TSTP Solution File: ANA034-2 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : ANA034-2 : 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 : n026.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 19:10:42 EDT 2022
% Result : Unsatisfiable 0.42s 0.61s
% Output : CNFRefutation 0.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 34
% Syntax : Number of formulae : 129 ( 61 unt; 18 typ; 0 def)
% Number of atoms : 640 ( 178 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 1480 ( 146 ~; 197 |; 0 &;1137 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 7 con; 0-3 aty)
% Number of variables : 234 ( 0 ^ 234 !; 0 ?; 234 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_0,type,
c_0: $i ).
thf(tp_c_HOL_Oabs,type,
c_HOL_Oabs: $i > $i > $i ).
thf(tp_c_less,type,
c_less: $i > $i > $i > $o ).
thf(tp_c_lessequals,type,
c_lessequals: $i > $i > $i > $o ).
thf(tp_c_times,type,
c_times: $i > $i > $i > $i ).
thf(tp_class_OrderedGroup_Olordered__ab__group__abs,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).
thf(tp_class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
thf(tp_class_Ring__and__Field_Oordered__idom,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(tp_class_Ring__and__Field_Opordered__cancel__semiring,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
thf(tp_class_Ring__and__Field_Opordered__semiring,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
thf(tp_t_b,type,
t_b: $i ).
thf(tp_v_a,type,
v_a: $i > $i ).
thf(tp_v_b,type,
v_b: $i > $i ).
thf(tp_v_c,type,
v_c: $i ).
thf(tp_v_ca,type,
v_ca: $i ).
thf(tp_v_f,type,
v_f: $i > $i ).
thf(tp_v_g,type,
v_g: $i > $i ).
thf(tp_v_x,type,
v_x: $i ).
thf(1,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Olordered__ab__group__abs @ T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
thf(2,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Opordered__semiring @ T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
thf(3,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
thf(4,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_Orderings_Oorder @ T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).
thf(5,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T_a )
| ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ V_a @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
thf(6,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_less @ V_x @ V_y @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
thf(7,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
| ~ ( c_lessequals @ c_0 @ V_b @ T_a )
| ~ ( c_lessequals @ c_0 @ V_a @ T_a )
| ( c_lessequals @ c_0 @ ( c_times @ V_a @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_0) ).
thf(8,axiom,
! [T_a: $i,V_c: $i,V_d: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ c_0 @ V_c @ T_a )
| ~ ( c_lessequals @ c_0 @ V_b @ T_a )
| ( c_lessequals @ ( c_times @ V_a @ V_c @ T_a ) @ ( c_times @ V_b @ V_d @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__mono_0) ).
thf(9,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Oabs @ ( c_times @ V_a @ V_b @ T_a ) @ T_a )
= ( c_times @ ( c_HOL_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs @ V_b @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__mult_0) ).
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,
class_Ring__and__Field_Oordered__idom @ t_b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
thf(13,negated_conjecture,
~ ( c_lessequals @ ( c_HOL_Oabs @ ( c_times @ ( v_a @ v_x ) @ ( v_b @ v_x ) @ t_b ) @ t_b ) @ ( c_times @ ( c_times @ v_c @ v_ca @ t_b ) @ ( c_HOL_Oabs @ ( c_times @ ( v_f @ v_x ) @ ( v_g @ v_x ) @ t_b ) @ t_b ) @ t_b ) @ t_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(14,negated_conjecture,
( ( c_times @ ( c_times @ v_c @ v_ca @ t_b ) @ ( c_HOL_Oabs @ ( c_times @ ( v_f @ v_x ) @ ( v_g @ v_x ) @ t_b ) @ t_b ) @ t_b )
= ( c_times @ ( c_times @ v_c @ ( c_HOL_Oabs @ ( v_f @ v_x ) @ t_b ) @ t_b ) @ ( c_times @ v_ca @ ( c_HOL_Oabs @ ( v_g @ v_x ) @ t_b ) @ t_b ) @ t_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(15,negated_conjecture,
c_lessequals @ ( c_HOL_Oabs @ ( v_b @ v_x ) @ t_b ) @ ( c_times @ v_ca @ ( c_HOL_Oabs @ ( v_g @ v_x ) @ t_b ) @ t_b ) @ t_b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(16,negated_conjecture,
c_lessequals @ ( c_HOL_Oabs @ ( v_a @ v_x ) @ t_b ) @ ( c_times @ v_c @ ( c_HOL_Oabs @ ( v_f @ v_x ) @ t_b ) @ t_b ) @ t_b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(17,negated_conjecture,
c_less @ c_0 @ v_c @ t_b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(18,plain,
$false = $false,
inference(unfold_def,[status(thm)],[11]) ).
thf(19,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Olordered__ab__group__abs @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(20,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(21,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(22,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(23,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T_a )
| ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ V_a @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(24,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_less @ V_x @ V_y @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(25,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
| ~ ( c_lessequals @ c_0 @ V_b @ T_a )
| ~ ( c_lessequals @ c_0 @ V_a @ T_a )
| ( c_lessequals @ c_0 @ ( c_times @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(26,plain,
( ( ! [T_a: $i,V_c: $i,V_d: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ c_0 @ V_c @ T_a )
| ~ ( c_lessequals @ c_0 @ V_b @ T_a )
| ( c_lessequals @ ( c_times @ V_a @ V_c @ T_a ) @ ( c_times @ V_b @ V_d @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(27,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Oabs @ ( c_times @ V_a @ V_b @ T_a ) @ T_a )
= ( c_times @ ( c_HOL_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(28,plain,
( ( class_Ring__and__Field_Oordered__idom @ t_b )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(29,plain,
( ( ~ ( c_lessequals @ ( c_HOL_Oabs @ ( c_times @ ( v_a @ v_x ) @ ( v_b @ v_x ) @ t_b ) @ t_b ) @ ( c_times @ ( c_times @ v_c @ v_ca @ t_b ) @ ( c_HOL_Oabs @ ( c_times @ ( v_f @ v_x ) @ ( v_g @ v_x ) @ t_b ) @ t_b ) @ t_b ) @ t_b ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(30,plain,
( ( ( c_times @ ( c_times @ v_c @ v_ca @ t_b ) @ ( c_HOL_Oabs @ ( c_times @ ( v_f @ v_x ) @ ( v_g @ v_x ) @ t_b ) @ t_b ) @ t_b )
= ( c_times @ ( c_times @ v_c @ ( c_HOL_Oabs @ ( v_f @ v_x ) @ t_b ) @ t_b ) @ ( c_times @ v_ca @ ( c_HOL_Oabs @ ( v_g @ v_x ) @ t_b ) @ t_b ) @ t_b ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(31,plain,
( ( c_lessequals @ ( c_HOL_Oabs @ ( v_b @ v_x ) @ t_b ) @ ( c_times @ v_ca @ ( c_HOL_Oabs @ ( v_g @ v_x ) @ t_b ) @ t_b ) @ t_b )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(32,plain,
( ( c_lessequals @ ( c_HOL_Oabs @ ( v_a @ v_x ) @ t_b ) @ ( c_times @ v_c @ ( c_HOL_Oabs @ ( v_f @ v_x ) @ t_b ) @ t_b ) @ t_b )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(33,plain,
( ( c_less @ c_0 @ v_c @ t_b )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(34,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[18]) ).
thf(35,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T_a )
| ! [V_a: $i] : ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ V_a @ T_a ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(36,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ~ ( c_less @ V_x @ V_y @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(37,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
| ! [V_b: $i] :
( ~ ( c_lessequals @ c_0 @ V_b @ T_a )
| ! [V_a: $i] :
( ~ ( c_lessequals @ c_0 @ V_a @ T_a )
| ( c_lessequals @ c_0 @ ( c_times @ V_a @ V_b @ T_a ) @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(38,plain,
( ( ! [T_a: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ! [V_a: $i,V_b: $i] :
( ~ ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ c_0 @ V_c @ T_a )
| ~ ( c_lessequals @ c_0 @ V_b @ T_a )
| ( c_lessequals @ ( c_times @ V_a @ V_c @ T_a ) @ ( c_times @ V_b @ V_d @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(39,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ! [V_a: $i,V_b: $i] :
( ( c_HOL_Oabs @ ( c_times @ V_a @ V_b @ T_a ) @ T_a )
= ( c_times @ ( c_HOL_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(40,plain,
( ( c_less @ c_0 @ v_c @ t_b )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(41,plain,
( ( c_lessequals @ ( c_HOL_Oabs @ ( v_a @ v_x ) @ t_b ) @ ( c_times @ v_c @ ( c_HOL_Oabs @ ( v_f @ v_x ) @ t_b ) @ t_b ) @ t_b )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(42,plain,
( ( c_lessequals @ ( c_HOL_Oabs @ ( v_b @ v_x ) @ t_b ) @ ( c_times @ v_ca @ ( c_HOL_Oabs @ ( v_g @ v_x ) @ t_b ) @ t_b ) @ t_b )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(43,plain,
( ( ( c_times @ ( c_times @ v_c @ v_ca @ t_b ) @ ( c_HOL_Oabs @ ( c_times @ ( v_f @ v_x ) @ ( v_g @ v_x ) @ t_b ) @ t_b ) @ t_b )
= ( c_times @ ( c_times @ v_c @ ( c_HOL_Oabs @ ( v_f @ v_x ) @ t_b ) @ t_b ) @ ( c_times @ v_ca @ ( c_HOL_Oabs @ ( v_g @ v_x ) @ t_b ) @ t_b ) @ t_b ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(44,plain,
( ( ~ ( c_lessequals @ ( c_HOL_Oabs @ ( c_times @ ( v_a @ v_x ) @ ( v_b @ v_x ) @ t_b ) @ t_b ) @ ( c_times @ ( c_times @ v_c @ v_ca @ t_b ) @ ( c_HOL_Oabs @ ( c_times @ ( v_f @ v_x ) @ ( v_g @ v_x ) @ t_b ) @ t_b ) @ t_b ) @ t_b ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(45,plain,
( ( class_Ring__and__Field_Oordered__idom @ t_b )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(46,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ! [V_a: $i,V_b: $i] :
( ( c_HOL_Oabs @ ( c_times @ V_a @ V_b @ T_a ) @ T_a )
= ( c_times @ ( c_HOL_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(47,plain,
( ( ! [T_a: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ! [V_a: $i,V_b: $i] :
( ~ ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ c_0 @ V_c @ T_a )
| ~ ( c_lessequals @ c_0 @ V_b @ T_a )
| ( c_lessequals @ ( c_times @ V_a @ V_c @ T_a ) @ ( c_times @ V_b @ V_d @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(48,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
| ! [V_b: $i] :
( ~ ( c_lessequals @ c_0 @ V_b @ T_a )
| ! [V_a: $i] :
( ~ ( c_lessequals @ c_0 @ V_a @ T_a )
| ( c_lessequals @ c_0 @ ( c_times @ V_a @ V_b @ T_a ) @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(49,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ~ ( c_less @ V_x @ V_y @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(50,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T_a )
| ! [V_a: $i] : ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ V_a @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(51,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(52,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(53,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(54,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Olordered__ab__group__abs @ T ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(55,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(56,plain,
( ( c_lessequals @ ( c_HOL_Oabs @ ( c_times @ ( v_a @ v_x ) @ ( v_b @ v_x ) @ t_b ) @ t_b ) @ ( c_times @ ( c_times @ v_c @ v_ca @ t_b ) @ ( c_HOL_Oabs @ ( c_times @ ( v_f @ v_x ) @ ( v_g @ v_x ) @ t_b ) @ t_b ) @ t_b ) @ t_b )
= $false ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(57,plain,
! [SV1: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV1 )
| ! [SY20: $i,SY21: $i] :
( ( c_HOL_Oabs @ ( c_times @ SY20 @ SY21 @ SV1 ) @ SV1 )
= ( c_times @ ( c_HOL_Oabs @ SY20 @ SV1 ) @ ( c_HOL_Oabs @ SY21 @ SV1 ) @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(58,plain,
! [SV2: $i] :
( ( ! [SY22: $i,SY23: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ SV2 )
| ~ ( c_lessequals @ SY22 @ SY23 @ SV2 )
| ! [SY24: $i,SY25: $i] :
( ~ ( c_lessequals @ SY24 @ SY25 @ SV2 )
| ~ ( c_lessequals @ c_0 @ SY22 @ SV2 )
| ~ ( c_lessequals @ c_0 @ SY25 @ SV2 )
| ( c_lessequals @ ( c_times @ SY24 @ SY22 @ SV2 ) @ ( c_times @ SY25 @ SY23 @ SV2 ) @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(59,plain,
! [SV3: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV3 )
| ! [SY26: $i] :
( ~ ( c_lessequals @ c_0 @ SY26 @ SV3 )
| ! [SY27: $i] :
( ~ ( c_lessequals @ c_0 @ SY27 @ SV3 )
| ( c_lessequals @ c_0 @ ( c_times @ SY27 @ SY26 @ SV3 ) @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(60,plain,
! [SV4: $i] :
( ( ~ ( class_Orderings_Oorder @ SV4 )
| ! [SY28: $i,SY29: $i] :
( ~ ( c_less @ SY28 @ SY29 @ SV4 )
| ( c_lessequals @ SY28 @ SY29 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(61,plain,
! [SV5: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV5 )
| ! [SY30: $i] : ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ SY30 @ SV5 ) @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(62,plain,
! [SV6: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV6 )
| ( class_Orderings_Oorder @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(63,plain,
! [SV7: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV7 )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(64,plain,
! [SV8: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV8 )
| ( class_Ring__and__Field_Opordered__semiring @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(65,plain,
! [SV9: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV9 )
| ( class_OrderedGroup_Olordered__ab__group__abs @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(66,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(67,plain,
! [SV1: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV1 ) )
= $true )
| ( ( ! [SY20: $i,SY21: $i] :
( ( c_HOL_Oabs @ ( c_times @ SY20 @ SY21 @ SV1 ) @ SV1 )
= ( c_times @ ( c_HOL_Oabs @ SY20 @ SV1 ) @ ( c_HOL_Oabs @ SY21 @ SV1 ) @ SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(68,plain,
! [SV10: $i,SV2: $i] :
( ( ! [SY31: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ SV2 )
| ~ ( c_lessequals @ SV10 @ SY31 @ SV2 )
| ! [SY32: $i,SY33: $i] :
( ~ ( c_lessequals @ SY32 @ SY33 @ SV2 )
| ~ ( c_lessequals @ c_0 @ SV10 @ SV2 )
| ~ ( c_lessequals @ c_0 @ SY33 @ SV2 )
| ( c_lessequals @ ( c_times @ SY32 @ SV10 @ SV2 ) @ ( c_times @ SY33 @ SY31 @ SV2 ) @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(69,plain,
! [SV3: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV3 ) )
= $true )
| ( ( ! [SY26: $i] :
( ~ ( c_lessequals @ c_0 @ SY26 @ SV3 )
| ! [SY27: $i] :
( ~ ( c_lessequals @ c_0 @ SY27 @ SV3 )
| ( c_lessequals @ c_0 @ ( c_times @ SY27 @ SY26 @ SV3 ) @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(70,plain,
! [SV4: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV4 ) )
= $true )
| ( ( ! [SY28: $i,SY29: $i] :
( ~ ( c_less @ SY28 @ SY29 @ SV4 )
| ( c_lessequals @ SY28 @ SY29 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(71,plain,
! [SV5: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV5 ) )
= $true )
| ( ( ! [SY30: $i] : ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ SY30 @ SV5 ) @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(72,plain,
! [SV6: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV6 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(73,plain,
! [SV7: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV7 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(74,plain,
! [SV8: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV8 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(75,plain,
! [SV9: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV9 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(76,plain,
! [SV1: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV1 )
= $false )
| ( ( ! [SY20: $i,SY21: $i] :
( ( c_HOL_Oabs @ ( c_times @ SY20 @ SY21 @ SV1 ) @ SV1 )
= ( c_times @ ( c_HOL_Oabs @ SY20 @ SV1 ) @ ( c_HOL_Oabs @ SY21 @ SV1 ) @ SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(77,plain,
! [SV11: $i,SV10: $i,SV2: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV2 )
| ~ ( c_lessequals @ SV10 @ SV11 @ SV2 )
| ! [SY34: $i,SY35: $i] :
( ~ ( c_lessequals @ SY34 @ SY35 @ SV2 )
| ~ ( c_lessequals @ c_0 @ SV10 @ SV2 )
| ~ ( c_lessequals @ c_0 @ SY35 @ SV2 )
| ( c_lessequals @ ( c_times @ SY34 @ SV10 @ SV2 ) @ ( c_times @ SY35 @ SV11 @ SV2 ) @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(78,plain,
! [SV3: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV3 )
= $false )
| ( ( ! [SY26: $i] :
( ~ ( c_lessequals @ c_0 @ SY26 @ SV3 )
| ! [SY27: $i] :
( ~ ( c_lessequals @ c_0 @ SY27 @ SV3 )
| ( c_lessequals @ c_0 @ ( c_times @ SY27 @ SY26 @ SV3 ) @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(79,plain,
! [SV4: $i] :
( ( ( class_Orderings_Oorder @ SV4 )
= $false )
| ( ( ! [SY28: $i,SY29: $i] :
( ~ ( c_less @ SY28 @ SY29 @ SV4 )
| ( c_lessequals @ SY28 @ SY29 @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(80,plain,
! [SV5: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV5 )
= $false )
| ( ( ! [SY30: $i] : ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ SY30 @ SV5 ) @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(81,plain,
! [SV6: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV6 )
= $false )
| ( ( class_Orderings_Oorder @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(82,plain,
! [SV7: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV7 )
= $false )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(83,plain,
! [SV8: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV8 )
= $false )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(84,plain,
! [SV9: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV9 )
= $false )
| ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(85,plain,
! [SV1: $i,SV12: $i] :
( ( ( ! [SY36: $i] :
( ( c_HOL_Oabs @ ( c_times @ SV12 @ SY36 @ SV1 ) @ SV1 )
= ( c_times @ ( c_HOL_Oabs @ SV12 @ SV1 ) @ ( c_HOL_Oabs @ SY36 @ SV1 ) @ SV1 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(86,plain,
! [SV11: $i,SV10: $i,SV2: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV2 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV10 @ SV11 @ SV2 )
| ! [SY34: $i,SY35: $i] :
( ~ ( c_lessequals @ SY34 @ SY35 @ SV2 )
| ~ ( c_lessequals @ c_0 @ SV10 @ SV2 )
| ~ ( c_lessequals @ c_0 @ SY35 @ SV2 )
| ( c_lessequals @ ( c_times @ SY34 @ SV10 @ SV2 ) @ ( c_times @ SY35 @ SV11 @ SV2 ) @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(87,plain,
! [SV3: $i,SV13: $i] :
( ( ( ~ ( c_lessequals @ c_0 @ SV13 @ SV3 )
| ! [SY37: $i] :
( ~ ( c_lessequals @ c_0 @ SY37 @ SV3 )
| ( c_lessequals @ c_0 @ ( c_times @ SY37 @ SV13 @ SV3 ) @ SV3 ) ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(88,plain,
! [SV4: $i,SV14: $i] :
( ( ( ! [SY38: $i] :
( ~ ( c_less @ SV14 @ SY38 @ SV4 )
| ( c_lessequals @ SV14 @ SY38 @ SV4 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(89,plain,
! [SV5: $i,SV15: $i] :
( ( ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ SV15 @ SV5 ) @ SV5 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(90,plain,
! [SV1: $i,SV16: $i,SV12: $i] :
( ( ( ( c_HOL_Oabs @ ( c_times @ SV12 @ SV16 @ SV1 ) @ SV1 )
= ( c_times @ ( c_HOL_Oabs @ SV12 @ SV1 ) @ ( c_HOL_Oabs @ SV16 @ SV1 ) @ SV1 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(91,plain,
! [SV11: $i,SV10: $i,SV2: $i] :
( ( ( class_Ring__and__Field_Opordered__semiring @ SV2 )
= $false )
| ( ( ~ ( c_lessequals @ SV10 @ SV11 @ SV2 )
| ! [SY34: $i,SY35: $i] :
( ~ ( c_lessequals @ SY34 @ SY35 @ SV2 )
| ~ ( c_lessequals @ c_0 @ SV10 @ SV2 )
| ~ ( c_lessequals @ c_0 @ SY35 @ SV2 )
| ( c_lessequals @ ( c_times @ SY34 @ SV10 @ SV2 ) @ ( c_times @ SY35 @ SV11 @ SV2 ) @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(92,plain,
! [SV3: $i,SV13: $i] :
( ( ( ~ ( c_lessequals @ c_0 @ SV13 @ SV3 ) )
= $true )
| ( ( ! [SY37: $i] :
( ~ ( c_lessequals @ c_0 @ SY37 @ SV3 )
| ( c_lessequals @ c_0 @ ( c_times @ SY37 @ SV13 @ SV3 ) @ SV3 ) ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(93,plain,
! [SV4: $i,SV17: $i,SV14: $i] :
( ( ( ~ ( c_less @ SV14 @ SV17 @ SV4 )
| ( c_lessequals @ SV14 @ SV17 @ SV4 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(94,plain,
! [SV2: $i,SV11: $i,SV10: $i] :
( ( ( ~ ( c_lessequals @ SV10 @ SV11 @ SV2 ) )
= $true )
| ( ( ! [SY34: $i,SY35: $i] :
( ~ ( c_lessequals @ SY34 @ SY35 @ SV2 )
| ~ ( c_lessequals @ c_0 @ SV10 @ SV2 )
| ~ ( c_lessequals @ c_0 @ SY35 @ SV2 )
| ( c_lessequals @ ( c_times @ SY34 @ SV10 @ SV2 ) @ ( c_times @ SY35 @ SV11 @ SV2 ) @ SV2 ) ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(95,plain,
! [SV3: $i,SV13: $i] :
( ( ( c_lessequals @ c_0 @ SV13 @ SV3 )
= $false )
| ( ( ! [SY37: $i] :
( ~ ( c_lessequals @ c_0 @ SY37 @ SV3 )
| ( c_lessequals @ c_0 @ ( c_times @ SY37 @ SV13 @ SV3 ) @ SV3 ) ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(96,plain,
! [SV4: $i,SV17: $i,SV14: $i] :
( ( ( ~ ( c_less @ SV14 @ SV17 @ SV4 ) )
= $true )
| ( ( c_lessequals @ SV14 @ SV17 @ SV4 )
= $true )
| ( ( class_Orderings_Oorder @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(97,plain,
! [SV2: $i,SV11: $i,SV10: $i] :
( ( ( c_lessequals @ SV10 @ SV11 @ SV2 )
= $false )
| ( ( ! [SY34: $i,SY35: $i] :
( ~ ( c_lessequals @ SY34 @ SY35 @ SV2 )
| ~ ( c_lessequals @ c_0 @ SV10 @ SV2 )
| ~ ( c_lessequals @ c_0 @ SY35 @ SV2 )
| ( c_lessequals @ ( c_times @ SY34 @ SV10 @ SV2 ) @ ( c_times @ SY35 @ SV11 @ SV2 ) @ SV2 ) ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(98,plain,
! [SV13: $i,SV3: $i,SV18: $i] :
( ( ( ~ ( c_lessequals @ c_0 @ SV18 @ SV3 )
| ( c_lessequals @ c_0 @ ( c_times @ SV18 @ SV13 @ SV3 ) @ SV3 ) )
= $true )
| ( ( c_lessequals @ c_0 @ SV13 @ SV3 )
= $false )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(99,plain,
! [SV4: $i,SV17: $i,SV14: $i] :
( ( ( c_less @ SV14 @ SV17 @ SV4 )
= $false )
| ( ( c_lessequals @ SV14 @ SV17 @ SV4 )
= $true )
| ( ( class_Orderings_Oorder @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(100,plain,
! [SV11: $i,SV10: $i,SV2: $i,SV19: $i] :
( ( ( ! [SY39: $i] :
( ~ ( c_lessequals @ SV19 @ SY39 @ SV2 )
| ~ ( c_lessequals @ c_0 @ SV10 @ SV2 )
| ~ ( c_lessequals @ c_0 @ SY39 @ SV2 )
| ( c_lessequals @ ( c_times @ SV19 @ SV10 @ SV2 ) @ ( c_times @ SY39 @ SV11 @ SV2 ) @ SV2 ) ) )
= $true )
| ( ( c_lessequals @ SV10 @ SV11 @ SV2 )
= $false )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(101,plain,
! [SV13: $i,SV3: $i,SV18: $i] :
( ( ( ~ ( c_lessequals @ c_0 @ SV18 @ SV3 ) )
= $true )
| ( ( c_lessequals @ c_0 @ ( c_times @ SV18 @ SV13 @ SV3 ) @ SV3 )
= $true )
| ( ( c_lessequals @ c_0 @ SV13 @ SV3 )
= $false )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(102,plain,
! [SV11: $i,SV10: $i,SV2: $i,SV20: $i,SV19: $i] :
( ( ( ~ ( c_lessequals @ SV19 @ SV20 @ SV2 )
| ~ ( c_lessequals @ c_0 @ SV10 @ SV2 )
| ~ ( c_lessequals @ c_0 @ SV20 @ SV2 )
| ( c_lessequals @ ( c_times @ SV19 @ SV10 @ SV2 ) @ ( c_times @ SV20 @ SV11 @ SV2 ) @ SV2 ) )
= $true )
| ( ( c_lessequals @ SV10 @ SV11 @ SV2 )
= $false )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(103,plain,
! [SV13: $i,SV3: $i,SV18: $i] :
( ( ( c_lessequals @ c_0 @ SV18 @ SV3 )
= $false )
| ( ( c_lessequals @ c_0 @ ( c_times @ SV18 @ SV13 @ SV3 ) @ SV3 )
= $true )
| ( ( c_lessequals @ c_0 @ SV13 @ SV3 )
= $false )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(104,plain,
! [SV11: $i,SV10: $i,SV2: $i,SV20: $i,SV19: $i] :
( ( ( ~ ( c_lessequals @ SV19 @ SV20 @ SV2 ) )
= $true )
| ( ( ~ ( c_lessequals @ c_0 @ SV10 @ SV2 )
| ~ ( c_lessequals @ c_0 @ SV20 @ SV2 )
| ( c_lessequals @ ( c_times @ SV19 @ SV10 @ SV2 ) @ ( c_times @ SV20 @ SV11 @ SV2 ) @ SV2 ) )
= $true )
| ( ( c_lessequals @ SV10 @ SV11 @ SV2 )
= $false )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(105,plain,
! [SV11: $i,SV10: $i,SV2: $i,SV20: $i,SV19: $i] :
( ( ( c_lessequals @ SV19 @ SV20 @ SV2 )
= $false )
| ( ( ~ ( c_lessequals @ c_0 @ SV10 @ SV2 )
| ~ ( c_lessequals @ c_0 @ SV20 @ SV2 )
| ( c_lessequals @ ( c_times @ SV19 @ SV10 @ SV2 ) @ ( c_times @ SV20 @ SV11 @ SV2 ) @ SV2 ) )
= $true )
| ( ( c_lessequals @ SV10 @ SV11 @ SV2 )
= $false )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(106,plain,
! [SV11: $i,SV19: $i,SV20: $i,SV2: $i,SV10: $i] :
( ( ( ~ ( c_lessequals @ c_0 @ SV10 @ SV2 ) )
= $true )
| ( ( ~ ( c_lessequals @ c_0 @ SV20 @ SV2 )
| ( c_lessequals @ ( c_times @ SV19 @ SV10 @ SV2 ) @ ( c_times @ SV20 @ SV11 @ SV2 ) @ SV2 ) )
= $true )
| ( ( c_lessequals @ SV19 @ SV20 @ SV2 )
= $false )
| ( ( c_lessequals @ SV10 @ SV11 @ SV2 )
= $false )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(107,plain,
! [SV11: $i,SV19: $i,SV20: $i,SV2: $i,SV10: $i] :
( ( ( c_lessequals @ c_0 @ SV10 @ SV2 )
= $false )
| ( ( ~ ( c_lessequals @ c_0 @ SV20 @ SV2 )
| ( c_lessequals @ ( c_times @ SV19 @ SV10 @ SV2 ) @ ( c_times @ SV20 @ SV11 @ SV2 ) @ SV2 ) )
= $true )
| ( ( c_lessequals @ SV19 @ SV20 @ SV2 )
= $false )
| ( ( c_lessequals @ SV10 @ SV11 @ SV2 )
= $false )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(108,plain,
! [SV11: $i,SV10: $i,SV19: $i,SV2: $i,SV20: $i] :
( ( ( ~ ( c_lessequals @ c_0 @ SV20 @ SV2 ) )
= $true )
| ( ( c_lessequals @ ( c_times @ SV19 @ SV10 @ SV2 ) @ ( c_times @ SV20 @ SV11 @ SV2 ) @ SV2 )
= $true )
| ( ( c_lessequals @ c_0 @ SV10 @ SV2 )
= $false )
| ( ( c_lessequals @ SV19 @ SV20 @ SV2 )
= $false )
| ( ( c_lessequals @ SV10 @ SV11 @ SV2 )
= $false )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(109,plain,
! [SV11: $i,SV10: $i,SV19: $i,SV2: $i,SV20: $i] :
( ( ( c_lessequals @ c_0 @ SV20 @ SV2 )
= $false )
| ( ( c_lessequals @ ( c_times @ SV19 @ SV10 @ SV2 ) @ ( c_times @ SV20 @ SV11 @ SV2 ) @ SV2 )
= $true )
| ( ( c_lessequals @ c_0 @ SV10 @ SV2 )
= $false )
| ( ( c_lessequals @ SV19 @ SV20 @ SV2 )
= $false )
| ( ( c_lessequals @ SV10 @ SV11 @ SV2 )
= $false )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(110,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[40,109,103,99,90,89,84,83,82,81,66,56,45,43,42,41]) ).
thf(111,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ANA034-2 : TPTP v8.1.0. Released v3.2.0.
% 0.14/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.35 % Computer : n026.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Fri Jul 8 05:32:39 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36
% 0.14/0.36 No.of.Axioms: 15
% 0.14/0.36
% 0.14/0.36 Length.of.Defs: 0
% 0.14/0.36
% 0.14/0.36 Contains.Choice.Funs: false
% 0.14/0.37 (rf:0,axioms:15,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:17,loop_count:0,foatp_calls:0,translation:fof_full)......
% 0.42/0.61
% 0.42/0.61 ********************************
% 0.42/0.61 * All subproblems solved! *
% 0.42/0.61 ********************************
% 0.42/0.61 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:15,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:110,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.42/0.62
% 0.42/0.62 %**** Beginning of derivation protocol ****
% 0.42/0.62 % SZS output start CNFRefutation
% See solution above
% 0.42/0.62
% 0.42/0.62 %**** End of derivation protocol ****
% 0.42/0.62 %**** no. of clauses in derivation: 111 ****
% 0.42/0.62 %**** clause counter: 110 ****
% 0.42/0.62
% 0.42/0.62 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:15,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:110,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------