(37,plain,
! [SV8: $i,SV4: $i] :
( ( ( ( ( divide @ SV4 @ SV8 )
!= zero ) )
= $true )
| ( ( ( ( divide @ SV8 @ SV4 )
!= zero )
| ( SV4 = SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(38,plain,
! [SV8: $i,SV4: $i] :
( ( ( ( divide @ SV4 @ SV8 )
= zero )
= $false )
| ( ( ( ( divide @ SV8 @ SV4 )
!= zero )
| ( SV4 = SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(39,plain,
! [SV4: $i,SV8: $i] :
( ( ( ( ( divide @ SV8 @ SV4 )
!= zero ) )
= $true )
| ( ( SV4 = SV8 )
= $true )
| ( ( ( divide @ SV4 @ SV8 )
= zero )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(40,plain,
! [SV4: $i,SV8: $i] :
( ( ( ( divide @ SV8 @ SV4 )
= zero )
= $false )
| ( ( SV4 = SV8 )
= $true )
| ( ( ( divide @ SV4 @ SV8 )
= zero )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(41,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[26,40,36,33,32,31,29]) ).
thf(42,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HEN003-5 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jul 1 14:34:38 EDT 2022
% 0.18/0.33 % CPUTime :
% 0.18/0.34
% 0.18/0.34 No.of.Axioms: 6
% 0.18/0.34
% 0.18/0.34 Length.of.Defs: 0
% 0.18/0.34
% 0.18/0.34 Contains.Choice.Funs: false
% 0.18/0.34 (rf:0,axioms:6,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:8,loop_count:0,foatp_calls:0,translation:fof_full).
% 0.18/0.38
% 0.18/0.38 ********************************
% 0.18/0.38 * All subproblems solved! *
% 0.18/0.38 ********************************
% 0.18/0.38 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:6,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:41,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.18/0.38
% 0.18/0.38 %**** Beginning of derivation protocol ****
% 0.18/0.38 % SZS output start CNFRefutation
% See solution above
% 0.18/0.38
% 0.18/0.38 %**** End of derivation protocol ****
% 0.18/0.38 %**** no. of clauses in derivation: 42 ****
% 0.18/0.38 %**** clause counter: 41 ****
% 0.18/0.38
% 0.18/0.38 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:6,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:41,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------