TSTP Solution File: ANA009-2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : ANA009-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n010.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 : Thu Jul 14 19:10:23 EDT 2022
% Result : Unsatisfiable 0.19s 0.39s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 19
% Syntax : Number of formulae : 62 ( 34 unt; 11 typ; 0 def)
% Number of atoms : 211 ( 66 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 373 ( 38 ~; 44 |; 0 &; 291 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 80 ( 0 ^ 80 !; 0 ?; 80 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_0,type,
c_0: $i ).
thf(tp_c_lessequals,type,
c_lessequals: $i > $i > $i > $o ).
thf(tp_c_plus,type,
c_plus: $i > $i > $i > $i ).
thf(tp_c_uminus,type,
c_uminus: $i > $i > $i ).
thf(tp_class_OrderedGroup_Oab__group__add,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(tp_class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
thf(tp_class_Ring__and__Field_Oordered__idom,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(tp_t_b,type,
t_b: $i ).
thf(tp_v_f,type,
v_f: $i > $i ).
thf(tp_v_lb,type,
v_lb: $i > $i ).
thf(tp_v_x,type,
v_x: $i ).
thf(1,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).
thf(2,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_37) ).
thf(3,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_plus @ V_a @ ( c_uminus @ V_a @ T_a ) @ T_a )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oright__minus_0) ).
thf(4,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a )
| ( c_lessequals @ ( c_plus @ V_a @ V_c @ T_a ) @ ( c_plus @ V_b @ V_c @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__right_1) ).
thf(5,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(6,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[5]) ).
thf(7,negated_conjecture,
class_Ring__and__Field_Oordered__idom @ t_b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
thf(8,negated_conjecture,
~ ( c_lessequals @ c_0 @ ( c_plus @ ( v_f @ v_x ) @ ( c_uminus @ ( v_lb @ v_x ) @ t_b ) @ t_b ) @ t_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(9,negated_conjecture,
! [V_U: $i] : ( c_lessequals @ ( v_lb @ V_U ) @ ( v_f @ V_U ) @ t_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(10,plain,
$false = $false,
inference(unfold_def,[status(thm)],[6]) ).
thf(11,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(12,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(13,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_plus @ V_a @ ( c_uminus @ V_a @ T_a ) @ T_a )
= c_0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(14,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a )
| ( c_lessequals @ ( c_plus @ V_a @ V_c @ T_a ) @ ( c_plus @ V_b @ V_c @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(15,plain,
( ( class_Ring__and__Field_Oordered__idom @ t_b )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(16,plain,
( ( ~ ( c_lessequals @ c_0 @ ( c_plus @ ( v_f @ v_x ) @ ( c_uminus @ ( v_lb @ v_x ) @ t_b ) @ t_b ) @ t_b ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(17,plain,
( ( ! [V_U: $i] : ( c_lessequals @ ( v_lb @ V_U ) @ ( v_f @ V_U ) @ t_b ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(18,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(19,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ! [V_a: $i] :
( ( c_plus @ V_a @ ( c_uminus @ V_a @ T_a ) @ T_a )
= c_0 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(20,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ! [V_b: $i] :
( ~ ( c_lessequals @ V_a @ V_b @ T_a )
| ! [V_c: $i] : ( c_lessequals @ ( c_plus @ V_a @ V_c @ T_a ) @ ( c_plus @ V_b @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(21,plain,
( ( ! [V_U: $i] : ( c_lessequals @ ( v_lb @ V_U ) @ ( v_f @ V_U ) @ t_b ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(22,plain,
( ( ~ ( c_lessequals @ c_0 @ ( c_plus @ ( v_f @ v_x ) @ ( c_uminus @ ( v_lb @ v_x ) @ t_b ) @ t_b ) @ t_b ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(23,plain,
( ( class_Ring__and__Field_Oordered__idom @ t_b )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(24,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ! [V_b: $i] :
( ~ ( c_lessequals @ V_a @ V_b @ T_a )
| ! [V_c: $i] : ( c_lessequals @ ( c_plus @ V_a @ V_c @ T_a ) @ ( c_plus @ V_b @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(25,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ! [V_a: $i] :
( ( c_plus @ V_a @ ( c_uminus @ V_a @ T_a ) @ T_a )
= c_0 ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(26,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(27,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(28,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(29,plain,
! [SV1: $i] :
( ( c_lessequals @ ( v_lb @ SV1 ) @ ( v_f @ SV1 ) @ t_b )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(30,plain,
( ( c_lessequals @ c_0 @ ( c_plus @ ( v_f @ v_x ) @ ( c_uminus @ ( v_lb @ v_x ) @ t_b ) @ t_b ) @ t_b )
= $false ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(31,plain,
! [SV2: $i] :
( ( ! [SY9: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV2 )
| ! [SY10: $i] :
( ~ ( c_lessequals @ SY9 @ SY10 @ SV2 )
| ! [SY11: $i] : ( c_lessequals @ ( c_plus @ SY9 @ SY11 @ SV2 ) @ ( c_plus @ SY10 @ SY11 @ SV2 ) @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(32,plain,
! [SV3: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV3 )
| ! [SY12: $i] :
( ( c_plus @ SY12 @ ( c_uminus @ SY12 @ SV3 ) @ SV3 )
= c_0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(33,plain,
! [SV4: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV4 )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(34,plain,
! [SV5: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV5 )
| ( class_OrderedGroup_Oab__group__add @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(35,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(36,plain,
! [SV6: $i,SV2: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV2 )
| ! [SY13: $i] :
( ~ ( c_lessequals @ SV6 @ SY13 @ SV2 )
| ! [SY14: $i] : ( c_lessequals @ ( c_plus @ SV6 @ SY14 @ SV2 ) @ ( c_plus @ SY13 @ SY14 @ SV2 ) @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(37,plain,
! [SV3: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV3 ) )
= $true )
| ( ( ! [SY12: $i] :
( ( c_plus @ SY12 @ ( c_uminus @ SY12 @ SV3 ) @ SV3 )
= c_0 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(38,plain,
! [SV4: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV4 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(39,plain,
! [SV5: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV5 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(40,plain,
! [SV6: $i,SV2: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV2 ) )
= $true )
| ( ( ! [SY13: $i] :
( ~ ( c_lessequals @ SV6 @ SY13 @ SV2 )
| ! [SY14: $i] : ( c_lessequals @ ( c_plus @ SV6 @ SY14 @ SV2 ) @ ( c_plus @ SY13 @ SY14 @ SV2 ) @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(41,plain,
! [SV3: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV3 )
= $false )
| ( ( ! [SY12: $i] :
( ( c_plus @ SY12 @ ( c_uminus @ SY12 @ SV3 ) @ SV3 )
= c_0 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(42,plain,
! [SV4: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV4 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(43,plain,
! [SV5: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV5 )
= $false )
| ( ( class_OrderedGroup_Oab__group__add @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(44,plain,
! [SV6: $i,SV2: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV2 )
= $false )
| ( ( ! [SY13: $i] :
( ~ ( c_lessequals @ SV6 @ SY13 @ SV2 )
| ! [SY14: $i] : ( c_lessequals @ ( c_plus @ SV6 @ SY14 @ SV2 ) @ ( c_plus @ SY13 @ SY14 @ SV2 ) @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(45,plain,
! [SV3: $i,SV7: $i] :
( ( ( ( c_plus @ SV7 @ ( c_uminus @ SV7 @ SV3 ) @ SV3 )
= c_0 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(46,plain,
! [SV2: $i,SV8: $i,SV6: $i] :
( ( ( ~ ( c_lessequals @ SV6 @ SV8 @ SV2 )
| ! [SY15: $i] : ( c_lessequals @ ( c_plus @ SV6 @ SY15 @ SV2 ) @ ( c_plus @ SV8 @ SY15 @ SV2 ) @ SV2 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(47,plain,
! [SV2: $i,SV8: $i,SV6: $i] :
( ( ( ~ ( c_lessequals @ SV6 @ SV8 @ SV2 ) )
= $true )
| ( ( ! [SY15: $i] : ( c_lessequals @ ( c_plus @ SV6 @ SY15 @ SV2 ) @ ( c_plus @ SV8 @ SY15 @ SV2 ) @ SV2 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(48,plain,
! [SV2: $i,SV8: $i,SV6: $i] :
( ( ( c_lessequals @ SV6 @ SV8 @ SV2 )
= $false )
| ( ( ! [SY15: $i] : ( c_lessequals @ ( c_plus @ SV6 @ SY15 @ SV2 ) @ ( c_plus @ SV8 @ SY15 @ SV2 ) @ SV2 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(49,plain,
! [SV8: $i,SV2: $i,SV9: $i,SV6: $i] :
( ( ( c_lessequals @ ( c_plus @ SV6 @ SV9 @ SV2 ) @ ( c_plus @ SV8 @ SV9 @ SV2 ) @ SV2 )
= $true )
| ( ( c_lessequals @ SV6 @ SV8 @ SV2 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(50,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[23,49,45,43,42,35,30,29]) ).
thf(51,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ANA009-2 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jul 8 04:10:01 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.35
% 0.19/0.35 No.of.Axioms: 7
% 0.19/0.35
% 0.19/0.35 Length.of.Defs: 0
% 0.19/0.35
% 0.19/0.35 Contains.Choice.Funs: false
% 0.19/0.35 (rf:0,axioms:7,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:9,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.19/0.39
% 0.19/0.39 ********************************
% 0.19/0.39 * All subproblems solved! *
% 0.19/0.39 ********************************
% 0.19/0.39 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:7,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:50,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.39
% 0.19/0.39 %**** Beginning of derivation protocol ****
% 0.19/0.39 % SZS output start CNFRefutation
% See solution above
% 0.19/0.39
% 0.19/0.39 %**** End of derivation protocol ****
% 0.19/0.39 %**** no. of clauses in derivation: 51 ****
% 0.19/0.39 %**** clause counter: 50 ****
% 0.19/0.39
% 0.19/0.39 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:7,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:50,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------