%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA022-2 : 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 : n011.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 06:50:18 AM UTC 2026
% Result : Unsatisfiable 21.20s 5.54s
% Output : Refutation 18.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 27
% Syntax : Number of formulae : 119 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 330 ( 61 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 1221 ( 167 ~; 155 |; 0 &; 899 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 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 : 197 ( 0 ^; 197 !; 0 ?; 197 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(v_k_decl,type,
v_k: $i > $i ).
thf(v_f_decl,type,
v_f: $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_x_decl,type,
v_x: $i ).
thf(v_g_decl,type,
v_g: $i > $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_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_less_decl,type,
c_less: $i > $i > $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__add_decl,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(c_plus_decl,type,
c_plus: $i > $i > $i > $i ).
thf(class_OrderedGroup_Oab__group__add_decl,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(c_uminus_decl,type,
c_uminus: $i > $i > $i ).
thf(20,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(69,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)],[20]) ).
thf(3,negated_conjecture,
t_b @ class_Ring__and__Field_Oordered__idom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
thf(30,plain,
t_b @ class_Ring__and__Field_Oordered__idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(27,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(86,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(87,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(cnf,[status(esa)],[86]) ).
thf(383,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)],[30,87]) ).
thf(384,plain,
! [A: $i] :
( ( ( t_b @ class_Ring__and__Field_Oordered__idom )
!= ( A @ class_Ring__and__Field_Oordered__idom ) )
| ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(simp,[status(thm)],[383]) ).
thf(385,plain,
t_b @ class_OrderedGroup_Ocomm__monoid__add,
inference(pattern_uni,[status(thm)],[384:[bind(A,$thf( t_b ))]]) ).
thf(1,negated_conjecture,
! [A: $i] : ( t_b @ ( A @ v_f @ ( A @ v_k @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(28,plain,
! [A: $i] : ( t_b @ ( A @ v_f @ ( A @ v_k @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,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(38,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)],[7]) ).
thf(39,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)],[38]) ).
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_g @ ( v_x @ v_k @ c_minus ) ) @ c_Orderings_Omax ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(29,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_g @ ( v_x @ v_k @ c_minus ) ) @ c_Orderings_Omax ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(31,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_g @ ( v_x @ v_k @ c_minus ) ) @ c_Orderings_Omax ) ) @ c_lessequals ) ) ),
inference(polarity_switch,[status(thm)],[29]) ).
thf(98,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( D @ 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_g @ ( v_x @ v_k @ c_minus ) ) @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) )
| ~ $true
| ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(paramod_ordered,[status(thm)],[39,31]) ).
thf(99,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( D @ 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_g @ ( v_x @ v_k @ c_minus ) ) @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) )
| ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(simp,[status(thm)],[98]) ).
thf(100,plain,
! [A: $i] :
( ~ ( t_b @ ( A @ ( t_b @ ( c_0 @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_k @ c_minus ) ) @ c_Orderings_Omax ) ) @ c_lessequals ) ) )
| ~ ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) @ c_HOL_Oabs ) @ ( A @ c_lessequals ) ) )
| ~ ( t_b @ class_Orderings_Oorder ) ),
inference(pattern_uni,[status(thm)],[99:[bind(A,$thf( t_b )),bind(B,$thf( B )),bind(C,$thf( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) @ c_HOL_Oabs ) )),bind(D,$thf( t_b @ ( c_0 @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_k @ c_minus ) ) @ c_Orderings_Omax ) ) ))]]) ).
thf(113,plain,
! [A: $i] :
( ~ ( t_b @ ( A @ ( t_b @ ( c_0 @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_k @ c_minus ) ) @ c_Orderings_Omax ) ) @ c_lessequals ) ) )
| ~ ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) @ c_HOL_Oabs ) @ ( A @ c_lessequals ) ) )
| ~ ( t_b @ class_Orderings_Oorder ) ),
inference(simp,[status(thm)],[100]) ).
thf(180,plain,
! [B: $i,A: $i] :
( ( ( t_b @ ( A @ v_f @ ( A @ v_k @ c_lessequals ) ) )
!= ( t_b @ ( B @ ( t_b @ ( c_0 @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_k @ c_minus ) ) @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) )
| ~ $true
| ~ ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) @ c_HOL_Oabs ) @ ( B @ c_lessequals ) ) )
| ~ ( t_b @ class_Orderings_Oorder ) ),
inference(paramod_ordered,[status(thm)],[28,113]) ).
thf(181,plain,
! [B: $i,A: $i] :
( ( ( t_b @ ( A @ v_f @ ( A @ v_k @ c_lessequals ) ) )
!= ( t_b @ ( B @ ( t_b @ ( c_0 @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_k @ c_minus ) ) @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) )
| ~ ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) @ c_HOL_Oabs ) @ ( B @ c_lessequals ) ) )
| ~ ( t_b @ class_Orderings_Oorder ) ),
inference(simp,[status(thm)],[180]) ).
thf(199,plain,
! [B: $i,A: $i] :
( ( t_b != t_b )
| ( ( A @ v_f )
!= B )
| ( ( A @ v_k )
!= ( t_b @ ( c_0 @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_k @ c_minus ) ) @ c_Orderings_Omax ) ) ) )
| ~ ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) @ c_HOL_Oabs ) @ ( B @ c_lessequals ) ) )
| ~ ( t_b @ class_Orderings_Oorder ) ),
inference(simp,[status(thm)],[181]) ).
thf(205,plain,
! [A: $i] :
( ( ( A @ v_k )
!= ( t_b @ ( c_0 @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_k @ c_minus ) ) @ c_Orderings_Omax ) ) ) )
| ~ ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) @ c_HOL_Oabs ) @ ( A @ v_f @ c_lessequals ) ) )
| ~ ( t_b @ class_Orderings_Oorder ) ),
inference(simp,[status(thm)],[199]) ).
thf(24,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(79,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(80,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(cnf,[status(esa)],[79]) ).
thf(328,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)],[30,80]) ).
thf(329,plain,
! [A: $i] :
( ( ( t_b @ class_Ring__and__Field_Oordered__idom )
!= ( A @ class_Ring__and__Field_Oordered__idom ) )
| ( A @ class_LOrder_Ojoin__semilorder ) ),
inference(simp,[status(thm)],[328]) ).
thf(330,plain,
t_b @ class_LOrder_Ojoin__semilorder,
inference(pattern_uni,[status(thm)],[329:[bind(A,$thf( t_b ))]]) ).
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(32,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(33,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
inference(cnf,[status(esa)],[32]) ).
thf(364,plain,
! [A: $i] :
( ( ( t_b @ class_LOrder_Ojoin__semilorder )
!= ( A @ class_LOrder_Ojoin__semilorder ) )
| ( A @ class_Orderings_Oorder )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[330,33]) ).
thf(365,plain,
! [A: $i] :
( ( ( t_b @ class_LOrder_Ojoin__semilorder )
!= ( A @ class_LOrder_Ojoin__semilorder ) )
| ( A @ class_Orderings_Oorder ) ),
inference(simp,[status(thm)],[364]) ).
thf(366,plain,
t_b @ class_Orderings_Oorder,
inference(pattern_uni,[status(thm)],[365:[bind(A,$thf( t_b ))]]) ).
thf(371,plain,
! [A: $i] :
( ( ( A @ v_k )
!= ( t_b @ ( c_0 @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_k @ c_minus ) ) @ c_Orderings_Omax ) ) ) )
| ~ ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) @ c_HOL_Oabs ) @ ( A @ v_f @ c_lessequals ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[205,366]) ).
thf(372,plain,
! [A: $i] :
( ( ( A @ v_k )
!= ( t_b @ ( c_0 @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_k @ c_minus ) ) @ c_Orderings_Omax ) ) ) )
| ~ ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) @ c_HOL_Oabs ) @ ( A @ v_f @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[371]) ).
thf(17,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(61,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)],[17]) ).
thf(10,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(44,plain,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(45,plain,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(cnf,[status(esa)],[44]) ).
thf(317,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)],[30,45]) ).
thf(318,plain,
! [A: $i] :
( ( ( t_b @ class_Ring__and__Field_Oordered__idom )
!= ( A @ class_Ring__and__Field_Oordered__idom ) )
| ( A @ class_Orderings_Olinorder ) ),
inference(simp,[status(thm)],[317]) ).
thf(319,plain,
t_b @ class_Orderings_Olinorder,
inference(pattern_uni,[status(thm)],[318:[bind(A,$thf( t_b ))]]) ).
thf(8,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(40,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)],[8]) ).
thf(41,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)],[40]) ).
thf(321,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)],[319,41]) ).
thf(322,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)],[321]) ).
thf(323,plain,
! [B: $i,A: $i] :
( ( t_b @ ( A @ ( B @ c_lessequals ) ) )
| ( t_b @ ( B @ ( A @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[322:[bind(A,$thf( t_b ))]]) ).
thf(324,plain,
! [B: $i,A: $i] :
( ( t_b @ ( A @ ( B @ c_lessequals ) ) )
| ( t_b @ ( B @ ( A @ c_less ) ) ) ),
inference(simp,[status(thm)],[323]) ).
thf(22,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(73,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)],[22]) ).
thf(373,plain,
! [A: $i] :
( ~ ( t_b @ ( A @ ( t_b @ ( c_0 @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_k @ c_minus ) ) @ c_Orderings_Omax ) ) @ c_lessequals ) ) )
| ~ ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) @ c_HOL_Oabs ) @ ( A @ c_lessequals ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[113,366]) ).
thf(374,plain,
! [A: $i] :
( ~ ( t_b @ ( A @ ( t_b @ ( c_0 @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_k @ c_minus ) ) @ c_Orderings_Omax ) ) @ c_lessequals ) ) )
| ~ ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) @ c_HOL_Oabs ) @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[373]) ).
thf(26,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(83,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)],[26]) ).
thf(9,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(42,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)],[9]) ).
thf(43,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(cnf,[status(esa)],[42]) ).
thf(169,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)],[30,43]) ).
thf(170,plain,
! [A: $i] :
( ( ( t_b @ class_Ring__and__Field_Oordered__idom )
!= ( A @ class_Ring__and__Field_Oordered__idom ) )
| ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(simp,[status(thm)],[169]) ).
thf(171,plain,
t_b @ class_OrderedGroup_Olordered__ab__group__abs,
inference(pattern_uni,[status(thm)],[170:[bind(A,$thf( t_b ))]]) ).
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(36,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(37,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(cnf,[status(esa)],[36]) ).
thf(172,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)],[171,37]) ).
thf(173,plain,
! [A: $i] :
( ( ( t_b @ class_OrderedGroup_Olordered__ab__group__abs )
!= ( A @ class_OrderedGroup_Olordered__ab__group__abs ) )
| ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(simp,[status(thm)],[172]) ).
thf(174,plain,
t_b @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
inference(pattern_uni,[status(thm)],[173:[bind(A,$thf( t_b ))]]) ).
thf(11,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(46,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)],[11]) ).
thf(15,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(57,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)],[15]) ).
thf(163,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)],[43,37]) ).
thf(164,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)],[163]) ).
thf(165,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(pattern_uni,[status(thm)],[164:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( c_0 @ c_plus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(cnf,[status(esa)],[46]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ( ( A @ ( B @ ( c_0 @ c_plus ) ) )
= B ) ),
inference(lifteq,[status(thm)],[47]) ).
thf(390,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)],[385,48]) ).
thf(391,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)],[390]) ).
thf(392,plain,
! [A: $i] :
( ( t_b @ ( A @ ( c_0 @ c_plus ) ) )
= A ),
inference(pattern_uni,[status(thm)],[391:[bind(A,$thf( t_b ))]]) ).
thf(393,plain,
! [A: $i] :
( ( t_b @ ( A @ ( c_0 @ c_plus ) ) )
= A ),
inference(simp,[status(thm)],[392]) ).
thf(18,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(64,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)],[18]) ).
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(34,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(16,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( C @ ( B @ c_minus ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__le__0__iff__le_1) ).
thf(59,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( C @ ( B @ c_minus ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(21,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(71,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(14,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(54,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)],[14]) ).
thf(12,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(49,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)],[12]) ).
thf(25,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(81,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)],[25]) ).
thf(23,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(76,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)],[23]) ).
thf(88,plain,
! [A: $i] :
( ( ( t_b @ ( A @ v_f @ ( A @ v_k @ 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_g @ ( v_x @ v_k @ c_minus ) ) @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,31]) ).
thf(89,plain,
! [A: $i] :
( ( t_b @ ( A @ v_f @ ( A @ v_k @ 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_g @ ( v_x @ v_k @ c_minus ) ) @ c_Orderings_Omax ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[88]) ).
thf(90,plain,
! [A: $i] :
( ( t_b != t_b )
| ( ( A @ v_f )
!= ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) @ c_HOL_Oabs ) ) )
| ( ( A @ v_k )
!= ( t_b @ ( c_0 @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_k @ c_minus ) ) @ c_Orderings_Omax ) ) ) ) ),
inference(simp,[status(thm)],[89]) ).
thf(91,plain,
! [A: $i] :
( ( ( A @ v_f )
!= ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) @ c_HOL_Oabs ) ) )
| ( ( A @ v_k )
!= ( t_b @ ( c_0 @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_k @ c_minus ) ) @ c_Orderings_Omax ) ) ) ) ),
inference(simp,[status(thm)],[90]) ).
thf(19,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(66,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)],[19]) ).
thf(35,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(cnf,[status(esa)],[34]) ).
thf(72,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(cnf,[status(esa)],[71]) ).
thf(325,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)],[30,72]) ).
thf(326,plain,
! [A: $i] :
( ( ( t_b @ class_Ring__and__Field_Oordered__idom )
!= ( A @ class_Ring__and__Field_Oordered__idom ) )
| ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(simp,[status(thm)],[325]) ).
thf(327,plain,
t_b @ class_OrderedGroup_Oab__group__add,
inference(pattern_uni,[status(thm)],[326:[bind(A,$thf( t_b ))]]) ).
thf(175,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)],[171,35]) ).
thf(176,plain,
! [A: $i] :
( ( ( t_b @ class_OrderedGroup_Olordered__ab__group__abs )
!= ( A @ class_OrderedGroup_Olordered__ab__group__abs ) )
| ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(simp,[status(thm)],[175]) ).
thf(177,plain,
t_b @ class_OrderedGroup_Opordered__ab__group__add,
inference(pattern_uni,[status(thm)],[176:[bind(A,$thf( t_b ))]]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_uminus ) @ ( B @ c_minus ) ) )
= ( A @ ( C @ ( B @ c_plus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__minus__eq__add_0) ).
thf(51,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_uminus ) @ ( B @ c_minus ) ) )
= ( A @ ( C @ ( B @ c_plus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(2353,plain,
$false,
inference(e,[status(thm)],[69,385,372,61,366,324,73,374,87,79,83,174,42,37,46,57,29,165,33,28,38,393,41,45,64,32,34,44,59,71,54,49,86,81,76,39,91,66,330,80,35,48,327,177,31,72,43,319,40,171,36,30,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA022-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % 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
% 0.11/0.39 % Computer : n011.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sat Sep 26 22:06:15 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 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
% 0.88/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.27/1.18 % [INFO] Parsing done (192ms).
% 1.27/1.19 % [INFO] Running in sequential loop mode.
% 2.16/1.60 % [INFO] eprover registered as external prover.
% 2.16/1.61 % [INFO] Scanning for conjecture ...
% 2.35/1.72 % [INFO] Found a conjecture (or negated_conjecture) and 24 axioms. Running axiom selection ...
% 2.35/1.80 % [INFO] Axiom selection finished. Selected 24 axioms (removed 0 axioms).
% 2.54/1.84 % [INFO] Problem is propositional (TPTP CNF).
% 2.54/1.84 % [INFO] Type checking passed.
% 2.54/1.85 % [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 ...
% 21.20/5.53 % External prover 'e' found a proof!
% 21.20/5.53 % [INFO] Killing All external provers ...
% 21.20/5.53 % Time passed: 4997ms (effective reasoning time: 4337ms)
% 21.20/5.54 % Axioms used in derivation (24): cls_OrderedGroup_Odiff__self_0, cls_OrderedGroup_Odiff__le__0__iff__le_1, cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2, cls_OrderedGroup_Ocompare__rls__2_0, cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0, clsrel_OrderedGroup_Olordered__ab__group__abs_6, cls_OrderedGroup_Oabs__of__nonpos_0, cls_OrderedGroup_Ocompare__rls__8_1, clsrel_Ring__and__Field_Oordered__idom_4, 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_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, cls_OrderedGroup_Odiff__minus__eq__add_0, clsrel_Ring__and__Field_Oordered__idom_33
% 21.20/5.54 % No. of inferences in proof: 119
% 21.20/5.54 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 4997 ms resp. 4337 ms w/o parsing
% 18.64/5.62 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 18.64/5.62 % [INFO] Killing All external provers ...
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