TSTP Solution File: ANA019-2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : ANA019-2 : 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 : n014.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 19:10:30 EDT 2022
% Result : Unsatisfiable 0.18s 0.42s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 35
% Syntax : Number of formulae : 121 ( 58 unt; 19 typ; 0 def)
% Number of atoms : 474 ( 148 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 820 ( 92 ~; 118 |; 0 &; 610 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 7 con; 0-3 aty)
% Number of variables : 141 ( 0 ^ 141 !; 0 ?; 141 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_0,type,
c_0: $i ).
thf(tp_c_1,type,
c_1: $i ).
thf(tp_c_HOL_Oabs,type,
c_HOL_Oabs: $i > $i > $i ).
thf(tp_c_Suc,type,
c_Suc: $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_minus,type,
c_minus: $i > $i > $i > $i ).
thf(tp_c_times,type,
c_times: $i > $i > $i > $i ).
thf(tp_class_LOrder_Ojoin__semilorder,type,
class_LOrder_Ojoin__semilorder: $i > $o ).
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_t_a,type,
t_a: $i ).
thf(tp_tc_nat,type,
tc_nat: $i ).
thf(tp_v_f,type,
v_f: $i > $i ).
thf(tp_v_h,type,
v_h: $i > $i ).
thf(tp_v_x,type,
v_x: $i ).
thf(tp_v_xa,type,
v_xa: $i > $i ).
thf(1,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Olordered__ab__group__abs @ T ) ),
file('/export/starexec/sandbox/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__cancel__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
thf(3,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).
thf(4,axiom,
! [T: $i] :
( ~ ( class_LOrder_Ojoin__semilorder @ T )
| ( class_Orderings_Oorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
thf(5,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/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_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/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
thf(7,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/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
thf(8,axiom,
! [T_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T_a )
| ( ( c_HOL_Oabs @ c_0 @ T_a )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_1) ).
thf(9,axiom,
! [V_n: $i] :
( ( c_less @ c_0 @ V_n @ tc_nat )
| ( V_n = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_0) ).
thf(10,axiom,
! [V_x: $i] :
( ~ ( c_less @ c_0 @ V_x @ tc_nat )
| ( V_x
= ( c_Suc @ ( c_minus @ V_x @ c_1 @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_OSuc__pred_H_0) ).
thf(11,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(12,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[11]) ).
thf(13,negated_conjecture,
class_Ring__and__Field_Oordered__idom @ t_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
thf(14,negated_conjecture,
! [V_U: $i] :
( ~ ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ ( v_xa @ V_U ) ) @ t_a ) @ ( c_times @ V_U @ ( c_HOL_Oabs @ ( v_h @ ( v_xa @ V_U ) ) @ t_a ) @ t_a ) @ t_a )
| ~ ( c_less @ c_0 @ V_U @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(15,negated_conjecture,
! [V_U: $i] : ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ ( c_Suc @ V_U ) ) @ t_a ) @ ( c_times @ v_x @ ( c_HOL_Oabs @ ( v_h @ ( c_Suc @ V_U ) ) @ t_a ) @ t_a ) @ t_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(16,negated_conjecture,
c_less @ c_0 @ v_x @ t_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(17,negated_conjecture,
( ( v_f @ c_0 )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(18,plain,
$false = $false,
inference(unfold_def,[status(thm)],[12]) ).
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__cancel__semiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(21,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(22,plain,
( ( ! [T: $i] :
( ~ ( class_LOrder_Ojoin__semilorder @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(23,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)],[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_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)],[7]) ).
thf(26,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T_a )
| ( ( c_HOL_Oabs @ c_0 @ T_a )
= c_0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(27,plain,
( ( ! [V_n: $i] :
( ( c_less @ c_0 @ V_n @ tc_nat )
| ( V_n = c_0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(28,plain,
( ( ! [V_x: $i] :
( ~ ( c_less @ c_0 @ V_x @ tc_nat )
| ( V_x
= ( c_Suc @ ( c_minus @ V_x @ c_1 @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(29,plain,
( ( class_Ring__and__Field_Oordered__idom @ t_a )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(30,plain,
( ( ! [V_U: $i] :
( ~ ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ ( v_xa @ V_U ) ) @ t_a ) @ ( c_times @ V_U @ ( c_HOL_Oabs @ ( v_h @ ( v_xa @ V_U ) ) @ t_a ) @ t_a ) @ t_a )
| ~ ( c_less @ c_0 @ V_U @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(31,plain,
( ( ! [V_U: $i] : ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ ( c_Suc @ V_U ) ) @ t_a ) @ ( c_times @ v_x @ ( c_HOL_Oabs @ ( v_h @ ( c_Suc @ V_U ) ) @ t_a ) @ t_a ) @ t_a ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(32,plain,
( ( c_less @ c_0 @ v_x @ t_a )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(33,plain,
( ( ( v_f @ c_0 )
= c_0 )
= $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_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)],[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_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)],[25]) ).
thf(38,plain,
( ( ! [V_n: $i] :
( ( V_n = c_0 )
| ( c_less @ c_0 @ V_n @ tc_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(39,plain,
( ( ( v_f @ c_0 )
= c_0 )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(40,plain,
( ( c_less @ c_0 @ v_x @ t_a )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(41,plain,
( ( ! [V_U: $i] : ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ ( c_Suc @ V_U ) ) @ t_a ) @ ( c_times @ v_x @ ( c_HOL_Oabs @ ( v_h @ ( c_Suc @ V_U ) ) @ t_a ) @ t_a ) @ t_a ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(42,plain,
( ( ! [V_U: $i] :
( ~ ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ ( v_xa @ V_U ) ) @ t_a ) @ ( c_times @ V_U @ ( c_HOL_Oabs @ ( v_h @ ( v_xa @ V_U ) ) @ t_a ) @ t_a ) @ t_a )
| ~ ( c_less @ c_0 @ V_U @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(43,plain,
( ( class_Ring__and__Field_Oordered__idom @ t_a )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(44,plain,
( ( ! [V_x: $i] :
( ~ ( c_less @ c_0 @ V_x @ tc_nat )
| ( V_x
= ( c_Suc @ ( c_minus @ V_x @ c_1 @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(45,plain,
( ( ! [V_n: $i] :
( ( V_n = c_0 )
| ( c_less @ c_0 @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(46,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T_a )
| ( ( c_HOL_Oabs @ c_0 @ T_a )
= c_0 ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(47,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)],[37]) ).
thf(48,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(49,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)],[35]) ).
thf(50,plain,
( ( ! [T: $i] :
( ~ ( class_LOrder_Ojoin__semilorder @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(51,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
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)],[20]) ).
thf(53,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Olordered__ab__group__abs @ T ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(54,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(55,plain,
! [SV1: $i] :
( ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ ( c_Suc @ SV1 ) ) @ t_a ) @ ( c_times @ v_x @ ( c_HOL_Oabs @ ( v_h @ ( c_Suc @ SV1 ) ) @ t_a ) @ t_a ) @ t_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(56,plain,
! [SV2: $i] :
( ( ~ ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ ( v_xa @ SV2 ) ) @ t_a ) @ ( c_times @ SV2 @ ( c_HOL_Oabs @ ( v_h @ ( v_xa @ SV2 ) ) @ t_a ) @ t_a ) @ t_a )
| ~ ( c_less @ c_0 @ SV2 @ t_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(57,plain,
! [SV3: $i] :
( ( ~ ( c_less @ c_0 @ SV3 @ tc_nat )
| ( SV3
= ( c_Suc @ ( c_minus @ SV3 @ c_1 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(58,plain,
! [SV4: $i] :
( ( ( SV4 = c_0 )
| ( c_less @ c_0 @ SV4 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(59,plain,
! [SV5: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV5 )
| ( ( c_HOL_Oabs @ c_0 @ SV5 )
= c_0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(60,plain,
! [SV6: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV6 )
| ! [SY17: $i] : ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ SY17 @ SV6 ) @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(61,plain,
! [SV7: $i] :
( ( ~ ( class_Orderings_Oorder @ SV7 )
| ! [SY18: $i,SY19: $i] :
( ~ ( c_less @ SY18 @ SY19 @ SV7 )
| ( c_lessequals @ SY18 @ SY19 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(62,plain,
! [SV8: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV8 )
| ! [SY20: $i] :
( ~ ( c_lessequals @ c_0 @ SY20 @ SV8 )
| ! [SY21: $i] :
( ~ ( c_lessequals @ c_0 @ SY21 @ SV8 )
| ( c_lessequals @ c_0 @ ( c_times @ SY21 @ SY20 @ SV8 ) @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(63,plain,
! [SV9: $i] :
( ( ~ ( class_LOrder_Ojoin__semilorder @ SV9 )
| ( class_Orderings_Oorder @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(64,plain,
! [SV10: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV10 )
| ( class_LOrder_Ojoin__semilorder @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(65,plain,
! [SV11: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV11 )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(66,plain,
! [SV12: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV12 )
| ( class_OrderedGroup_Olordered__ab__group__abs @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(67,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(68,plain,
! [SV2: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ ( v_xa @ SV2 ) ) @ t_a ) @ ( c_times @ SV2 @ ( c_HOL_Oabs @ ( v_h @ ( v_xa @ SV2 ) ) @ t_a ) @ t_a ) @ t_a ) )
= $true )
| ( ( ~ ( c_less @ c_0 @ SV2 @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(69,plain,
! [SV3: $i] :
( ( ( ~ ( c_less @ c_0 @ SV3 @ tc_nat ) )
= $true )
| ( ( SV3
= ( c_Suc @ ( c_minus @ SV3 @ c_1 @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(70,plain,
! [SV4: $i] :
( ( ( SV4 = c_0 )
= $true )
| ( ( c_less @ c_0 @ SV4 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(71,plain,
! [SV5: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV5 ) )
= $true )
| ( ( ( c_HOL_Oabs @ c_0 @ SV5 )
= c_0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(72,plain,
! [SV6: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV6 ) )
= $true )
| ( ( ! [SY17: $i] : ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ SY17 @ SV6 ) @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(73,plain,
! [SV7: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV7 ) )
= $true )
| ( ( ! [SY18: $i,SY19: $i] :
( ~ ( c_less @ SY18 @ SY19 @ SV7 )
| ( c_lessequals @ SY18 @ SY19 @ SV7 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(74,plain,
! [SV8: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV8 ) )
= $true )
| ( ( ! [SY20: $i] :
( ~ ( c_lessequals @ c_0 @ SY20 @ SV8 )
| ! [SY21: $i] :
( ~ ( c_lessequals @ c_0 @ SY21 @ SV8 )
| ( c_lessequals @ c_0 @ ( c_times @ SY21 @ SY20 @ SV8 ) @ SV8 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(75,plain,
! [SV9: $i] :
( ( ( ~ ( class_LOrder_Ojoin__semilorder @ SV9 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(76,plain,
! [SV10: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV10 ) )
= $true )
| ( ( class_LOrder_Ojoin__semilorder @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(77,plain,
! [SV11: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV11 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(78,plain,
! [SV12: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV12 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(79,plain,
! [SV2: $i] :
( ( ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ ( v_xa @ SV2 ) ) @ t_a ) @ ( c_times @ SV2 @ ( c_HOL_Oabs @ ( v_h @ ( v_xa @ SV2 ) ) @ t_a ) @ t_a ) @ t_a )
= $false )
| ( ( ~ ( c_less @ c_0 @ SV2 @ t_a ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(80,plain,
! [SV3: $i] :
( ( ( c_less @ c_0 @ SV3 @ tc_nat )
= $false )
| ( ( SV3
= ( c_Suc @ ( c_minus @ SV3 @ c_1 @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(81,plain,
! [SV5: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV5 )
= $false )
| ( ( ( c_HOL_Oabs @ c_0 @ SV5 )
= c_0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(82,plain,
! [SV6: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV6 )
= $false )
| ( ( ! [SY17: $i] : ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ SY17 @ SV6 ) @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(83,plain,
! [SV7: $i] :
( ( ( class_Orderings_Oorder @ SV7 )
= $false )
| ( ( ! [SY18: $i,SY19: $i] :
( ~ ( c_less @ SY18 @ SY19 @ SV7 )
| ( c_lessequals @ SY18 @ SY19 @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(84,plain,
! [SV8: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV8 )
= $false )
| ( ( ! [SY20: $i] :
( ~ ( c_lessequals @ c_0 @ SY20 @ SV8 )
| ! [SY21: $i] :
( ~ ( c_lessequals @ c_0 @ SY21 @ SV8 )
| ( c_lessequals @ c_0 @ ( c_times @ SY21 @ SY20 @ SV8 ) @ SV8 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(85,plain,
! [SV9: $i] :
( ( ( class_LOrder_Ojoin__semilorder @ SV9 )
= $false )
| ( ( class_Orderings_Oorder @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(86,plain,
! [SV10: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV10 )
= $false )
| ( ( class_LOrder_Ojoin__semilorder @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(87,plain,
! [SV11: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV11 )
= $false )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(88,plain,
! [SV12: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV12 )
= $false )
| ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(89,plain,
! [SV2: $i] :
( ( ( c_less @ c_0 @ SV2 @ t_a )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ ( v_xa @ SV2 ) ) @ t_a ) @ ( c_times @ SV2 @ ( c_HOL_Oabs @ ( v_h @ ( v_xa @ SV2 ) ) @ t_a ) @ t_a ) @ t_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(90,plain,
! [SV6: $i,SV13: $i] :
( ( ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ SV13 @ SV6 ) @ SV6 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(91,plain,
! [SV7: $i,SV14: $i] :
( ( ( ! [SY22: $i] :
( ~ ( c_less @ SV14 @ SY22 @ SV7 )
| ( c_lessequals @ SV14 @ SY22 @ SV7 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(92,plain,
! [SV8: $i,SV15: $i] :
( ( ( ~ ( c_lessequals @ c_0 @ SV15 @ SV8 )
| ! [SY23: $i] :
( ~ ( c_lessequals @ c_0 @ SY23 @ SV8 )
| ( c_lessequals @ c_0 @ ( c_times @ SY23 @ SV15 @ SV8 ) @ SV8 ) ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(93,plain,
! [SV7: $i,SV16: $i,SV14: $i] :
( ( ( ~ ( c_less @ SV14 @ SV16 @ SV7 )
| ( c_lessequals @ SV14 @ SV16 @ SV7 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(94,plain,
! [SV8: $i,SV15: $i] :
( ( ( ~ ( c_lessequals @ c_0 @ SV15 @ SV8 ) )
= $true )
| ( ( ! [SY23: $i] :
( ~ ( c_lessequals @ c_0 @ SY23 @ SV8 )
| ( c_lessequals @ c_0 @ ( c_times @ SY23 @ SV15 @ SV8 ) @ SV8 ) ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(95,plain,
! [SV7: $i,SV16: $i,SV14: $i] :
( ( ( ~ ( c_less @ SV14 @ SV16 @ SV7 ) )
= $true )
| ( ( c_lessequals @ SV14 @ SV16 @ SV7 )
= $true )
| ( ( class_Orderings_Oorder @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(96,plain,
! [SV8: $i,SV15: $i] :
( ( ( c_lessequals @ c_0 @ SV15 @ SV8 )
= $false )
| ( ( ! [SY23: $i] :
( ~ ( c_lessequals @ c_0 @ SY23 @ SV8 )
| ( c_lessequals @ c_0 @ ( c_times @ SY23 @ SV15 @ SV8 ) @ SV8 ) ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(97,plain,
! [SV7: $i,SV16: $i,SV14: $i] :
( ( ( c_less @ SV14 @ SV16 @ SV7 )
= $false )
| ( ( c_lessequals @ SV14 @ SV16 @ SV7 )
= $true )
| ( ( class_Orderings_Oorder @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(98,plain,
! [SV15: $i,SV8: $i,SV17: $i] :
( ( ( ~ ( c_lessequals @ c_0 @ SV17 @ SV8 )
| ( c_lessequals @ c_0 @ ( c_times @ SV17 @ SV15 @ SV8 ) @ SV8 ) )
= $true )
| ( ( c_lessequals @ c_0 @ SV15 @ SV8 )
= $false )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(99,plain,
! [SV15: $i,SV8: $i,SV17: $i] :
( ( ( ~ ( c_lessequals @ c_0 @ SV17 @ SV8 ) )
= $true )
| ( ( c_lessequals @ c_0 @ ( c_times @ SV17 @ SV15 @ SV8 ) @ SV8 )
= $true )
| ( ( c_lessequals @ c_0 @ SV15 @ SV8 )
= $false )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(100,plain,
! [SV15: $i,SV8: $i,SV17: $i] :
( ( ( c_lessequals @ c_0 @ SV17 @ SV8 )
= $false )
| ( ( c_lessequals @ c_0 @ ( c_times @ SV17 @ SV15 @ SV8 ) @ SV8 )
= $true )
| ( ( c_lessequals @ c_0 @ SV15 @ SV8 )
= $false )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(101,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[39,100,97,90,89,88,87,86,85,81,80,70,67,55,43,40]) ).
thf(102,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : ANA019-2 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n014.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 8 02:58:06 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.35
% 0.12/0.35 No.of.Axioms: 15
% 0.12/0.35
% 0.12/0.35 Length.of.Defs: 0
% 0.12/0.35
% 0.12/0.35 Contains.Choice.Funs: false
% 0.12/0.35 (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)....
% 0.18/0.42
% 0.18/0.42 ********************************
% 0.18/0.42 * All subproblems solved! *
% 0.18/0.42 ********************************
% 0.18/0.42 % SZS status Unsatisfiable for /export/starexec/sandbox/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:101,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.18/0.42
% 0.18/0.42 %**** Beginning of derivation protocol ****
% 0.18/0.42 % SZS output start CNFRefutation
% See solution above
% 0.18/0.42
% 0.18/0.42 %**** End of derivation protocol ****
% 0.18/0.42 %**** no. of clauses in derivation: 102 ****
% 0.18/0.42 %**** clause counter: 101 ****
% 0.18/0.42
% 0.18/0.42 % SZS status Unsatisfiable for /export/starexec/sandbox/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:101,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------