%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA026-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n001.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 : Sun Sep 27 06:50:19 AM UTC 2026
% Result : Unsatisfiable 167.42s 50.43s
% Output : Refutation 153.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 31
% Syntax : Number of formulae : 336 ( 69 unt; 0 typ; 0 def)
% Number of atoms : 995 ( 353 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 4246 ( 613 ~; 523 |; 0 &;3110 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 usr; 5 con; 0-3 aty)
% Number of variables : 695 ( 0 ^; 695 !; 0 ?; 695 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(v_g_decl,type,
v_g: $i > $i ).
thf(v_k_decl,type,
v_k: $i > $i ).
thf(t_b_decl,type,
t_b: $i ).
thf(c_Orderings_Omax_decl,type,
c_Orderings_Omax: $i > $i > $i > $i ).
thf(c_minus_decl,type,
c_minus: $i > $i > $i > $i ).
thf(v_f_decl,type,
v_f: $i > $i ).
thf(v_x_decl,type,
v_x: $i ).
thf(c_0_decl,type,
c_0: $i ).
thf(c_HOL_Oabs_decl,type,
c_HOL_Oabs: $i > $i > $i ).
thf(class_Ring__and__Field_Oordered__idom_decl,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(class_LOrder_Ojoin__semilorder_decl,type,
class_LOrder_Ojoin__semilorder: $i > $o ).
thf(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__abs_decl,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__group__add_decl,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le_decl,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
thf(class_OrderedGroup_Oab__group__add_decl,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(c_plus_decl,type,
c_plus: $i > $i > $i > $i ).
thf(c_less_decl,type,
c_less: $i > $i > $i > $o ).
thf(class_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__add_decl,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(c_uminus_decl,type,
c_uminus: $i > $i > $i ).
thf(14,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
thf(58,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(59,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(cnf,[status(esa)],[58]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_6) ).
thf(40,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(41,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(cnf,[status(esa)],[40]) ).
thf(121,plain,
! [B: $i,A: $i] :
( ( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
!= ( B @ class_OrderedGroup_Olordered__ab__group__abs ) )
| ( B @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ $true
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(paramod_ordered,[status(thm)],[59,41]) ).
thf(122,plain,
! [B: $i,A: $i] :
( ( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
!= ( B @ class_OrderedGroup_Olordered__ab__group__abs ) )
| ( B @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(simp,[status(thm)],[121]) ).
thf(123,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(pattern_uni,[status(thm)],[122:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(31,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Oabs ) )
= ( A @ ( B @ c_uminus ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonpos_0) ).
thf(99,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Oabs ) )
= ( A @ ( B @ c_uminus ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_minus ) ) )
= ( A @ ( A @ ( C @ c_uminus ) @ ( B @ c_plus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oab__group__add__class_Odiff__minus_0) ).
thf(67,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_minus ) ) )
= ( A @ ( A @ ( C @ c_uminus ) @ ( B @ c_plus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(68,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_minus ) ) )
= ( A @ ( A @ ( C @ c_uminus ) @ ( B @ c_plus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(cnf,[status(esa)],[67]) ).
thf(69,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ class_OrderedGroup_Oab__group__add )
| ( ( A @ ( A @ ( C @ c_uminus ) @ ( B @ c_plus ) ) )
= ( A @ ( C @ ( B @ c_minus ) ) ) ) ),
inference(lifteq,[status(thm)],[68]) ).
thf(100,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Oabs ) )
= ( A @ ( B @ c_uminus ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(cnf,[status(esa)],[99]) ).
thf(101,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs )
| ( ( A @ ( B @ c_uminus ) )
= ( A @ ( B @ c_HOL_Oabs ) ) ) ),
inference(lifteq,[status(thm)],[100]) ).
thf(3,negated_conjecture,
t_b @ class_Ring__and__Field_Oordered__idom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
thf(34,plain,
t_b @ class_Ring__and__Field_Oordered__idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
thf(60,plain,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(61,plain,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(cnf,[status(esa)],[60]) ).
thf(247,plain,
! [A: $i] :
( ( ( t_b @ class_Ring__and__Field_Oordered__idom )
!= ( A @ class_Ring__and__Field_Oordered__idom ) )
| ( A @ class_Orderings_Olinorder )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,61]) ).
thf(248,plain,
! [A: $i] :
( ( ( t_b @ class_Ring__and__Field_Oordered__idom )
!= ( A @ class_Ring__and__Field_Oordered__idom ) )
| ( A @ class_Orderings_Olinorder ) ),
inference(simp,[status(thm)],[247]) ).
thf(249,plain,
t_b @ class_Orderings_Olinorder,
inference(pattern_uni,[status(thm)],[248:[bind(A,$thf( t_b ))]]) ).
thf(26,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_minus ) ) @ c_plus ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_plus ) ) @ c_minus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__3_0) ).
thf(86,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_minus ) ) @ c_plus ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_plus ) ) @ c_minus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(87,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_minus ) ) @ c_plus ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_plus ) ) @ c_minus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(cnf,[status(esa)],[86]) ).
thf(88,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ class_OrderedGroup_Oab__group__add )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_minus ) ) @ c_plus ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_plus ) ) @ c_minus ) ) ) ) ),
inference(lifteq,[status(thm)],[87]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).
thf(42,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(43,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(cnf,[status(esa)],[42]) ).
thf(118,plain,
! [A: $i] :
( ( ( t_b @ class_Ring__and__Field_Oordered__idom )
!= ( A @ class_Ring__and__Field_Oordered__idom ) )
| ( A @ class_OrderedGroup_Oab__group__add )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,43]) ).
thf(119,plain,
! [A: $i] :
( ( ( t_b @ class_Ring__and__Field_Oordered__idom )
!= ( A @ class_Ring__and__Field_Oordered__idom ) )
| ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(simp,[status(thm)],[118]) ).
thf(120,plain,
t_b @ class_OrderedGroup_Oab__group__add,
inference(pattern_uni,[status(thm)],[119:[bind(A,$thf( t_b ))]]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_plus ) ) @ c_minus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__10_1) ).
thf(44,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_plus ) ) @ c_minus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(45,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_plus ) ) @ c_minus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(cnf,[status(esa)],[44]) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ class_OrderedGroup_Oab__group__add )
| ( ( A @ ( C @ ( A @ ( C @ ( B @ c_plus ) ) @ c_minus ) ) )
= B ) ),
inference(lifteq,[status(thm)],[45]) ).
thf(190,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_b @ class_OrderedGroup_Oab__group__add )
!= ( A @ class_OrderedGroup_Oab__group__add ) )
| ~ $true
| ( ( A @ ( C @ ( A @ ( C @ ( B @ c_plus ) ) @ c_minus ) ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[120,46]) ).
thf(191,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_b @ class_OrderedGroup_Oab__group__add )
!= ( A @ class_OrderedGroup_Oab__group__add ) )
| ( ( A @ ( C @ ( A @ ( C @ ( B @ c_plus ) ) @ c_minus ) ) )
= B ) ),
inference(simp,[status(thm)],[190]) ).
thf(192,plain,
! [B: $i,A: $i] :
( ( t_b @ ( B @ ( t_b @ ( B @ ( A @ c_plus ) ) @ c_minus ) ) )
= A ),
inference(pattern_uni,[status(thm)],[191:[bind(A,$thf( t_b ))]]) ).
thf(208,plain,
! [B: $i,A: $i] :
( ( t_b @ ( B @ ( t_b @ ( B @ ( A @ c_plus ) ) @ c_minus ) ) )
= A ),
inference(simp,[status(thm)],[192]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_minus ) ) @ ( B @ c_plus ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_plus ) ) @ c_minus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__2_0) ).
thf(49,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_minus ) ) @ ( B @ c_plus ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_plus ) ) @ c_minus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(50,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_minus ) ) @ ( B @ c_plus ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_plus ) ) @ c_minus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(cnf,[status(esa)],[49]) ).
thf(51,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ class_OrderedGroup_Oab__group__add )
| ( ( A @ ( A @ ( D @ ( C @ c_minus ) ) @ ( B @ c_plus ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_plus ) ) @ c_minus ) ) ) ) ),
inference(lifteq,[status(thm)],[50]) ).
thf(518,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_b @ class_OrderedGroup_Oab__group__add )
!= ( A @ class_OrderedGroup_Oab__group__add ) )
| ~ $true
| ( ( A @ ( A @ ( D @ ( C @ c_minus ) ) @ ( B @ c_plus ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_plus ) ) @ c_minus ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[120,51]) ).
thf(519,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_b @ class_OrderedGroup_Oab__group__add )
!= ( A @ class_OrderedGroup_Oab__group__add ) )
| ( ( A @ ( A @ ( D @ ( C @ c_minus ) ) @ ( B @ c_plus ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_plus ) ) @ c_minus ) ) ) ) ),
inference(simp,[status(thm)],[518]) ).
thf(520,plain,
! [C: $i,B: $i,A: $i] :
( ( t_b @ ( t_b @ ( C @ ( B @ c_minus ) ) @ ( A @ c_plus ) ) )
= ( t_b @ ( C @ ( t_b @ ( B @ ( A @ c_plus ) ) @ c_minus ) ) ) ),
inference(pattern_uni,[status(thm)],[519:[bind(A,$thf( t_b ))]]) ).
thf(540,plain,
! [C: $i,B: $i,A: $i] :
( ( t_b @ ( t_b @ ( C @ ( B @ c_minus ) ) @ ( A @ c_plus ) ) )
= ( t_b @ ( C @ ( t_b @ ( B @ ( A @ c_plus ) ) @ c_minus ) ) ) ),
inference(simp,[status(thm)],[520]) ).
thf(552,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( t_b @ ( t_b @ ( C @ ( B @ c_minus ) ) @ ( A @ c_plus ) ) )
!= ( t_b @ ( E @ ( D @ c_plus ) ) ) )
| ( ( t_b @ ( E @ ( t_b @ ( C @ ( t_b @ ( B @ ( A @ c_plus ) ) @ c_minus ) ) @ c_minus ) ) )
= D ) ),
inference(paramod_ordered,[status(thm)],[540,208]) ).
thf(553,plain,
! [C: $i,B: $i,A: $i] :
( ( t_b @ ( t_b @ ( C @ ( B @ c_minus ) ) @ ( t_b @ ( C @ ( t_b @ ( B @ ( A @ c_plus ) ) @ c_minus ) ) @ c_minus ) ) )
= A ),
inference(pattern_uni,[status(thm)],[552:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( A )),bind(E,$thf( t_b @ ( G @ ( F @ c_minus ) ) ))]]) ).
thf(564,plain,
! [C: $i,B: $i,A: $i] :
( ( t_b @ ( t_b @ ( C @ ( B @ c_minus ) ) @ ( t_b @ ( C @ ( t_b @ ( B @ ( A @ c_plus ) ) @ c_minus ) ) @ c_minus ) ) )
= A ),
inference(simp,[status(thm)],[553]) ).
thf(581,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( t_b @ ( B @ ( t_b @ ( B @ ( A @ c_plus ) ) @ c_minus ) ) )
!= ( t_b @ ( E @ ( t_b @ ( D @ ( C @ c_plus ) ) @ c_minus ) ) ) )
| ( ( t_b @ ( t_b @ ( E @ ( D @ c_minus ) ) @ ( A @ c_minus ) ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[208,564]) ).
thf(582,plain,
! [B: $i,A: $i] :
( ( t_b @ ( t_b @ ( B @ ( B @ c_minus ) ) @ ( A @ c_minus ) ) )
= A ),
inference(pattern_uni,[status(thm)],[581:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B )),bind(E,$thf( B ))]]) ).
thf(23,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( B @ ( D @ c_Orderings_Omax ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) ).
thf(79,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( B @ ( D @ c_Orderings_Omax ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(80,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( B @ ( D @ c_Orderings_Omax ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(cnf,[status(esa)],[79]) ).
thf(1457,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_b @ class_OrderedGroup_Oab__group__add )
!= ( A @ class_OrderedGroup_Oab__group__add ) )
| ~ $true
| ( ( A @ ( A @ ( C @ c_uminus ) @ ( B @ c_plus ) ) )
= ( A @ ( C @ ( B @ c_minus ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[120,69]) ).
thf(1458,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_b @ class_OrderedGroup_Oab__group__add )
!= ( A @ class_OrderedGroup_Oab__group__add ) )
| ( ( A @ ( A @ ( C @ c_uminus ) @ ( B @ c_plus ) ) )
= ( A @ ( C @ ( B @ c_minus ) ) ) ) ),
inference(simp,[status(thm)],[1457]) ).
thf(1459,plain,
! [B: $i,A: $i] :
( ( t_b @ ( t_b @ ( B @ c_uminus ) @ ( A @ c_plus ) ) )
= ( t_b @ ( B @ ( A @ c_minus ) ) ) ),
inference(pattern_uni,[status(thm)],[1458:[bind(A,$thf( t_b ))]]) ).
thf(1506,plain,
! [B: $i,A: $i] :
( ( t_b @ ( t_b @ ( B @ c_uminus ) @ ( A @ c_plus ) ) )
= ( t_b @ ( B @ ( A @ c_minus ) ) ) ),
inference(simp,[status(thm)],[1459]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).
thf(75,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(76,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(cnf,[status(esa)],[75]) ).
thf(392,plain,
! [A: $i] :
( ( ( t_b @ class_Ring__and__Field_Oordered__idom )
!= ( A @ class_Ring__and__Field_Oordered__idom ) )
| ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,76]) ).
thf(393,plain,
! [A: $i] :
( ( ( t_b @ class_Ring__and__Field_Oordered__idom )
!= ( A @ class_Ring__and__Field_Oordered__idom ) )
| ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(simp,[status(thm)],[392]) ).
thf(394,plain,
t_b @ class_OrderedGroup_Ocomm__monoid__add,
inference(pattern_uni,[status(thm)],[393:[bind(A,$thf( t_b ))]]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( c_0 @ c_plus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).
thf(62,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( c_0 @ c_plus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( c_0 @ c_plus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(cnf,[status(esa)],[62]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ( ( A @ ( B @ ( c_0 @ c_plus ) ) )
= B ) ),
inference(lifteq,[status(thm)],[63]) ).
thf(943,plain,
! [B: $i,A: $i] :
( ( ( t_b @ class_OrderedGroup_Ocomm__monoid__add )
!= ( A @ class_OrderedGroup_Ocomm__monoid__add ) )
| ~ $true
| ( ( A @ ( B @ ( c_0 @ c_plus ) ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[394,64]) ).
thf(944,plain,
! [B: $i,A: $i] :
( ( ( t_b @ class_OrderedGroup_Ocomm__monoid__add )
!= ( A @ class_OrderedGroup_Ocomm__monoid__add ) )
| ( ( A @ ( B @ ( c_0 @ c_plus ) ) )
= B ) ),
inference(simp,[status(thm)],[943]) ).
thf(945,plain,
! [A: $i] :
( ( t_b @ ( A @ ( c_0 @ c_plus ) ) )
= A ),
inference(pattern_uni,[status(thm)],[944:[bind(A,$thf( t_b ))]]) ).
thf(959,plain,
! [A: $i] :
( ( t_b @ ( A @ ( c_0 @ c_plus ) ) )
= A ),
inference(simp,[status(thm)],[945]) ).
thf(1538,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_b @ ( t_b @ ( B @ c_uminus ) @ ( A @ c_plus ) ) )
!= ( t_b @ ( C @ ( c_0 @ c_plus ) ) ) )
| ( ( t_b @ ( B @ ( A @ c_minus ) ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[1506,959]) ).
thf(1539,plain,
! [A: $i] :
( ( t_b @ ( A @ ( c_0 @ c_minus ) ) )
= ( t_b @ ( A @ c_uminus ) ) ),
inference(pattern_uni,[status(thm)],[1538:[bind(A,$thf( c_0 )),bind(B,$thf( D )),bind(C,$thf( t_b @ ( D @ c_uminus ) ))]]) ).
thf(1556,plain,
! [A: $i] :
( ( t_b @ ( A @ ( c_0 @ c_minus ) ) )
= ( t_b @ ( A @ c_uminus ) ) ),
inference(simp,[status(thm)],[1539]) ).
thf(643,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( t_b @ ( t_b @ ( B @ ( B @ c_minus ) ) @ ( A @ c_minus ) ) )
!= ( t_b @ ( t_b @ ( E @ ( D @ c_minus ) ) @ ( t_b @ ( E @ ( t_b @ ( D @ ( C @ c_plus ) ) @ c_minus ) ) @ c_minus ) ) ) )
| ( A = C ) ),
inference(paramod_ordered,[status(thm)],[582,564]) ).
thf(644,plain,
! [B: $i,A: $i] :
( ( t_b @ ( A @ ( t_b @ ( A @ ( B @ c_plus ) ) @ c_minus ) ) )
= B ),
inference(pattern_uni,[status(thm)],[643:[bind(A,$thf( t_b @ ( B @ ( t_b @ ( B @ ( I @ c_plus ) ) @ c_minus ) ) )),bind(B,$thf( B )),bind(C,$thf( I )),bind(D,$thf( B )),bind(E,$thf( B ))]]) ).
thf(657,plain,
! [B: $i,A: $i] :
( ( t_b @ ( A @ ( t_b @ ( A @ ( B @ c_plus ) ) @ c_minus ) ) )
= B ),
inference(simp,[status(thm)],[644]) ).
thf(977,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_b @ ( A @ ( c_0 @ c_plus ) ) )
!= ( t_b @ ( B @ ( C @ c_plus ) ) ) )
| ( ( t_b @ ( B @ ( A @ c_minus ) ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[959,657]) ).
thf(978,plain,
! [A: $i] :
( ( t_b @ ( A @ ( A @ c_minus ) ) )
= c_0 ),
inference(pattern_uni,[status(thm)],[977:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( c_0 ))]]) ).
thf(1003,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_b @ ( A @ ( A @ c_minus ) ) )
!= ( t_b @ ( C @ ( C @ c_minus ) ) ) )
| ( ( t_b @ ( c_0 @ ( B @ c_minus ) ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[978,582]) ).
thf(1004,plain,
! [A: $i] :
( ( t_b @ ( c_0 @ ( A @ c_minus ) ) )
= A ),
inference(pattern_uni,[status(thm)],[1003:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(1066,plain,
! [A: $i] :
( ( t_b @ ( c_0 @ ( A @ c_minus ) ) )
= A ),
inference(simp,[status(thm)],[1004]) ).
thf(1602,plain,
! [B: $i,A: $i] :
( ( ( t_b @ ( A @ ( c_0 @ c_minus ) ) )
!= ( t_b @ ( c_0 @ ( B @ c_minus ) ) ) )
| ( ( t_b @ ( A @ c_uminus ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[1556,1066]) ).
thf(1603,plain,
( ( t_b @ ( c_0 @ c_uminus ) )
= c_0 ),
inference(pattern_uni,[status(thm)],[1602:[bind(A,$thf( c_0 )),bind(B,$thf( c_0 ))]]) ).
thf(2,negated_conjecture,
~ ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( t_b @ ( v_x @ v_k @ ( v_x @ v_f @ c_minus ) ) @ c_Orderings_Omax ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(33,plain,
~ ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( t_b @ ( v_x @ v_k @ ( v_x @ v_f @ c_minus ) ) @ c_Orderings_Omax ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(35,plain,
~ ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( t_b @ ( v_x @ v_k @ ( v_x @ v_f @ c_minus ) ) @ c_Orderings_Omax ) ) @ c_lessequals ) ) ),
inference(polarity_switch,[status(thm)],[33]) ).
thf(220,plain,
! [B: $i,A: $i] :
( ( ( t_b @ ( B @ ( t_b @ ( B @ ( A @ c_plus ) ) @ c_minus ) ) )
!= ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) ) )
| ~ ( t_b @ ( t_b @ ( A @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( t_b @ ( v_x @ v_k @ ( v_x @ v_f @ c_minus ) ) @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[208,35]) ).
thf(229,plain,
! [B: $i,A: $i] :
( ( t_b != t_b )
| ( B
!= ( v_x @ v_g ) )
| ( ( t_b @ ( B @ ( A @ c_plus ) ) )
!= ( v_x @ v_f ) )
| ~ ( t_b @ ( t_b @ ( A @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( t_b @ ( v_x @ v_k @ ( v_x @ v_f @ c_minus ) ) @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[220]) ).
thf(235,plain,
! [A: $i] :
( ( ( t_b @ ( v_x @ v_g @ ( A @ c_plus ) ) )
!= ( v_x @ v_f ) )
| ~ ( t_b @ ( t_b @ ( A @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( t_b @ ( v_x @ v_k @ ( v_x @ v_f @ c_minus ) ) @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[229]) ).
thf(985,plain,
! [B: $i,A: $i] :
( ( ( t_b @ ( A @ ( c_0 @ c_plus ) ) )
!= ( t_b @ ( v_x @ v_g @ ( B @ c_plus ) ) ) )
| ( A
!= ( v_x @ v_f ) )
| ~ ( t_b @ ( t_b @ ( B @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( t_b @ ( v_x @ v_k @ ( v_x @ v_f @ c_minus ) ) @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[959,235]) ).
thf(986,plain,
( ( ( v_x @ v_f )
!= ( v_x @ v_g ) )
| ~ ( t_b @ ( t_b @ ( c_0 @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( t_b @ ( v_x @ v_k @ ( v_x @ v_f @ c_minus ) ) @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[985:[bind(A,$thf( v_x @ v_g )),bind(B,$thf( c_0 ))]]) ).
thf(1608,plain,
! [A: $i] :
( ( ( t_b @ ( A @ ( c_0 @ c_minus ) ) )
!= ( t_b @ ( v_x @ v_k @ ( v_x @ v_f @ c_minus ) ) ) )
| ( ( v_x @ v_f )
!= ( v_x @ v_g ) )
| ~ ( t_b @ ( t_b @ ( c_0 @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( t_b @ ( A @ c_uminus ) @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[1556,986]) ).
thf(1621,plain,
! [A: $i] :
( ( t_b != t_b )
| ( A
!= ( v_x @ v_k ) )
| ( ( v_x @ v_f )
!= c_0 )
| ( ( v_x @ v_f )
!= ( v_x @ v_g ) )
| ~ ( t_b @ ( t_b @ ( c_0 @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( t_b @ ( A @ c_uminus ) @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1608]) ).
thf(1640,plain,
( ( ( v_x @ v_f )
!= c_0 )
| ( ( v_x @ v_f )
!= ( v_x @ v_g ) )
| ~ ( t_b @ ( t_b @ ( c_0 @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( t_b @ ( v_x @ v_k @ c_uminus ) @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1621]) ).
thf(3585,plain,
( ( ( t_b @ ( v_x @ v_k @ c_uminus ) )
!= ( t_b @ ( c_0 @ c_uminus ) ) )
| ( ( v_x @ v_f )
!= c_0 )
| ( ( v_x @ v_f )
!= ( v_x @ v_g ) )
| ~ ( t_b @ ( t_b @ ( c_0 @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( c_0 @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[1603,1640]) ).
thf(3603,plain,
( ( t_b != t_b )
| ( ( v_x @ v_k )
!= c_0 )
| ( ( v_x @ v_f )
!= c_0 )
| ( ( v_x @ v_f )
!= ( v_x @ v_g ) )
| ~ ( t_b @ ( t_b @ ( c_0 @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( c_0 @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[3585]) ).
thf(3614,plain,
( ( ( v_x @ v_k )
!= c_0 )
| ( ( v_x @ v_f )
!= c_0 )
| ( ( v_x @ v_f )
!= ( v_x @ v_g ) )
| ~ ( t_b @ ( t_b @ ( c_0 @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( c_0 @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[3603]) ).
thf(4487,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ ( D @ c_Orderings_Omax ) ) @ c_lessequals ) ) )
!= ( t_b @ ( t_b @ ( c_0 @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( c_0 @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) )
| ( ( v_x @ v_k )
!= c_0 )
| ( ( v_x @ v_f )
!= c_0 )
| ( ( v_x @ v_f )
!= ( v_x @ v_g ) )
| ~ $true
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(paramod_ordered,[status(thm)],[80,3614]) ).
thf(4488,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ ( D @ c_Orderings_Omax ) ) @ c_lessequals ) ) )
!= ( t_b @ ( t_b @ ( c_0 @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( c_0 @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) )
| ( ( v_x @ v_k )
!= c_0 )
| ( ( v_x @ v_f )
!= c_0 )
| ( ( v_x @ v_f )
!= ( v_x @ v_g ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(simp,[status(thm)],[4487]) ).
thf(4489,plain,
( ( ( v_x @ v_k )
!= c_0 )
| ( ( v_x @ v_f )
!= c_0 )
| ( ( v_x @ v_f )
!= ( v_x @ v_g ) )
| ~ ( t_b @ ( t_b @ ( c_0 @ c_HOL_Oabs ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( t_b @ ( t_b @ ( c_0 @ c_HOL_Oabs ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( t_b @ class_Orderings_Olinorder ) ),
inference(pattern_uni,[status(thm)],[4488:[bind(A,$thf( t_b )),bind(B,$thf( c_0 )),bind(C,$thf( t_b @ ( c_0 @ c_HOL_Oabs ) )),bind(D,$thf( c_0 ))]]) ).
thf(4512,plain,
( ( ( v_x @ v_k )
!= c_0 )
| ( ( v_x @ v_f )
!= c_0 )
| ( ( v_x @ v_f )
!= ( v_x @ v_g ) )
| ~ ( t_b @ ( t_b @ ( c_0 @ c_HOL_Oabs ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( t_b @ class_Orderings_Olinorder ) ),
inference(simp,[status(thm)],[4489]) ).
thf(127,plain,
! [A: $i] :
( ( ( t_b @ class_Ring__and__Field_Oordered__idom )
!= ( A @ class_Ring__and__Field_Oordered__idom ) )
| ( A @ class_OrderedGroup_Olordered__ab__group__abs )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,59]) ).
thf(128,plain,
! [A: $i] :
( ( ( t_b @ class_Ring__and__Field_Oordered__idom )
!= ( A @ class_Ring__and__Field_Oordered__idom ) )
| ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(simp,[status(thm)],[127]) ).
thf(129,plain,
t_b @ class_OrderedGroup_Olordered__ab__group__abs,
inference(pattern_uni,[status(thm)],[128:[bind(A,$thf( t_b ))]]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_HOL_Oabs ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
thf(73,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_HOL_Oabs ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(74,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_HOL_Oabs ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(cnf,[status(esa)],[73]) ).
thf(1914,plain,
! [B: $i,A: $i] :
( ( ( t_b @ class_OrderedGroup_Olordered__ab__group__abs )
!= ( A @ class_OrderedGroup_Olordered__ab__group__abs ) )
| ( A @ ( A @ ( B @ c_HOL_Oabs ) @ ( c_0 @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[129,74]) ).
thf(1915,plain,
! [B: $i,A: $i] :
( ( ( t_b @ class_OrderedGroup_Olordered__ab__group__abs )
!= ( A @ class_OrderedGroup_Olordered__ab__group__abs ) )
| ( A @ ( A @ ( B @ c_HOL_Oabs ) @ ( c_0 @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1914]) ).
thf(1916,plain,
! [A: $i] : ( t_b @ ( t_b @ ( A @ c_HOL_Oabs ) @ ( c_0 @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[1915:[bind(A,$thf( t_b ))]]) ).
thf(1968,plain,
! [A: $i] : ( t_b @ ( t_b @ ( A @ c_HOL_Oabs ) @ ( c_0 @ c_lessequals ) ) ),
inference(simp,[status(thm)],[1916]) ).
thf(4696,plain,
( ( ( v_x @ v_k )
!= c_0 )
| ( ( v_x @ v_f )
!= c_0 )
| ( ( v_x @ v_f )
!= ( v_x @ v_g ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[4512,1968,249]) ).
thf(4697,plain,
( ( ( v_x @ v_k )
!= c_0 )
| ( ( v_x @ v_f )
!= c_0 )
| ( ( v_x @ v_f )
!= ( v_x @ v_g ) ) ),
inference(simp,[status(thm)],[4696]) ).
thf(1536,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_b @ ( t_b @ ( B @ c_uminus ) @ ( A @ c_plus ) ) )
!= ( t_b @ ( D @ ( C @ c_plus ) ) ) )
| ( ( t_b @ ( D @ ( t_b @ ( B @ ( A @ c_minus ) ) @ c_minus ) ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[1506,208]) ).
thf(1537,plain,
! [B: $i,A: $i] :
( ( t_b @ ( t_b @ ( B @ c_uminus ) @ ( t_b @ ( B @ ( A @ c_minus ) ) @ c_minus ) ) )
= A ),
inference(pattern_uni,[status(thm)],[1536:[bind(A,$thf( A )),bind(B,$thf( E )),bind(C,$thf( A )),bind(D,$thf( t_b @ ( E @ c_uminus ) ))]]) ).
thf(1555,plain,
! [B: $i,A: $i] :
( ( t_b @ ( t_b @ ( B @ c_uminus ) @ ( t_b @ ( B @ ( A @ c_minus ) ) @ c_minus ) ) )
= A ),
inference(simp,[status(thm)],[1537]) ).
thf(2199,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_b @ ( t_b @ ( B @ ( B @ c_minus ) ) @ ( A @ c_minus ) ) )
!= ( t_b @ ( D @ ( C @ c_minus ) ) ) )
| ( ( t_b @ ( t_b @ ( D @ c_uminus ) @ ( A @ c_minus ) ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[582,1555]) ).
thf(2200,plain,
! [B: $i,A: $i] :
( ( t_b @ ( t_b @ ( t_b @ ( B @ ( B @ c_minus ) ) @ c_uminus ) @ ( A @ c_minus ) ) )
= A ),
inference(pattern_uni,[status(thm)],[2199:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( A )),bind(D,$thf( t_b @ ( F @ ( F @ c_minus ) ) ))]]) ).
thf(2298,plain,
! [B: $i,A: $i] :
( ( t_b @ ( t_b @ ( t_b @ ( B @ ( B @ c_minus ) ) @ c_uminus ) @ ( A @ c_minus ) ) )
= A ),
inference(simp,[status(thm)],[2200]) ).
thf(2607,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_b @ ( t_b @ ( t_b @ ( B @ ( B @ c_minus ) ) @ c_uminus ) @ ( A @ c_minus ) ) )
!= ( t_b @ ( C @ ( t_b @ ( C @ ( D @ c_plus ) ) @ c_minus ) ) ) )
| ( A = D ) ),
inference(paramod_ordered,[status(thm)],[2298,657]) ).
thf(2608,plain,
! [B: $i,A: $i] :
( ( t_b @ ( t_b @ ( t_b @ ( B @ ( B @ c_minus ) ) @ c_uminus ) @ ( A @ c_plus ) ) )
= A ),
inference(pattern_uni,[status(thm)],[2607:[bind(A,$thf( t_b @ ( t_b @ ( t_b @ ( K @ ( K @ c_minus ) ) @ c_uminus ) @ ( E @ c_plus ) ) )),bind(B,$thf( K )),bind(C,$thf( t_b @ ( t_b @ ( K @ ( K @ c_minus ) ) @ c_uminus ) )),bind(D,$thf( E ))]]) ).
thf(2712,plain,
! [B: $i,A: $i] :
( ( t_b @ ( t_b @ ( t_b @ ( B @ ( B @ c_minus ) ) @ c_uminus ) @ ( A @ c_plus ) ) )
= A ),
inference(simp,[status(thm)],[2608]) ).
thf(2219,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_b @ ( A @ ( t_b @ ( A @ ( B @ c_plus ) ) @ c_minus ) ) )
!= ( t_b @ ( D @ ( C @ c_minus ) ) ) )
| ( ( t_b @ ( t_b @ ( D @ c_uminus ) @ ( B @ c_minus ) ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[657,1555]) ).
thf(2220,plain,
! [B: $i,A: $i] :
( ( t_b @ ( B @ ( A @ c_plus ) ) )
= ( t_b @ ( t_b @ ( B @ c_uminus ) @ ( A @ c_minus ) ) ) ),
inference(pattern_uni,[status(thm)],[2219:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( t_b @ ( F @ ( E @ c_plus ) ) )),bind(D,$thf( F ))]]) ).
thf(2303,plain,
! [B: $i,A: $i] :
( ( t_b @ ( B @ ( A @ c_plus ) ) )
= ( t_b @ ( t_b @ ( B @ c_uminus ) @ ( A @ c_minus ) ) ) ),
inference(simp,[status(thm)],[2220]) ).
thf(4130,plain,
! [B: $i,A: $i] :
( ( t_b @ ( t_b @ ( t_b @ ( t_b @ ( B @ ( B @ c_minus ) ) @ c_uminus ) @ c_uminus ) @ ( A @ c_minus ) ) )
= A ),
inference(rewrite,[status(thm)],[2712,2303]) ).
thf(4214,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_b @ ( A @ ( c_0 @ c_minus ) ) )
!= ( t_b @ ( C @ ( C @ c_minus ) ) ) )
| ( ( t_b @ ( t_b @ ( t_b @ ( t_b @ ( A @ c_uminus ) @ c_uminus ) @ c_uminus ) @ ( B @ c_minus ) ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[1556,4130]) ).
thf(4215,plain,
! [A: $i] :
( ( t_b @ ( t_b @ ( t_b @ ( t_b @ ( c_0 @ c_uminus ) @ c_uminus ) @ c_uminus ) @ ( A @ c_minus ) ) )
= A ),
inference(pattern_uni,[status(thm)],[4214:[bind(A,$thf( c_0 )),bind(B,$thf( B )),bind(C,$thf( c_0 ))]]) ).
thf(4351,plain,
! [A: $i] :
( ( t_b @ ( t_b @ ( t_b @ ( t_b @ ( c_0 @ c_uminus ) @ c_uminus ) @ c_uminus ) @ ( A @ c_minus ) ) )
= A ),
inference(simp,[status(thm)],[4215]) ).
thf(2252,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_b @ ( A @ ( A @ c_minus ) ) )
!= ( t_b @ ( C @ ( B @ c_minus ) ) ) )
| ( ( t_b @ ( t_b @ ( C @ c_uminus ) @ ( c_0 @ c_minus ) ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[978,1555]) ).
thf(2253,plain,
! [A: $i] :
( ( t_b @ ( t_b @ ( A @ c_uminus ) @ ( c_0 @ c_minus ) ) )
= A ),
inference(pattern_uni,[status(thm)],[2252:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(2346,plain,
! [A: $i] :
( ( t_b @ ( t_b @ ( A @ c_uminus ) @ c_uminus ) )
= A ),
inference(rewrite,[status(thm)],[2253,1556]) ).
thf(4532,plain,
! [A: $i] :
( ( t_b @ ( t_b @ ( c_0 @ c_uminus ) @ ( A @ c_minus ) ) )
= A ),
inference(rewrite,[status(thm)],[4351,2346]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Olinorder__not__le_0) ).
thf(56,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Olinorder__not__le_1) ).
thf(77,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(78,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(cnf,[status(esa)],[77]) ).
thf(258,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_b @ class_Orderings_Olinorder )
!= ( A @ class_Orderings_Olinorder ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[249,78]) ).
thf(259,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_b @ class_Orderings_Olinorder )
!= ( A @ class_Orderings_Olinorder ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) ) ),
inference(simp,[status(thm)],[258]) ).
thf(260,plain,
! [B: $i,A: $i] :
( ~ ( t_b @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( t_b @ ( B @ ( A @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[259:[bind(A,$thf( t_b ))]]) ).
thf(262,plain,
! [B: $i,A: $i] :
( ~ ( t_b @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( t_b @ ( B @ ( A @ c_less ) ) ) ),
inference(simp,[status(thm)],[260]) ).
thf(2007,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_b @ ( t_b @ ( A @ c_HOL_Oabs ) @ ( c_0 @ c_lessequals ) ) )
!= ( t_b @ ( B @ ( C @ c_lessequals ) ) ) )
| ~ $true
| ~ ( t_b @ ( C @ ( B @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[1968,262]) ).
thf(2008,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_b @ ( t_b @ ( A @ c_HOL_Oabs ) @ ( c_0 @ c_lessequals ) ) )
!= ( t_b @ ( B @ ( C @ c_lessequals ) ) ) )
| ~ ( t_b @ ( C @ ( B @ c_less ) ) ) ),
inference(simp,[status(thm)],[2007]) ).
thf(2009,plain,
! [A: $i] :
~ ( t_b @ ( c_0 @ ( t_b @ ( A @ c_HOL_Oabs ) @ c_less ) ) ),
inference(pattern_uni,[status(thm)],[2008:[bind(A,$thf( D )),bind(B,$thf( t_b @ ( D @ c_HOL_Oabs ) )),bind(C,$thf( c_0 ))]]) ).
thf(2035,plain,
! [A: $i] :
~ ( t_b @ ( c_0 @ ( t_b @ ( A @ c_HOL_Oabs ) @ c_less ) ) ),
inference(simp,[status(thm)],[2009]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
thf(36,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(37,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
inference(cnf,[status(esa)],[36]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_plus ) ) @ ( B @ c_less ) ) )
| ~ ( A @ ( D @ ( A @ ( C @ ( B @ c_minus ) ) @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__6_0) ).
thf(52,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_plus ) ) @ ( B @ c_less ) ) )
| ~ ( A @ ( D @ ( A @ ( C @ ( B @ c_minus ) ) @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1411,plain,
! [A: $i] :
( ( ( t_b @ ( c_0 @ ( A @ c_minus ) ) )
!= ( t_b @ ( v_x @ v_k @ ( v_x @ v_f @ c_minus ) ) ) )
| ( ( v_x @ v_f )
!= ( v_x @ v_g ) )
| ~ ( t_b @ ( t_b @ ( c_0 @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( A @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[1066,986]) ).
thf(1417,plain,
! [A: $i] :
( ( t_b != t_b )
| ( ( v_x @ v_k )
!= c_0 )
| ( A
!= ( v_x @ v_f ) )
| ( ( v_x @ v_f )
!= ( v_x @ v_g ) )
| ~ ( t_b @ ( t_b @ ( c_0 @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( A @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1411]) ).
thf(1430,plain,
( ( ( v_x @ v_k )
!= c_0 )
| ( ( v_x @ v_f )
!= ( v_x @ v_g ) )
| ~ ( t_b @ ( t_b @ ( c_0 @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( v_x @ v_f @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1417]) ).
thf(187,plain,
! [A: $i] :
( ( ( t_b @ class_OrderedGroup_Olordered__ab__group__abs )
!= ( A @ class_OrderedGroup_Olordered__ab__group__abs ) )
| ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[129,41]) ).
thf(188,plain,
! [A: $i] :
( ( ( t_b @ class_OrderedGroup_Olordered__ab__group__abs )
!= ( A @ class_OrderedGroup_Olordered__ab__group__abs ) )
| ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(simp,[status(thm)],[187]) ).
thf(189,plain,
t_b @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
inference(pattern_uni,[status(thm)],[188:[bind(A,$thf( t_b ))]]) ).
thf(57,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(cnf,[status(esa)],[56]) ).
thf(255,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_b @ class_Orderings_Olinorder )
!= ( A @ class_Orderings_Olinorder ) )
| ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[249,57]) ).
thf(256,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_b @ class_Orderings_Olinorder )
!= ( A @ class_Orderings_Olinorder ) )
| ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_less ) ) ) ),
inference(simp,[status(thm)],[255]) ).
thf(257,plain,
! [B: $i,A: $i] :
( ( t_b @ ( A @ ( B @ c_lessequals ) ) )
| ( t_b @ ( B @ ( A @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[256:[bind(A,$thf( t_b ))]]) ).
thf(261,plain,
! [B: $i,A: $i] :
( ( t_b @ ( A @ ( B @ c_lessequals ) ) )
| ( t_b @ ( B @ ( A @ c_less ) ) ) ),
inference(simp,[status(thm)],[257]) ).
thf(28,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).
thf(92,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(93,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(cnf,[status(esa)],[92]) ).
thf(2349,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_b @ ( t_b @ ( A @ c_uminus ) @ c_uminus ) )
!= ( t_b @ ( C @ c_uminus ) ) )
| ( ( t_b @ ( A @ ( t_b @ ( C @ ( B @ c_minus ) ) @ c_minus ) ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[2346,1555]) ).
thf(2350,plain,
! [B: $i,A: $i] :
( ( t_b @ ( B @ ( t_b @ ( t_b @ ( B @ c_uminus ) @ ( A @ c_minus ) ) @ c_minus ) ) )
= A ),
inference(pattern_uni,[status(thm)],[2349:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( t_b @ ( D @ c_uminus ) ))]]) ).
thf(2373,plain,
! [B: $i,A: $i] :
( ( t_b @ ( B @ ( t_b @ ( t_b @ ( B @ c_uminus ) @ ( A @ c_minus ) ) @ c_minus ) ) )
= A ),
inference(simp,[status(thm)],[2350]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_uminus ) @ c_HOL_Oabs ) )
= ( A @ ( B @ c_HOL_Oabs ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__minus__cancel_0) ).
thf(96,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_uminus ) @ c_HOL_Oabs ) )
= ( A @ ( B @ c_HOL_Oabs ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(97,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_uminus ) @ c_HOL_Oabs ) )
= ( A @ ( B @ c_HOL_Oabs ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(cnf,[status(esa)],[96]) ).
thf(98,plain,
! [B: $i,A: $i] :
( ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs )
| ( ( A @ ( A @ ( B @ c_uminus ) @ c_HOL_Oabs ) )
= ( A @ ( B @ c_HOL_Oabs ) ) ) ),
inference(lifteq,[status(thm)],[97]) ).
thf(3853,plain,
! [B: $i,A: $i] :
( ( ( t_b @ class_OrderedGroup_Olordered__ab__group__abs )
!= ( A @ class_OrderedGroup_Olordered__ab__group__abs ) )
| ~ $true
| ( ( A @ ( A @ ( B @ c_uminus ) @ c_HOL_Oabs ) )
= ( A @ ( B @ c_HOL_Oabs ) ) ) ),
inference(paramod_ordered,[status(thm)],[129,98]) ).
thf(3854,plain,
! [B: $i,A: $i] :
( ( ( t_b @ class_OrderedGroup_Olordered__ab__group__abs )
!= ( A @ class_OrderedGroup_Olordered__ab__group__abs ) )
| ( ( A @ ( A @ ( B @ c_uminus ) @ c_HOL_Oabs ) )
= ( A @ ( B @ c_HOL_Oabs ) ) ) ),
inference(simp,[status(thm)],[3853]) ).
thf(3855,plain,
! [A: $i] :
( ( t_b @ ( t_b @ ( A @ c_uminus ) @ c_HOL_Oabs ) )
= ( t_b @ ( A @ c_HOL_Oabs ) ) ),
inference(pattern_uni,[status(thm)],[3854:[bind(A,$thf( t_b ))]]) ).
thf(3887,plain,
! [A: $i] :
( ( t_b @ ( t_b @ ( A @ c_uminus ) @ c_HOL_Oabs ) )
= ( t_b @ ( A @ c_HOL_Oabs ) ) ),
inference(simp,[status(thm)],[3855]) ).
thf(25,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_plus ) ) @ ( A @ ( C @ ( B @ c_plus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__right_0) ).
thf(84,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_plus ) ) @ ( A @ ( C @ ( B @ c_plus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(2354,plain,
! [A: $i] :
( ( ( t_b @ ( t_b @ ( A @ c_uminus ) @ c_uminus ) )
!= ( t_b @ ( c_0 @ c_uminus ) ) )
| ( c_0 = A ) ),
inference(paramod_ordered,[status(thm)],[1603,2346]) ).
thf(2364,plain,
! [A: $i] :
( ( t_b != t_b )
| ( ( t_b @ ( A @ c_uminus ) )
!= c_0 )
| ( c_0 = A ) ),
inference(simp,[status(thm)],[2354]) ).
thf(2371,plain,
! [A: $i] :
( ( ( t_b @ ( A @ c_uminus ) )
!= c_0 )
| ( c_0 = A ) ),
inference(simp,[status(thm)],[2364]) ).
thf(27,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_minus ) ) @ c_minus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_plus ) ) @ ( B @ c_minus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__4_0) ).
thf(89,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_minus ) ) @ c_minus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_plus ) ) @ ( B @ c_minus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(85,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_plus ) ) @ ( A @ ( C @ ( B @ c_plus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(cnf,[status(esa)],[84]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).
thf(38,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_minus ) ) )
= c_0 )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__self_0) ).
thf(70,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_minus ) ) )
= c_0 )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(17,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( D @ ( B @ c_minus ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_plus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__8_1) ).
thf(65,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( D @ ( B @ c_minus ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_plus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(398,plain,
! [A: $i] :
( ( ( t_b @ class_Ring__and__Field_Oordered__idom )
!= ( A @ class_Ring__and__Field_Oordered__idom ) )
| ( A @ class_LOrder_Ojoin__semilorder )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,93]) ).
thf(399,plain,
! [A: $i] :
( ( ( t_b @ class_Ring__and__Field_Oordered__idom )
!= ( A @ class_Ring__and__Field_Oordered__idom ) )
| ( A @ class_LOrder_Ojoin__semilorder ) ),
inference(simp,[status(thm)],[398]) ).
thf(400,plain,
t_b @ class_LOrder_Ojoin__semilorder,
inference(pattern_uni,[status(thm)],[399:[bind(A,$thf( t_b ))]]) ).
thf(401,plain,
! [A: $i] :
( ( ( t_b @ class_LOrder_Ojoin__semilorder )
!= ( A @ class_LOrder_Ojoin__semilorder ) )
| ( A @ class_Orderings_Oorder )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[400,37]) ).
thf(402,plain,
! [A: $i] :
( ( ( t_b @ class_LOrder_Ojoin__semilorder )
!= ( A @ class_LOrder_Ojoin__semilorder ) )
| ( A @ class_Orderings_Oorder ) ),
inference(simp,[status(thm)],[401]) ).
thf(403,plain,
t_b @ class_Orderings_Oorder,
inference(pattern_uni,[status(thm)],[402:[bind(A,$thf( t_b ))]]) ).
thf(53,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_plus ) ) @ ( B @ c_less ) ) )
| ~ ( A @ ( D @ ( A @ ( C @ ( B @ c_minus ) ) @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(cnf,[status(esa)],[52]) ).
thf(24,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_minus ) ) @ c_uminus ) )
= ( A @ ( B @ ( C @ c_minus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__diff__eq_0) ).
thf(81,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_minus ) ) @ c_uminus ) )
= ( A @ ( B @ ( C @ c_minus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(82,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_minus ) ) @ c_uminus ) )
= ( A @ ( B @ ( C @ c_minus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(cnf,[status(esa)],[81]) ).
thf(83,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ class_OrderedGroup_Oab__group__add )
| ( ( A @ ( A @ ( C @ ( B @ c_minus ) ) @ c_uminus ) )
= ( A @ ( B @ ( C @ c_minus ) ) ) ) ),
inference(lifteq,[status(thm)],[82]) ).
thf(2406,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_b @ class_OrderedGroup_Oab__group__add )
!= ( A @ class_OrderedGroup_Oab__group__add ) )
| ~ $true
| ( ( A @ ( A @ ( C @ ( B @ c_minus ) ) @ c_uminus ) )
= ( A @ ( B @ ( C @ c_minus ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[120,83]) ).
thf(2407,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_b @ class_OrderedGroup_Oab__group__add )
!= ( A @ class_OrderedGroup_Oab__group__add ) )
| ( ( A @ ( A @ ( C @ ( B @ c_minus ) ) @ c_uminus ) )
= ( A @ ( B @ ( C @ c_minus ) ) ) ) ),
inference(simp,[status(thm)],[2406]) ).
thf(2408,plain,
! [B: $i,A: $i] :
( ( t_b @ ( t_b @ ( B @ ( A @ c_minus ) ) @ c_uminus ) )
= ( t_b @ ( A @ ( B @ c_minus ) ) ) ),
inference(pattern_uni,[status(thm)],[2407:[bind(A,$thf( t_b ))]]) ).
thf(2557,plain,
! [B: $i,A: $i] :
( ( t_b @ ( t_b @ ( B @ ( A @ c_minus ) ) @ c_uminus ) )
= ( t_b @ ( A @ ( B @ c_minus ) ) ) ),
inference(simp,[status(thm)],[2408]) ).
thf(4577,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_b @ ( t_b @ ( c_0 @ c_uminus ) @ ( A @ c_minus ) ) )
!= ( t_b @ ( B @ ( C @ c_minus ) ) ) )
| ( A
= ( t_b @ ( t_b @ ( C @ ( B @ c_minus ) ) @ c_uminus ) ) ) ),
inference(paramod_ordered,[status(thm)],[4532,2557]) ).
thf(4578,plain,
! [A: $i] :
( ( t_b @ ( t_b @ ( A @ ( t_b @ ( c_0 @ c_uminus ) @ c_minus ) ) @ c_uminus ) )
= A ),
inference(pattern_uni,[status(thm)],[4577:[bind(A,$thf( A )),bind(B,$thf( t_b @ ( c_0 @ c_uminus ) )),bind(C,$thf( A ))]]) ).
thf(4840,plain,
! [A: $i] :
( ( t_b @ ( t_b @ ( A @ ( c_0 @ c_minus ) ) @ c_uminus ) )
= A ),
inference(rewrite,[status(thm)],[4578,1603]) ).
thf(1580,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_b @ ( A @ ( c_0 @ c_minus ) ) )
!= ( t_b @ ( t_b @ ( C @ ( C @ c_minus ) ) @ ( B @ c_minus ) ) ) )
| ( ( t_b @ ( A @ c_uminus ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[1556,582]) ).
thf(1581,plain,
! [A: $i] :
( ( t_b @ ( t_b @ ( A @ ( A @ c_minus ) ) @ c_uminus ) )
= c_0 ),
inference(pattern_uni,[status(thm)],[1580:[bind(A,$thf( t_b @ ( E @ ( E @ c_minus ) ) )),bind(B,$thf( c_0 )),bind(C,$thf( E ))]]) ).
thf(1658,plain,
! [A: $i] :
( ( t_b @ ( t_b @ ( A @ ( A @ c_minus ) ) @ c_uminus ) )
= c_0 ),
inference(simp,[status(thm)],[1581]) ).
thf(3896,plain,
! [B: $i,A: $i] :
( ( ( t_b @ ( t_b @ ( A @ ( A @ c_minus ) ) @ c_uminus ) )
!= ( t_b @ ( B @ c_uminus ) ) )
| ( ( t_b @ ( c_0 @ c_HOL_Oabs ) )
= ( t_b @ ( B @ c_HOL_Oabs ) ) ) ),
inference(paramod_ordered,[status(thm)],[1658,3887]) ).
thf(3897,plain,
! [A: $i] :
( ( t_b @ ( t_b @ ( A @ ( A @ c_minus ) ) @ c_HOL_Oabs ) )
= ( t_b @ ( c_0 @ c_HOL_Oabs ) ) ),
inference(pattern_uni,[status(thm)],[3896:[bind(A,$thf( D )),bind(B,$thf( t_b @ ( D @ ( D @ c_minus ) ) ))]]) ).
thf(3941,plain,
! [A: $i] :
( ( t_b @ ( t_b @ ( A @ ( A @ c_minus ) ) @ c_HOL_Oabs ) )
= ( t_b @ ( c_0 @ c_HOL_Oabs ) ) ),
inference(simp,[status(thm)],[3897]) ).
thf(700,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( t_b @ ( A @ ( t_b @ ( A @ ( B @ c_plus ) ) @ c_minus ) ) )
!= ( t_b @ ( E @ ( t_b @ ( D @ ( C @ c_plus ) ) @ c_minus ) ) ) )
| ( ( t_b @ ( t_b @ ( E @ ( D @ c_minus ) ) @ ( B @ c_minus ) ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[657,564]) ).
thf(701,plain,
! [B: $i,A: $i] :
( ( t_b @ ( t_b @ ( A @ ( A @ c_minus ) ) @ ( B @ c_minus ) ) )
= B ),
inference(pattern_uni,[status(thm)],[700:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A )),bind(E,$thf( A ))]]) ).
thf(1,negated_conjecture,
! [A: $i] : ( t_b @ ( A @ v_k @ ( A @ v_g @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(32,plain,
! [A: $i] : ( t_b @ ( A @ v_k @ ( A @ v_g @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
thf(54,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(55,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(cnf,[status(esa)],[54]) ).
thf(145,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( t_b @ ( A @ v_k @ ( A @ v_g @ c_lessequals ) ) )
!= ( B @ ( D @ ( C @ c_lessequals ) ) ) )
| ( B @ ( D @ ( E @ c_lessequals ) ) )
| ~ ( B @ ( C @ ( E @ c_lessequals ) ) )
| ~ $true
| ~ ( B @ class_Orderings_Oorder ) ),
inference(paramod_ordered,[status(thm)],[32,55]) ).
thf(146,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( t_b @ ( A @ v_k @ ( A @ v_g @ c_lessequals ) ) )
!= ( B @ ( D @ ( C @ c_lessequals ) ) ) )
| ( B @ ( D @ ( E @ c_lessequals ) ) )
| ~ ( B @ ( C @ ( E @ c_lessequals ) ) )
| ~ ( B @ class_Orderings_Oorder ) ),
inference(simp,[status(thm)],[145]) ).
thf(147,plain,
! [B: $i,A: $i] :
( ( t_b @ ( B @ v_k @ ( A @ c_lessequals ) ) )
| ~ ( t_b @ ( B @ v_g @ ( A @ c_lessequals ) ) )
| ~ ( t_b @ class_Orderings_Oorder ) ),
inference(pattern_uni,[status(thm)],[146:[bind(A,$thf( G )),bind(B,$thf( t_b )),bind(C,$thf( G @ v_g )),bind(D,$thf( G @ v_k )),bind(E,$thf( E ))]]) ).
thf(153,plain,
! [B: $i,A: $i] :
( ( t_b @ ( B @ v_k @ ( A @ c_lessequals ) ) )
| ~ ( t_b @ ( B @ v_g @ ( A @ c_lessequals ) ) )
| ~ ( t_b @ class_Orderings_Oorder ) ),
inference(simp,[status(thm)],[147]) ).
thf(304,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_b @ ( B @ v_k @ ( A @ c_lessequals ) ) )
!= ( t_b @ ( C @ ( D @ c_lessequals ) ) ) )
| ~ $true
| ~ ( t_b @ ( D @ ( C @ c_less ) ) )
| ~ ( t_b @ ( B @ v_g @ ( A @ c_lessequals ) ) )
| ~ ( t_b @ class_Orderings_Oorder ) ),
inference(paramod_ordered,[status(thm)],[153,262]) ).
thf(305,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_b @ ( B @ v_k @ ( A @ c_lessequals ) ) )
!= ( t_b @ ( C @ ( D @ c_lessequals ) ) ) )
| ~ ( t_b @ ( D @ ( C @ c_less ) ) )
| ~ ( t_b @ ( B @ v_g @ ( A @ c_lessequals ) ) )
| ~ ( t_b @ class_Orderings_Oorder ) ),
inference(simp,[status(thm)],[304]) ).
thf(306,plain,
! [B: $i,A: $i] :
( ~ ( t_b @ ( A @ ( B @ v_k @ c_less ) ) )
| ~ ( t_b @ ( B @ v_g @ ( A @ c_lessequals ) ) )
| ~ ( t_b @ class_Orderings_Oorder ) ),
inference(pattern_uni,[status(thm)],[305:[bind(A,$thf( A )),bind(B,$thf( E )),bind(C,$thf( E @ v_k )),bind(D,$thf( A ))]]) ).
thf(327,plain,
! [B: $i,A: $i] :
( ~ ( t_b @ ( A @ ( B @ v_k @ c_less ) ) )
| ~ ( t_b @ ( B @ v_g @ ( A @ c_lessequals ) ) )
| ~ ( t_b @ class_Orderings_Oorder ) ),
inference(simp,[status(thm)],[306]) ).
thf(406,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ class_Orderings_Oorder )
!= ( t_b @ class_Orderings_Oorder ) )
| ~ ( t_b @ ( B @ ( C @ v_k @ c_less ) ) )
| ~ ( t_b @ ( C @ v_g @ ( B @ c_lessequals ) ) )
| ~ $true
| ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
inference(paramod_ordered,[status(thm)],[37,327]) ).
thf(407,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ class_Orderings_Oorder )
!= ( t_b @ class_Orderings_Oorder ) )
| ~ ( t_b @ ( B @ ( C @ v_k @ c_less ) ) )
| ~ ( t_b @ ( C @ v_g @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
inference(simp,[status(thm)],[406]) ).
thf(408,plain,
! [B: $i,A: $i] :
( ~ ( t_b @ ( A @ ( B @ v_k @ c_less ) ) )
| ~ ( t_b @ ( B @ v_g @ ( A @ c_lessequals ) ) )
| ~ ( t_b @ class_LOrder_Ojoin__semilorder ) ),
inference(pattern_uni,[status(thm)],[407:[bind(A,$thf( t_b ))]]) ).
thf(428,plain,
! [B: $i,A: $i] :
( ~ ( t_b @ ( A @ ( B @ v_k @ c_less ) ) )
| ~ ( t_b @ ( B @ v_g @ ( A @ c_lessequals ) ) )
| ~ ( t_b @ class_LOrder_Ojoin__semilorder ) ),
inference(simp,[status(thm)],[408]) ).
thf(432,plain,
! [B: $i,A: $i] :
( ~ ( t_b @ ( A @ ( B @ v_k @ c_less ) ) )
| ~ ( t_b @ ( B @ v_g @ ( A @ c_lessequals ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[428,400]) ).
thf(433,plain,
! [B: $i,A: $i] :
( ~ ( t_b @ ( A @ ( B @ v_k @ c_less ) ) )
| ~ ( t_b @ ( B @ v_g @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[432]) ).
thf(441,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_b @ ( B @ ( A @ c_less ) ) )
!= ( t_b @ ( C @ ( D @ v_k @ c_less ) ) ) )
| ~ $true
| ~ ( t_b @ ( D @ v_g @ ( C @ c_lessequals ) ) )
| ( t_b @ ( A @ ( B @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[261,433]) ).
thf(442,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_b @ ( B @ ( A @ c_less ) ) )
!= ( t_b @ ( C @ ( D @ v_k @ c_less ) ) ) )
| ~ ( t_b @ ( D @ v_g @ ( C @ c_lessequals ) ) )
| ( t_b @ ( A @ ( B @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[441]) ).
thf(443,plain,
! [B: $i,A: $i] :
( ~ ( t_b @ ( B @ v_g @ ( A @ c_lessequals ) ) )
| ( t_b @ ( B @ v_k @ ( A @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[442:[bind(A,$thf( E @ v_k )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( E ))]]) ).
thf(457,plain,
! [B: $i,A: $i] :
( ~ ( t_b @ ( B @ v_g @ ( A @ c_lessequals ) ) )
| ( t_b @ ( B @ v_k @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[443]) ).
thf(102,plain,
! [A: $i] :
( ( ( t_b @ ( A @ v_k @ ( A @ v_g @ c_lessequals ) ) )
!= ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( t_b @ ( v_x @ v_k @ ( v_x @ v_f @ c_minus ) ) @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[32,35]) ).
thf(103,plain,
! [A: $i] :
( ( t_b @ ( A @ v_k @ ( A @ v_g @ c_lessequals ) ) )
!= ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( t_b @ ( v_x @ v_k @ ( v_x @ v_f @ c_minus ) ) @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[102]) ).
thf(104,plain,
! [A: $i] :
( ( t_b != t_b )
| ( ( A @ v_k )
!= ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) @ c_HOL_Oabs ) ) )
| ( ( A @ v_g )
!= ( t_b @ ( c_0 @ ( t_b @ ( v_x @ v_k @ ( v_x @ v_f @ c_minus ) ) @ c_Orderings_Omax ) ) ) ) ),
inference(simp,[status(thm)],[103]) ).
thf(105,plain,
! [A: $i] :
( ( ( A @ v_k )
!= ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) @ c_HOL_Oabs ) ) )
| ( ( A @ v_g )
!= ( t_b @ ( c_0 @ ( t_b @ ( v_x @ v_k @ ( v_x @ v_f @ c_minus ) ) @ c_Orderings_Omax ) ) ) ) ),
inference(simp,[status(thm)],[104]) ).
thf(1101,plain,
! [A: $i] :
( ( ( t_b @ ( c_0 @ ( A @ c_minus ) ) )
!= ( t_b @ ( v_x @ v_k @ ( v_x @ v_f @ c_minus ) ) ) )
| ~ ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( A @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[1066,35]) ).
thf(1121,plain,
! [A: $i] :
( ( t_b != t_b )
| ( ( v_x @ v_k )
!= c_0 )
| ( A
!= ( v_x @ v_f ) )
| ~ ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( A @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1101]) ).
thf(1139,plain,
( ( ( v_x @ v_k )
!= c_0 )
| ~ ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( v_x @ v_f @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1121]) ).
thf(1856,plain,
! [A: $i] :
( ( ( t_b @ ( A @ ( c_0 @ c_minus ) ) )
!= ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) ) )
| ( ( v_x @ v_k )
!= c_0 )
| ~ ( t_b @ ( t_b @ ( t_b @ ( A @ c_uminus ) @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( v_x @ v_f @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[1556,1139]) ).
thf(1869,plain,
! [A: $i] :
( ( t_b != t_b )
| ( A
!= ( v_x @ v_g ) )
| ( ( v_x @ v_f )
!= c_0 )
| ( ( v_x @ v_k )
!= c_0 )
| ~ ( t_b @ ( t_b @ ( t_b @ ( A @ c_uminus ) @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( v_x @ v_f @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1856]) ).
thf(1884,plain,
( ( ( v_x @ v_f )
!= c_0 )
| ( ( v_x @ v_k )
!= c_0 )
| ~ ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ c_uminus ) @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( v_x @ v_f @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1869]) ).
thf(4354,plain,
( ( ( v_x @ v_f )
!= c_0 )
| ( ( v_x @ v_k )
!= c_0 )
| ~ ( t_b @ ( t_b @ ( v_x @ v_g @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( v_x @ v_f @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) ),
inference(rewrite,[status(thm)],[1884,3887]) ).
thf(142,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( D @ c_lessequals ) ) )
!= ( E @ ( F @ ( G @ c_lessequals ) ) ) )
| ~ $true
| ~ ( E @ ( G @ ( F @ c_less ) ) )
| ~ ( E @ class_Orderings_Olinorder )
| ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(paramod_ordered,[status(thm)],[55,78]) ).
thf(143,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( D @ c_lessequals ) ) )
!= ( E @ ( F @ ( G @ c_lessequals ) ) ) )
| ~ ( E @ ( G @ ( F @ c_less ) ) )
| ~ ( E @ class_Orderings_Olinorder )
| ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(simp,[status(thm)],[142]) ).
thf(144,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_less ) ) )
| ~ ( A @ class_Orderings_Olinorder )
| ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(pattern_uni,[status(thm)],[143:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( C )),bind(G,$thf( D ))]]) ).
thf(148,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( t_b @ ( A @ v_k @ ( A @ v_g @ c_lessequals ) ) )
!= ( B @ ( C @ ( E @ c_lessequals ) ) ) )
| ( B @ ( D @ ( E @ c_lessequals ) ) )
| ~ $true
| ~ ( B @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( B @ class_Orderings_Oorder ) ),
inference(paramod_ordered,[status(thm)],[32,55]) ).
thf(149,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( t_b @ ( A @ v_k @ ( A @ v_g @ c_lessequals ) ) )
!= ( B @ ( C @ ( E @ c_lessequals ) ) ) )
| ( B @ ( D @ ( E @ c_lessequals ) ) )
| ~ ( B @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( B @ class_Orderings_Oorder ) ),
inference(simp,[status(thm)],[148]) ).
thf(150,plain,
! [B: $i,A: $i] :
( ( t_b @ ( A @ ( B @ v_g @ c_lessequals ) ) )
| ~ ( t_b @ ( A @ ( B @ v_k @ c_lessequals ) ) )
| ~ ( t_b @ class_Orderings_Oorder ) ),
inference(pattern_uni,[status(thm)],[149:[bind(A,$thf( G )),bind(B,$thf( t_b )),bind(C,$thf( G @ v_k )),bind(D,$thf( D )),bind(E,$thf( G @ v_g ))]]) ).
thf(155,plain,
! [B: $i,A: $i] :
( ( t_b @ ( A @ ( B @ v_g @ c_lessequals ) ) )
| ~ ( t_b @ ( A @ ( B @ v_k @ c_lessequals ) ) )
| ~ ( t_b @ class_Orderings_Oorder ) ),
inference(simp,[status(thm)],[150]) ).
thf(5147,plain,
! [B: $i,A: $i] :
( ( t_b @ ( A @ ( B @ v_g @ c_lessequals ) ) )
| ~ ( t_b @ ( A @ ( B @ v_k @ c_lessequals ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[155,403]) ).
thf(5148,plain,
! [B: $i,A: $i] :
( ( t_b @ ( A @ ( B @ v_g @ c_lessequals ) ) )
| ~ ( t_b @ ( A @ ( B @ v_k @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[5147]) ).
thf(39,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(cnf,[status(esa)],[38]) ).
thf(90,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_minus ) ) @ c_minus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_plus ) ) @ ( B @ c_minus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(cnf,[status(esa)],[89]) ).
thf(91,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ class_OrderedGroup_Oab__group__add )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_minus ) ) @ c_minus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_plus ) ) @ ( B @ c_minus ) ) ) ) ),
inference(lifteq,[status(thm)],[90]) ).
thf(66,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( D @ ( B @ c_minus ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_plus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(cnf,[status(esa)],[65]) ).
thf(1100,plain,
! [A: $i] :
( ( ( t_b @ ( c_0 @ ( A @ c_minus ) ) )
!= ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) ) )
| ~ ( t_b @ ( t_b @ ( A @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( t_b @ ( v_x @ v_k @ ( v_x @ v_f @ c_minus ) ) @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[1066,35]) ).
thf(1123,plain,
! [A: $i] :
( ( t_b != t_b )
| ( ( v_x @ v_g )
!= c_0 )
| ( A
!= ( v_x @ v_f ) )
| ~ ( t_b @ ( t_b @ ( A @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( t_b @ ( v_x @ v_k @ ( v_x @ v_f @ c_minus ) ) @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1100]) ).
thf(1141,plain,
( ( ( v_x @ v_g )
!= c_0 )
| ~ ( t_b @ ( t_b @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( t_b @ ( v_x @ v_k @ ( v_x @ v_f @ c_minus ) ) @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1123]) ).
thf(2894,plain,
! [A: $i] :
( ( ( t_b @ ( A @ ( c_0 @ c_minus ) ) )
!= ( t_b @ ( v_x @ v_k @ ( v_x @ v_f @ c_minus ) ) ) )
| ( ( v_x @ v_g )
!= c_0 )
| ~ ( t_b @ ( t_b @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( t_b @ ( A @ c_uminus ) @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[1556,1141]) ).
thf(2915,plain,
! [A: $i] :
( ( t_b != t_b )
| ( A
!= ( v_x @ v_k ) )
| ( ( v_x @ v_f )
!= c_0 )
| ( ( v_x @ v_g )
!= c_0 )
| ~ ( t_b @ ( t_b @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( t_b @ ( A @ c_uminus ) @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[2894]) ).
thf(2931,plain,
( ( ( v_x @ v_f )
!= c_0 )
| ( ( v_x @ v_g )
!= c_0 )
| ~ ( t_b @ ( t_b @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( t_b @ ( v_x @ v_k @ c_uminus ) @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[2915]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
thf(94,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(95,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(cnf,[status(esa)],[94]) ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_plus ) ) @ ( A @ ( B @ ( D @ c_plus ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__left_1) ).
thf(47,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_plus ) ) @ ( A @ ( B @ ( D @ c_plus ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(48,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_plus ) ) @ ( A @ ( B @ ( D @ c_plus ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(cnf,[status(esa)],[47]) ).
thf(130,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ class_Orderings_Oorder )
!= ( B @ class_Orderings_Oorder ) )
| ( B @ ( D @ ( E @ c_lessequals ) ) )
| ~ ( B @ ( C @ ( E @ c_lessequals ) ) )
| ~ ( B @ ( D @ ( C @ c_lessequals ) ) )
| ~ $true
| ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
inference(paramod_ordered,[status(thm)],[37,55]) ).
thf(131,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ class_Orderings_Oorder )
!= ( B @ class_Orderings_Oorder ) )
| ( B @ ( D @ ( E @ c_lessequals ) ) )
| ~ ( B @ ( C @ ( E @ c_lessequals ) ) )
| ~ ( B @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
inference(simp,[status(thm)],[130]) ).
thf(132,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
inference(pattern_uni,[status(thm)],[131:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(154,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
inference(simp,[status(thm)],[132]) ).
thf(71,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_minus ) ) )
= c_0 )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(cnf,[status(esa)],[70]) ).
thf(72,plain,
! [B: $i,A: $i] :
( ~ ( A @ class_OrderedGroup_Oab__group__add )
| ( ( A @ ( B @ ( B @ c_minus ) ) )
= c_0 ) ),
inference(lifteq,[status(thm)],[71]) ).
thf(136,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( D @ c_lessequals ) ) )
!= ( E @ ( G @ ( F @ c_lessequals ) ) ) )
| ( E @ ( G @ ( H @ c_lessequals ) ) )
| ~ ( E @ ( F @ ( H @ c_lessequals ) ) )
| ~ $true
| ~ ( E @ class_Orderings_Oorder )
| ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(paramod_ordered,[status(thm)],[55,55]) ).
thf(137,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( D @ c_lessequals ) ) )
!= ( E @ ( G @ ( F @ c_lessequals ) ) ) )
| ( E @ ( G @ ( H @ c_lessequals ) ) )
| ~ ( E @ ( F @ ( H @ c_lessequals ) ) )
| ~ ( E @ class_Orderings_Oorder )
| ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(simp,[status(thm)],[136]) ).
thf(138,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( E @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder )
| ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(pattern_uni,[status(thm)],[137:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( D )),bind(G,$thf( C ))]]) ).
thf(158,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( E @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(simp,[status(thm)],[138]) ).
thf(184,plain,
! [A: $i] :
( ( ( t_b @ class_OrderedGroup_Olordered__ab__group__abs )
!= ( A @ class_OrderedGroup_Olordered__ab__group__abs ) )
| ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[129,39]) ).
thf(185,plain,
! [A: $i] :
( ( ( t_b @ class_OrderedGroup_Olordered__ab__group__abs )
!= ( A @ class_OrderedGroup_Olordered__ab__group__abs ) )
| ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(simp,[status(thm)],[184]) ).
thf(186,plain,
t_b @ class_OrderedGroup_Opordered__ab__group__add,
inference(pattern_uni,[status(thm)],[185:[bind(A,$thf( t_b ))]]) ).
thf(221,plain,
! [B: $i,A: $i] :
( ( ( t_b @ ( B @ ( t_b @ ( B @ ( A @ c_plus ) ) @ c_minus ) ) )
!= ( t_b @ ( v_x @ v_k @ ( v_x @ v_f @ c_minus ) ) ) )
| ~ ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( A @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[208,35]) ).
thf(228,plain,
! [B: $i,A: $i] :
( ( t_b != t_b )
| ( B
!= ( v_x @ v_k ) )
| ( ( t_b @ ( B @ ( A @ c_plus ) ) )
!= ( v_x @ v_f ) )
| ~ ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( A @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[221]) ).
thf(234,plain,
! [A: $i] :
( ( ( t_b @ ( v_x @ v_k @ ( A @ c_plus ) ) )
!= ( v_x @ v_f ) )
| ~ ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( A @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[228]) ).
thf(973,plain,
! [B: $i,A: $i] :
( ( ( t_b @ ( A @ ( c_0 @ c_plus ) ) )
!= ( t_b @ ( v_x @ v_k @ ( B @ c_plus ) ) ) )
| ( A
!= ( v_x @ v_f ) )
| ~ ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( B @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[959,234]) ).
thf(974,plain,
( ( ( v_x @ v_f )
!= ( v_x @ v_k ) )
| ~ ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( c_0 @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[973:[bind(A,$thf( v_x @ v_k )),bind(B,$thf( c_0 ))]]) ).
thf(2094,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ ( D @ c_Orderings_Omax ) ) @ c_lessequals ) ) )
!= ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( c_0 @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) )
| ( ( v_x @ v_f )
!= ( v_x @ v_k ) )
| ~ $true
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(paramod_ordered,[status(thm)],[80,974]) ).
thf(2095,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ ( D @ c_Orderings_Omax ) ) @ c_lessequals ) ) )
!= ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( c_0 @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) )
| ( ( v_x @ v_f )
!= ( v_x @ v_k ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(simp,[status(thm)],[2094]) ).
thf(2096,plain,
( ( ( v_x @ v_f )
!= ( v_x @ v_k ) )
| ~ ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) @ c_HOL_Oabs ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) @ c_HOL_Oabs ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( t_b @ class_Orderings_Olinorder ) ),
inference(pattern_uni,[status(thm)],[2095:[bind(A,$thf( t_b )),bind(B,$thf( c_0 )),bind(C,$thf( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) @ c_HOL_Oabs ) )),bind(D,$thf( c_0 ))]]) ).
thf(2187,plain,
( ( ( v_x @ v_f )
!= ( v_x @ v_k ) )
| ~ ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) @ c_HOL_Oabs ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( t_b @ class_Orderings_Olinorder ) ),
inference(simp,[status(thm)],[2096]) ).
thf(2785,plain,
( ( ( v_x @ v_f )
!= ( v_x @ v_k ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[2187,1968,249]) ).
thf(2786,plain,
( ( v_x @ v_f )
!= ( v_x @ v_k ) ),
inference(simp,[status(thm)],[2785]) ).
thf(4073,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_uminus ) )
!= ( t_b @ ( c_0 @ c_uminus ) ) )
| ( ( A @ ( B @ c_HOL_Oabs ) )
= c_0 )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(paramod_ordered,[status(thm)],[101,1603]) ).
thf(4074,plain,
( ( ( t_b @ ( c_0 @ c_HOL_Oabs ) )
= c_0 )
| ~ ( t_b @ ( c_0 @ ( c_0 @ c_lessequals ) ) )
| ~ ( t_b @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(pattern_uni,[status(thm)],[4073:[bind(A,$thf( t_b )),bind(B,$thf( c_0 ))]]) ).
thf(5195,plain,
( ( ( t_b @ ( c_0 @ c_HOL_Oabs ) )
= c_0 )
| ~ ( t_b @ ( c_0 @ ( c_0 @ c_lessequals ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[4074,129]) ).
thf(5196,plain,
( ( ( t_b @ ( c_0 @ c_HOL_Oabs ) )
= c_0 )
| ~ ( t_b @ ( c_0 @ ( c_0 @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[5195]) ).
thf(124,plain,
! [B: $i,A: $i] :
( ( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
!= ( B @ class_OrderedGroup_Olordered__ab__group__abs ) )
| ( B @ class_OrderedGroup_Opordered__ab__group__add )
| ~ $true
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(paramod_ordered,[status(thm)],[59,39]) ).
thf(125,plain,
! [B: $i,A: $i] :
( ( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
!= ( B @ class_OrderedGroup_Olordered__ab__group__abs ) )
| ( B @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(simp,[status(thm)],[124]) ).
thf(126,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(pattern_uni,[status(thm)],[125:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(1857,plain,
! [A: $i] :
( ( ( t_b @ ( c_0 @ ( A @ c_minus ) ) )
!= ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) ) )
| ( ( v_x @ v_k )
!= c_0 )
| ~ ( t_b @ ( t_b @ ( A @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( v_x @ v_f @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[1066,1139]) ).
thf(1876,plain,
! [A: $i] :
( ( t_b != t_b )
| ( ( v_x @ v_g )
!= c_0 )
| ( A
!= ( v_x @ v_f ) )
| ( ( v_x @ v_k )
!= c_0 )
| ~ ( t_b @ ( t_b @ ( A @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( v_x @ v_f @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1857]) ).
thf(1891,plain,
( ( ( v_x @ v_g )
!= c_0 )
| ( ( v_x @ v_k )
!= c_0 )
| ~ ( t_b @ ( t_b @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( v_x @ v_f @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1876]) ).
thf(4410,plain,
( ( ( t_b @ ( v_x @ v_k @ c_uminus ) )
!= ( t_b @ ( c_0 @ c_uminus ) ) )
| ( ( v_x @ v_f )
!= c_0 )
| ( ( v_x @ v_g )
!= c_0 )
| ~ ( t_b @ ( t_b @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( c_0 @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[1603,2931]) ).
thf(4435,plain,
( ( t_b != t_b )
| ( ( v_x @ v_k )
!= c_0 )
| ( ( v_x @ v_f )
!= c_0 )
| ( ( v_x @ v_g )
!= c_0 )
| ~ ( t_b @ ( t_b @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( c_0 @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[4410]) ).
thf(4450,plain,
( ( ( v_x @ v_k )
!= c_0 )
| ( ( v_x @ v_f )
!= c_0 )
| ( ( v_x @ v_g )
!= c_0 )
| ~ ( t_b @ ( t_b @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( c_0 @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[4435]) ).
thf(4711,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ ( D @ c_Orderings_Omax ) ) @ c_lessequals ) ) )
!= ( t_b @ ( t_b @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( c_0 @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) )
| ( ( v_x @ v_k )
!= c_0 )
| ( ( v_x @ v_f )
!= c_0 )
| ( ( v_x @ v_g )
!= c_0 )
| ~ $true
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(paramod_ordered,[status(thm)],[80,4450]) ).
thf(4712,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ ( D @ c_Orderings_Omax ) ) @ c_lessequals ) ) )
!= ( t_b @ ( t_b @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( c_0 @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) )
| ( ( v_x @ v_k )
!= c_0 )
| ( ( v_x @ v_f )
!= c_0 )
| ( ( v_x @ v_g )
!= c_0 )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(simp,[status(thm)],[4711]) ).
thf(4713,plain,
( ( ( v_x @ v_k )
!= c_0 )
| ( ( v_x @ v_f )
!= c_0 )
| ( ( v_x @ v_g )
!= c_0 )
| ~ ( t_b @ ( t_b @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( t_b @ ( t_b @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( t_b @ class_Orderings_Olinorder ) ),
inference(pattern_uni,[status(thm)],[4712:[bind(A,$thf( t_b )),bind(B,$thf( c_0 )),bind(C,$thf( t_b @ ( v_x @ v_f @ c_HOL_Oabs ) )),bind(D,$thf( c_0 ))]]) ).
thf(4736,plain,
( ( ( v_x @ v_k )
!= c_0 )
| ( ( v_x @ v_f )
!= c_0 )
| ( ( v_x @ v_g )
!= c_0 )
| ~ ( t_b @ ( t_b @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( t_b @ class_Orderings_Olinorder ) ),
inference(simp,[status(thm)],[4713]) ).
thf(4954,plain,
( ( ( v_x @ v_k )
!= c_0 )
| ( ( v_x @ v_f )
!= c_0 )
| ( ( v_x @ v_g )
!= c_0 )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[4736,1968,249]) ).
thf(4955,plain,
( ( ( v_x @ v_k )
!= c_0 )
| ( ( v_x @ v_f )
!= c_0 )
| ( ( v_x @ v_g )
!= c_0 ) ),
inference(simp,[status(thm)],[4954]) ).
thf(106,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_b @ ( A @ v_k @ ( A @ v_g @ c_lessequals ) ) )
!= ( B @ ( C @ ( D @ c_lessequals ) ) ) )
| ~ $true
| ~ ( B @ ( D @ ( C @ c_less ) ) )
| ~ ( B @ class_Orderings_Olinorder ) ),
inference(paramod_ordered,[status(thm)],[32,78]) ).
thf(107,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_b @ ( A @ v_k @ ( A @ v_g @ c_lessequals ) ) )
!= ( B @ ( C @ ( D @ c_lessequals ) ) ) )
| ~ ( B @ ( D @ ( C @ c_less ) ) )
| ~ ( B @ class_Orderings_Olinorder ) ),
inference(simp,[status(thm)],[106]) ).
thf(108,plain,
! [A: $i] :
( ~ ( t_b @ ( A @ v_g @ ( A @ v_k @ c_less ) ) )
| ~ ( t_b @ class_Orderings_Olinorder ) ),
inference(pattern_uni,[status(thm)],[107:[bind(A,$thf( F )),bind(B,$thf( t_b )),bind(C,$thf( F @ v_k )),bind(D,$thf( F @ v_g ))]]) ).
thf(109,plain,
! [A: $i] :
( ~ ( t_b @ ( A @ v_g @ ( A @ v_k @ c_less ) ) )
| ~ ( t_b @ class_Orderings_Olinorder ) ),
inference(simp,[status(thm)],[108]) ).
thf(253,plain,
! [A: $i] :
( ~ ( t_b @ ( A @ v_g @ ( A @ v_k @ c_less ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[109,249]) ).
thf(254,plain,
! [A: $i] :
~ ( t_b @ ( A @ v_g @ ( A @ v_k @ c_less ) ) ),
inference(simp,[status(thm)],[253]) ).
thf(444,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_b @ ( A @ v_k @ ( A @ v_g @ c_lessequals ) ) )
!= ( t_b @ ( C @ v_g @ ( B @ c_lessequals ) ) ) )
| ~ ( t_b @ ( B @ ( C @ v_k @ c_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[32,433]) ).
thf(445,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_b @ ( A @ v_k @ ( A @ v_g @ c_lessequals ) ) )
!= ( t_b @ ( C @ v_g @ ( B @ c_lessequals ) ) ) )
| ~ ( t_b @ ( B @ ( C @ v_k @ c_less ) ) ) ),
inference(simp,[status(thm)],[444]) ).
thf(450,plain,
! [C: $i,B: $i,A: $i] :
( ( t_b != t_b )
| ( ( A @ v_k )
!= ( C @ v_g ) )
| ( ( A @ v_g )
!= B )
| ~ ( t_b @ ( B @ ( C @ v_k @ c_less ) ) ) ),
inference(simp,[status(thm)],[445]) ).
thf(454,plain,
! [B: $i,A: $i] :
( ( ( A @ v_k )
!= ( B @ v_g ) )
| ~ ( t_b @ ( A @ v_g @ ( B @ v_k @ c_less ) ) ) ),
inference(simp,[status(thm)],[450]) ).
thf(62684,plain,
$false,
inference(e,[status(thm)],[123,99,69,101,249,88,582,4697,120,4532,56,2035,1640,42,37,52,1430,4130,189,46,57,78,261,93,2373,3887,84,61,2371,89,74,60,85,38,70,33,92,65,1968,1555,403,53,4840,3941,77,96,701,457,129,41,73,105,4354,64,32,34,44,59,1139,54,144,5148,49,2557,86,2346,81,1603,76,39,98,91,66,1556,1066,2303,80,35,2931,394,986,95,2298,48,67,1658,1141,154,72,978,43,40,158,186,55,75,2786,58,433,5196,36,262,51,126,79,400,1891,94,47,62,4955,254,83,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA026-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.43 % Computer : n001.cluster.edu
% 0.10/0.43 % Model : x86_64 x86_64
% 0.10/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.43 % Memory : 8046.5625MB
% 0.10/0.43 % OS : Linux 6.8.0-71-generic
% 0.10/0.43 % CPULimit : 300
% 0.10/0.43 % WCLimit : 300
% 0.10/0.43 % DateTime : Sat Sep 26 22:12:44 UTC 2026
% 0.10/0.43 % CPUTime :
% 0.10/0.44 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.68/1.04 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.98/1.22 % [INFO] Parsing done (175ms).
% 0.98/1.23 % [INFO] Running in sequential loop mode.
% 1.76/1.72 % [INFO] eprover registered as external prover.
% 1.76/1.74 % [INFO] Scanning for conjecture ...
% 1.90/1.87 % [INFO] Found a conjecture (or negated_conjecture) and 28 axioms. Running axiom selection ...
% 2.05/1.97 % [INFO] Axiom selection finished. Selected 28 axioms (removed 0 axioms).
% 2.21/2.03 % [INFO] Problem is propositional (TPTP CNF).
% 2.21/2.04 % [INFO] Type checking passed.
% 2.21/2.05 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 167.42/50.42 % External prover 'e' found a proof!
% 167.42/50.42 % [INFO] Killing All external provers ...
% 167.42/50.43 % Time passed: 49764ms (effective reasoning time: 49191ms)
% 167.42/50.43 % Axioms used in derivation (28): cls_OrderedGroup_Odiff__self_0, cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2, cls_Orderings_Olinorder__not__le_1, cls_OrderedGroup_Ocompare__rls__2_0, cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0, cls_OrderedGroup_Oabs__of__nonpos_0, cls_OrderedGroup_Ocompare__rls__4_0, cls_OrderedGroup_Ocompare__rls__8_1, clsrel_Ring__and__Field_Oordered__idom_33, cls_OrderedGroup_Oadd__le__cancel__left_1, cls_OrderedGroup_Ocompare__rls__10_1, clsrel_Ring__and__Field_Oordered__idom_23, cls_Orderings_Olinorder__not__le_0, cls_Orderings_Oorder__class_Oorder__trans_0, cls_OrderedGroup_Oadd__le__cancel__right_0, cls_OrderedGroup_Oabs__ge__zero_0, cls_OrderedGroup_Ocompare__rls__3_0, cls_Orderings_Oorder__less__imp__le_0, clsrel_OrderedGroup_Olordered__ab__group__abs_6, cls_OrderedGroup_Ocompare__rls__6_0, clsrel_LOrder_Ojoin__semilorder_1, clsrel_Ring__and__Field_Oordered__idom_35, cls_OrderedGroup_Oabs__minus__cancel_0, clsrel_Ring__and__Field_Oordered__idom_50, cls_OrderedGroup_Ominus__diff__eq_0, clsrel_OrderedGroup_Olordered__ab__group__abs_1, clsrel_Ring__and__Field_Oordered__idom_4, cls_OrderedGroup_Oab__group__add__class_Odiff__minus_0
% 167.42/50.43 % No. of inferences in proof: 336
% 167.42/50.43 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 49764 ms resp. 49191 ms w/o parsing
% 153.33/50.55 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 153.33/50.56 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------