%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ANA037-2 : TPTP v9.3.1. Released v3.2.0.
% 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 : n010.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 10:09:37 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.24s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 73 ( 47 unt; 0 typ; 0 def)
% Number of atoms : 363 ( 93 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 718 ( 87 ~; 104 |; 0 &; 527 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 7 con; 0-3 aty)
% Number of variables : 146 ( 0 ^; 146 !; 0 ?; 146 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_0,type,
c_0: $i ).
thf(tp_c_HOL_Oabs,type,
c_HOL_Oabs: $i > $i > $i ).
thf(tp_c_Orderings_Omax,type,
c_Orderings_Omax: $i > $i > $i > $i ).
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_Orderings_Olinorder,type,
class_Orderings_Olinorder: $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__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_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_xa,type,
v_xa: $i ).
thf(1,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Orderings_Oorder @ T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).
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_Orderings_Olinorder @ T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
thf(4,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ c_0 @ V_c @ T_a )
| ( c_lessequals @ ( c_times @ V_a @ V_c @ T_a ) @ ( c_times @ V_b @ V_c @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0) ).
thf(5,axiom,
! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
thf(6,axiom,
! [T_b: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_b )
| ( c_lessequals @ V_x @ ( c_Orderings_Omax @ V_x @ V_y @ T_b ) @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Ole__maxI1_0) ).
thf(7,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(8,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[7]) ).
thf(9,negated_conjecture,
class_Ring__and__Field_Oordered__idom @ t_b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
thf(10,negated_conjecture,
~ ( c_lessequals @ ( c_HOL_Oabs @ ( v_a @ v_xa ) @ t_b ) @ ( c_times @ ( c_Orderings_Omax @ v_c @ v_ca @ t_b ) @ ( v_f @ v_xa ) @ t_b ) @ t_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_8) ).
thf(11,negated_conjecture,
c_lessequals @ ( c_HOL_Oabs @ ( v_a @ v_xa ) @ t_b ) @ ( c_times @ v_c @ ( v_f @ v_xa ) @ t_b ) @ t_b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(12,negated_conjecture,
c_lessequals @ c_0 @ ( v_f @ v_xa ) @ t_b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(13,plain,
$false = $false,
inference(unfold_def,[status(thm)],[8]) ).
thf(14,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(15,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(16,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Orderings_Olinorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(17,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ c_0 @ V_c @ T_a )
| ( c_lessequals @ ( c_times @ V_a @ V_c @ T_a ) @ ( c_times @ V_b @ V_c @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(18,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(19,plain,
( ( ! [T_b: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_b )
| ( c_lessequals @ V_x @ ( c_Orderings_Omax @ V_x @ V_y @ T_b ) @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(20,plain,
( ( class_Ring__and__Field_Oordered__idom @ t_b )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(21,plain,
( ( ~ ( c_lessequals @ ( c_HOL_Oabs @ ( v_a @ v_xa ) @ t_b ) @ ( c_times @ ( c_Orderings_Omax @ v_c @ v_ca @ t_b ) @ ( v_f @ v_xa ) @ t_b ) @ t_b ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(22,plain,
( ( c_lessequals @ ( c_HOL_Oabs @ ( v_a @ v_xa ) @ t_b ) @ ( c_times @ v_c @ ( v_f @ v_xa ) @ t_b ) @ t_b )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(23,plain,
( ( c_lessequals @ c_0 @ ( v_f @ v_xa ) @ t_b )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(24,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[13]) ).
thf(25,plain,
( ( c_lessequals @ c_0 @ ( v_f @ v_xa ) @ t_b )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(26,plain,
( ( c_lessequals @ ( c_HOL_Oabs @ ( v_a @ v_xa ) @ t_b ) @ ( c_times @ v_c @ ( v_f @ v_xa ) @ t_b ) @ t_b )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(27,plain,
( ( ~ ( c_lessequals @ ( c_HOL_Oabs @ ( v_a @ v_xa ) @ t_b ) @ ( c_times @ ( c_Orderings_Omax @ v_c @ v_ca @ t_b ) @ ( v_f @ v_xa ) @ t_b ) @ t_b ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(28,plain,
( ( class_Ring__and__Field_Oordered__idom @ t_b )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(29,plain,
( ( ! [T_b: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_b )
| ( c_lessequals @ V_x @ ( c_Orderings_Omax @ V_x @ V_y @ T_b ) @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(30,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(31,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ c_0 @ V_c @ T_a )
| ( c_lessequals @ ( c_times @ V_a @ V_c @ T_a ) @ ( c_times @ V_b @ V_c @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(32,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Orderings_Olinorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(33,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(34,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(35,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[24]) ).
thf(36,plain,
( ( c_lessequals @ ( c_HOL_Oabs @ ( v_a @ v_xa ) @ t_b ) @ ( c_times @ ( c_Orderings_Omax @ v_c @ v_ca @ t_b ) @ ( v_f @ v_xa ) @ t_b ) @ t_b )
= $false ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(37,plain,
! [SV1: $i] :
( ( ! [SY14: $i,SY15: $i] :
( ~ ( class_Orderings_Olinorder @ SV1 )
| ( c_lessequals @ SY14 @ ( c_Orderings_Omax @ SY14 @ SY15 @ SV1 ) @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(38,plain,
! [SV2: $i] :
( ( ! [SY16: $i,SY17: $i,SY18: $i] :
( ~ ( class_Orderings_Oorder @ SV2 )
| ~ ( c_lessequals @ SY16 @ SY17 @ SV2 )
| ~ ( c_lessequals @ SY18 @ SY16 @ SV2 )
| ( c_lessequals @ SY18 @ SY17 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(39,plain,
! [SV3: $i] :
( ( ! [SY19: $i,SY20: $i,SY21: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ SV3 )
| ~ ( c_lessequals @ SY19 @ SY20 @ SV3 )
| ~ ( c_lessequals @ c_0 @ SY21 @ SV3 )
| ( c_lessequals @ ( c_times @ SY19 @ SY21 @ SV3 ) @ ( c_times @ SY20 @ SY21 @ SV3 ) @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(40,plain,
! [SV4: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV4 )
| ( class_Orderings_Olinorder @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(41,plain,
! [SV5: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV5 )
| ( class_Ring__and__Field_Opordered__semiring @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(42,plain,
! [SV6: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV6 )
| ( class_Orderings_Oorder @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(43,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(44,plain,
! [SV7: $i,SV1: $i] :
( ( ! [SY22: $i] :
( ~ ( class_Orderings_Olinorder @ SV1 )
| ( c_lessequals @ SV7 @ ( c_Orderings_Omax @ SV7 @ SY22 @ SV1 ) @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(45,plain,
! [SV8: $i,SV2: $i] :
( ( ! [SY23: $i,SY24: $i] :
( ~ ( class_Orderings_Oorder @ SV2 )
| ~ ( c_lessequals @ SV8 @ SY23 @ SV2 )
| ~ ( c_lessequals @ SY24 @ SV8 @ SV2 )
| ( c_lessequals @ SY24 @ SY23 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(46,plain,
! [SV9: $i,SV3: $i] :
( ( ! [SY25: $i,SY26: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ SV3 )
| ~ ( c_lessequals @ SV9 @ SY25 @ SV3 )
| ~ ( c_lessequals @ c_0 @ SY26 @ SV3 )
| ( c_lessequals @ ( c_times @ SV9 @ SY26 @ SV3 ) @ ( c_times @ SY25 @ SY26 @ SV3 ) @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(47,plain,
! [SV4: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV4 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(48,plain,
! [SV5: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV5 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(49,plain,
! [SV6: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV6 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(50,plain,
! [SV10: $i,SV7: $i,SV1: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV1 )
| ( c_lessequals @ SV7 @ ( c_Orderings_Omax @ SV7 @ SV10 @ SV1 ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(51,plain,
! [SV11: $i,SV8: $i,SV2: $i] :
( ( ! [SY27: $i] :
( ~ ( class_Orderings_Oorder @ SV2 )
| ~ ( c_lessequals @ SV8 @ SV11 @ SV2 )
| ~ ( c_lessequals @ SY27 @ SV8 @ SV2 )
| ( c_lessequals @ SY27 @ SV11 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(52,plain,
! [SV12: $i,SV9: $i,SV3: $i] :
( ( ! [SY28: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ SV3 )
| ~ ( c_lessequals @ SV9 @ SV12 @ SV3 )
| ~ ( c_lessequals @ c_0 @ SY28 @ SV3 )
| ( c_lessequals @ ( c_times @ SV9 @ SY28 @ SV3 ) @ ( c_times @ SV12 @ SY28 @ SV3 ) @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(53,plain,
! [SV4: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV4 )
= $false )
| ( ( class_Orderings_Olinorder @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(54,plain,
! [SV5: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV5 )
= $false )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(55,plain,
! [SV6: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV6 )
= $false )
| ( ( class_Orderings_Oorder @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(56,plain,
! [SV10: $i,SV7: $i,SV1: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV1 ) )
= $true )
| ( ( c_lessequals @ SV7 @ ( c_Orderings_Omax @ SV7 @ SV10 @ SV1 ) @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(57,plain,
! [SV13: $i,SV11: $i,SV8: $i,SV2: $i] :
( ( ~ ( class_Orderings_Oorder @ SV2 )
| ~ ( c_lessequals @ SV8 @ SV11 @ SV2 )
| ~ ( c_lessequals @ SV13 @ SV8 @ SV2 )
| ( c_lessequals @ SV13 @ SV11 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(58,plain,
! [SV14: $i,SV12: $i,SV9: $i,SV3: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV3 )
| ~ ( c_lessequals @ SV9 @ SV12 @ SV3 )
| ~ ( c_lessequals @ c_0 @ SV14 @ SV3 )
| ( c_lessequals @ ( c_times @ SV9 @ SV14 @ SV3 ) @ ( c_times @ SV12 @ SV14 @ SV3 ) @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(59,plain,
! [SV10: $i,SV7: $i,SV1: $i] :
( ( ( class_Orderings_Olinorder @ SV1 )
= $false )
| ( ( c_lessequals @ SV7 @ ( c_Orderings_Omax @ SV7 @ SV10 @ SV1 ) @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(60,plain,
! [SV13: $i,SV11: $i,SV8: $i,SV2: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV2 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV8 @ SV11 @ SV2 )
| ~ ( c_lessequals @ SV13 @ SV8 @ SV2 )
| ( c_lessequals @ SV13 @ SV11 @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(61,plain,
! [SV14: $i,SV12: $i,SV9: $i,SV3: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV3 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV9 @ SV12 @ SV3 )
| ~ ( c_lessequals @ c_0 @ SV14 @ SV3 )
| ( c_lessequals @ ( c_times @ SV9 @ SV14 @ SV3 ) @ ( c_times @ SV12 @ SV14 @ SV3 ) @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(62,plain,
! [SV13: $i,SV11: $i,SV8: $i,SV2: $i] :
( ( ( class_Orderings_Oorder @ SV2 )
= $false )
| ( ( ~ ( c_lessequals @ SV8 @ SV11 @ SV2 )
| ~ ( c_lessequals @ SV13 @ SV8 @ SV2 )
| ( c_lessequals @ SV13 @ SV11 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(63,plain,
! [SV14: $i,SV12: $i,SV9: $i,SV3: $i] :
( ( ( class_Ring__and__Field_Opordered__semiring @ SV3 )
= $false )
| ( ( ~ ( c_lessequals @ SV9 @ SV12 @ SV3 )
| ~ ( c_lessequals @ c_0 @ SV14 @ SV3 )
| ( c_lessequals @ ( c_times @ SV9 @ SV14 @ SV3 ) @ ( c_times @ SV12 @ SV14 @ SV3 ) @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(64,plain,
! [SV13: $i,SV2: $i,SV11: $i,SV8: $i] :
( ( ( ~ ( c_lessequals @ SV8 @ SV11 @ SV2 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV13 @ SV8 @ SV2 )
| ( c_lessequals @ SV13 @ SV11 @ SV2 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(65,plain,
! [SV14: $i,SV3: $i,SV12: $i,SV9: $i] :
( ( ( ~ ( c_lessequals @ SV9 @ SV12 @ SV3 ) )
= $true )
| ( ( ~ ( c_lessequals @ c_0 @ SV14 @ SV3 )
| ( c_lessequals @ ( c_times @ SV9 @ SV14 @ SV3 ) @ ( c_times @ SV12 @ SV14 @ SV3 ) @ SV3 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(66,plain,
! [SV13: $i,SV2: $i,SV11: $i,SV8: $i] :
( ( ( c_lessequals @ SV8 @ SV11 @ SV2 )
= $false )
| ( ( ~ ( c_lessequals @ SV13 @ SV8 @ SV2 )
| ( c_lessequals @ SV13 @ SV11 @ SV2 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(67,plain,
! [SV14: $i,SV3: $i,SV12: $i,SV9: $i] :
( ( ( c_lessequals @ SV9 @ SV12 @ SV3 )
= $false )
| ( ( ~ ( c_lessequals @ c_0 @ SV14 @ SV3 )
| ( c_lessequals @ ( c_times @ SV9 @ SV14 @ SV3 ) @ ( c_times @ SV12 @ SV14 @ SV3 ) @ SV3 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(68,plain,
! [SV11: $i,SV2: $i,SV8: $i,SV13: $i] :
( ( ( ~ ( c_lessequals @ SV13 @ SV8 @ SV2 ) )
= $true )
| ( ( c_lessequals @ SV13 @ SV11 @ SV2 )
= $true )
| ( ( c_lessequals @ SV8 @ SV11 @ SV2 )
= $false )
| ( ( class_Orderings_Oorder @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(69,plain,
! [SV12: $i,SV9: $i,SV3: $i,SV14: $i] :
( ( ( ~ ( c_lessequals @ c_0 @ SV14 @ SV3 ) )
= $true )
| ( ( c_lessequals @ ( c_times @ SV9 @ SV14 @ SV3 ) @ ( c_times @ SV12 @ SV14 @ SV3 ) @ SV3 )
= $true )
| ( ( c_lessequals @ SV9 @ SV12 @ SV3 )
= $false )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[67]) ).
thf(70,plain,
! [SV11: $i,SV2: $i,SV8: $i,SV13: $i] :
( ( ( c_lessequals @ SV13 @ SV8 @ SV2 )
= $false )
| ( ( c_lessequals @ SV13 @ SV11 @ SV2 )
= $true )
| ( ( c_lessequals @ SV8 @ SV11 @ SV2 )
= $false )
| ( ( class_Orderings_Oorder @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(71,plain,
! [SV12: $i,SV9: $i,SV3: $i,SV14: $i] :
( ( ( c_lessequals @ c_0 @ SV14 @ SV3 )
= $false )
| ( ( c_lessequals @ ( c_times @ SV9 @ SV14 @ SV3 ) @ ( c_times @ SV12 @ SV14 @ SV3 ) @ SV3 )
= $true )
| ( ( c_lessequals @ SV9 @ SV12 @ SV3 )
= $false )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(72,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[25,71,70,59,55,54,53,43,36,28,26]) ).
thf(73,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA037-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.19 % Computer : n010.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Oct 6 18:18:10 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.24
% 0.09/0.24 No.of.Axioms: 10
% 0.09/0.24
% 0.09/0.24 Length.of.Defs: 0
% 0.09/0.24
% 0.09/0.24 Contains.Choice.Funs: false
% 0.09/0.24 .
% 0.09/0.24
% 0.09/0.24 ********************************
% 0.09/0.24 * All subproblems solved! *
% 0.09/0.24 ********************************
% 0.09/0.24 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:10,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:72,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.24
% 0.09/0.24 %**** Beginning of derivation protocol ****
% 0.09/0.24 % SZS output start CNFRefutation
% See solution above
% 0.09/0.24
% 0.09/0.24 %**** End of derivation protocol ****
% 0.09/0.24 %**** no. of clauses in derivation: 73 ****
% 0.09/0.24 %**** clause counter: 72 ****
% 0.09/0.24
% 0.09/0.24 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:10,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:72,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------