%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA031-2 : 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 : n017.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 06:50:20 AM UTC 2026
% Result : Unsatisfiable 28.20s 7.33s
% Output : Refutation 23.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 108 ( 36 unt; 0 typ; 0 def)
% Number of atoms : 262 ( 140 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 1929 ( 145 ~; 118 |; 0 &;1666 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 5 con; 0-3 aty)
% Number of variables : 250 ( 0 ^; 250 !; 0 ?; 250 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_HOL_Oabs_decl,type,
c_HOL_Oabs: $i > $i > $i ).
thf(v_b_decl,type,
v_b: $i > $i ).
thf(t_b_decl,type,
t_b: $i ).
thf(c_times_decl,type,
c_times: $i > $i > $i > $i ).
thf(v_c_decl,type,
v_c: $i ).
thf(v_g_decl,type,
v_g: $i > $i ).
thf(v_x_decl,type,
v_x: $i > $i ).
thf(v_f_decl,type,
v_f: $i > $i ).
thf(class_Ring__and__Field_Oordered__idom_decl,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__abs_decl,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).
thf(c_0_decl,type,
c_0: $i ).
thf(class_OrderedGroup_Osemigroup__mult_decl,type,
class_OrderedGroup_Osemigroup__mult: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__mult_decl,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
thf(class_Ring__and__Field_Opordered__semiring_decl,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
thf(3,negated_conjecture,
t_b @ class_Ring__and__Field_Oordered__idom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
thf(14,plain,
t_b @ class_Ring__and__Field_Oordered__idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,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(32,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)],[11]) ).
thf(33,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(cnf,[status(esa)],[32]) ).
thf(70,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)],[14,33]) ).
thf(71,plain,
! [A: $i] :
( ( ( t_b @ class_Ring__and__Field_Oordered__idom )
!= ( A @ class_Ring__and__Field_Oordered__idom ) )
| ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(simp,[status(thm)],[70]) ).
thf(72,plain,
t_b @ class_OrderedGroup_Olordered__ab__group__abs,
inference(pattern_uni,[status(thm)],[71:[bind(A,$thf( t_b ))]]) ).
thf(4,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(16,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)],[4]) ).
thf(17,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)],[16]) ).
thf(77,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)],[72,17]) ).
thf(78,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)],[77]) ).
thf(79,plain,
! [A: $i] : ( t_b @ ( t_b @ ( A @ c_HOL_Oabs ) @ ( c_0 @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[78:[bind(A,$thf( t_b ))]]) ).
thf(80,plain,
! [A: $i] : ( t_b @ ( t_b @ ( A @ c_HOL_Oabs ) @ ( c_0 @ c_lessequals ) ) ),
inference(simp,[status(thm)],[79]) ).
thf(2,negated_conjecture,
! [A: $i] :
~ ( t_b @ ( t_b @ ( t_b @ ( t_b @ ( A @ v_x @ v_g @ c_HOL_Oabs ) @ ( t_b @ ( A @ v_x @ v_f @ c_HOL_Oabs ) @ c_times ) ) @ ( A @ c_times ) ) @ ( t_b @ ( t_b @ ( A @ v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( A @ v_x @ v_b @ c_HOL_Oabs ) @ c_times ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(13,plain,
! [A: $i] :
~ ( t_b @ ( t_b @ ( t_b @ ( t_b @ ( A @ v_x @ v_g @ c_HOL_Oabs ) @ ( t_b @ ( A @ v_x @ v_f @ c_HOL_Oabs ) @ c_times ) ) @ ( A @ c_times ) ) @ ( t_b @ ( t_b @ ( A @ v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( A @ v_x @ v_b @ c_HOL_Oabs ) @ c_times ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,plain,
! [A: $i] :
~ ( t_b @ ( t_b @ ( t_b @ ( t_b @ ( A @ v_x @ v_g @ c_HOL_Oabs ) @ ( t_b @ ( A @ v_x @ v_f @ c_HOL_Oabs ) @ c_times ) ) @ ( A @ c_times ) ) @ ( t_b @ ( t_b @ ( A @ v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( A @ v_x @ v_b @ c_HOL_Oabs ) @ c_times ) ) @ c_lessequals ) ) ),
inference(polarity_switch,[status(thm)],[13]) ).
thf(81,plain,
! [B: $i,A: $i] :
( ( ( t_b @ ( t_b @ ( A @ c_HOL_Oabs ) @ ( c_0 @ c_lessequals ) ) )
!= ( t_b @ ( t_b @ ( t_b @ ( t_b @ ( B @ v_x @ v_g @ c_HOL_Oabs ) @ ( t_b @ ( B @ v_x @ v_f @ c_HOL_Oabs ) @ c_times ) ) @ ( B @ c_times ) ) @ ( t_b @ ( t_b @ ( B @ v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( B @ v_x @ v_b @ c_HOL_Oabs ) @ c_times ) ) @ c_lessequals ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[80,15]) ).
thf(82,plain,
! [B: $i,A: $i] :
( ( t_b @ ( t_b @ ( A @ c_HOL_Oabs ) @ ( c_0 @ c_lessequals ) ) )
!= ( t_b @ ( t_b @ ( t_b @ ( t_b @ ( B @ v_x @ v_g @ c_HOL_Oabs ) @ ( t_b @ ( B @ v_x @ v_f @ c_HOL_Oabs ) @ c_times ) ) @ ( B @ c_times ) ) @ ( t_b @ ( t_b @ ( B @ v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( B @ v_x @ v_b @ c_HOL_Oabs ) @ c_times ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[81]) ).
thf(83,plain,
! [B: $i,A: $i] :
( ( t_b != t_b )
| ( ( t_b @ ( A @ c_HOL_Oabs ) )
!= ( t_b @ ( t_b @ ( t_b @ ( B @ v_x @ v_g @ c_HOL_Oabs ) @ ( t_b @ ( B @ v_x @ v_f @ c_HOL_Oabs ) @ c_times ) ) @ ( B @ c_times ) ) ) )
| ( ( t_b @ ( t_b @ ( B @ v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( B @ v_x @ v_b @ c_HOL_Oabs ) @ c_times ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[82]) ).
thf(84,plain,
! [B: $i,A: $i] :
( ( ( t_b @ ( A @ c_HOL_Oabs ) )
!= ( t_b @ ( t_b @ ( t_b @ ( B @ v_x @ v_g @ c_HOL_Oabs ) @ ( t_b @ ( B @ v_x @ v_f @ c_HOL_Oabs ) @ c_times ) ) @ ( B @ c_times ) ) ) )
| ( ( t_b @ ( t_b @ ( B @ v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( B @ v_x @ v_b @ c_HOL_Oabs ) @ c_times ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[83]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
thf(30,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(31,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(cnf,[status(esa)],[30]) ).
thf(63,plain,
! [A: $i] :
( ( ( t_b @ class_Ring__and__Field_Oordered__idom )
!= ( A @ class_Ring__and__Field_Oordered__idom ) )
| ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,31]) ).
thf(64,plain,
! [A: $i] :
( ( ( t_b @ class_Ring__and__Field_Oordered__idom )
!= ( A @ class_Ring__and__Field_Oordered__idom ) )
| ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(simp,[status(thm)],[63]) ).
thf(65,plain,
t_b @ class_Ring__and__Field_Opordered__semiring,
inference(pattern_uni,[status(thm)],[64:[bind(A,$thf( t_b ))]]) ).
thf(1,negated_conjecture,
! [A: $i] : ( t_b @ ( t_b @ ( t_b @ ( A @ v_g @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ ( t_b @ ( A @ v_b @ c_HOL_Oabs ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(12,plain,
! [A: $i] : ( t_b @ ( t_b @ ( t_b @ ( A @ v_g @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ ( t_b @ ( A @ v_b @ c_HOL_Oabs ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( ( t_b @ ( t_b @ ( t_b @ ( A @ v_g @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ ( t_b @ ( A @ v_b @ c_HOL_Oabs ) @ c_lessequals ) ) )
!= ( t_b @ ( t_b @ ( t_b @ ( t_b @ ( B @ v_x @ v_g @ c_HOL_Oabs ) @ ( t_b @ ( B @ v_x @ v_f @ c_HOL_Oabs ) @ c_times ) ) @ ( B @ c_times ) ) @ ( t_b @ ( t_b @ ( B @ v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( B @ v_x @ v_b @ c_HOL_Oabs ) @ c_times ) ) @ c_lessequals ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,15]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( t_b @ ( t_b @ ( t_b @ ( A @ v_g @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ ( t_b @ ( A @ v_b @ c_HOL_Oabs ) @ c_lessequals ) ) )
!= ( t_b @ ( t_b @ ( t_b @ ( t_b @ ( B @ v_x @ v_g @ c_HOL_Oabs ) @ ( t_b @ ( B @ v_x @ v_f @ c_HOL_Oabs ) @ c_times ) ) @ ( B @ c_times ) ) @ ( t_b @ ( t_b @ ( B @ v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( B @ v_x @ v_b @ c_HOL_Oabs ) @ c_times ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[34]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( t_b != t_b )
| ( ( t_b @ ( t_b @ ( A @ v_g @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) )
!= ( t_b @ ( t_b @ ( t_b @ ( B @ v_x @ v_g @ c_HOL_Oabs ) @ ( t_b @ ( B @ v_x @ v_f @ c_HOL_Oabs ) @ c_times ) ) @ ( B @ c_times ) ) ) )
| ( ( t_b @ ( A @ v_b @ c_HOL_Oabs ) )
!= ( t_b @ ( t_b @ ( B @ v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( B @ v_x @ v_b @ c_HOL_Oabs ) @ c_times ) ) ) ) ),
inference(simp,[status(thm)],[35]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( ( t_b @ ( t_b @ ( A @ v_g @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) )
!= ( t_b @ ( t_b @ ( t_b @ ( B @ v_x @ v_g @ c_HOL_Oabs ) @ ( t_b @ ( B @ v_x @ v_f @ c_HOL_Oabs ) @ c_times ) ) @ ( B @ c_times ) ) ) )
| ( ( t_b @ ( A @ v_b @ c_HOL_Oabs ) )
!= ( t_b @ ( t_b @ ( B @ v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( B @ v_x @ v_b @ c_HOL_Oabs ) @ c_times ) ) ) ) ),
inference(simp,[status(thm)],[36]) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( t_b != t_b )
| ( ( t_b @ ( A @ v_g @ c_HOL_Oabs ) )
!= ( t_b @ ( t_b @ ( B @ v_x @ v_g @ c_HOL_Oabs ) @ ( t_b @ ( B @ v_x @ v_f @ c_HOL_Oabs ) @ c_times ) ) ) )
| ( v_c != B )
| ( ( t_b @ ( A @ v_b @ c_HOL_Oabs ) )
!= ( t_b @ ( t_b @ ( B @ v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( B @ v_x @ v_b @ c_HOL_Oabs ) @ c_times ) ) ) ) ),
inference(simp,[status(thm)],[37]) ).
thf(42,plain,
! [A: $i] :
( ( ( t_b @ ( A @ v_g @ c_HOL_Oabs ) )
!= ( t_b @ ( t_b @ ( v_c @ v_x @ v_g @ c_HOL_Oabs ) @ ( t_b @ ( v_c @ v_x @ v_f @ c_HOL_Oabs ) @ c_times ) ) ) )
| ( ( t_b @ ( A @ v_b @ c_HOL_Oabs ) )
!= ( t_b @ ( t_b @ ( v_c @ v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( v_c @ v_x @ v_b @ c_HOL_Oabs ) @ c_times ) ) ) ) ),
inference(simp,[status(thm)],[41]) ).
thf(43,plain,
! [A: $i] :
( ( ( t_b @ ( t_b @ ( v_c @ v_x @ v_g @ c_HOL_Oabs ) @ ( t_b @ ( v_c @ v_x @ v_f @ c_HOL_Oabs ) @ c_times ) ) )
!= ( t_b @ ( t_b @ ( v_c @ v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( v_c @ v_x @ v_b @ c_HOL_Oabs ) @ c_times ) ) ) )
| ( ( t_b @ ( A @ v_g @ c_HOL_Oabs ) )
!= ( t_b @ ( A @ v_b @ c_HOL_Oabs ) ) )
| ( ( t_b @ ( A @ v_b @ c_HOL_Oabs ) )
!= ( t_b @ ( t_b @ ( v_c @ v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( v_c @ v_x @ v_b @ c_HOL_Oabs ) @ c_times ) ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[42]) ).
thf(46,plain,
! [A: $i] :
( ( t_b != t_b )
| ( ( t_b @ ( v_c @ v_x @ v_f @ c_HOL_Oabs ) )
!= ( t_b @ ( v_c @ v_x @ v_g @ c_HOL_Oabs ) ) )
| ( ( t_b @ ( v_c @ v_x @ v_f @ c_HOL_Oabs ) )
!= ( t_b @ ( v_c @ v_x @ v_b @ c_HOL_Oabs ) ) )
| ( t_b != t_b )
| ( ( A @ v_g )
!= ( A @ v_b ) )
| ( ( t_b @ ( A @ v_b @ c_HOL_Oabs ) )
!= ( t_b @ ( t_b @ ( v_c @ v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( v_c @ v_x @ v_b @ c_HOL_Oabs ) @ c_times ) ) ) ) ),
inference(simp,[status(thm)],[43]) ).
thf(49,plain,
! [A: $i] :
( ( ( t_b @ ( v_c @ v_x @ v_f @ c_HOL_Oabs ) )
!= ( t_b @ ( v_c @ v_x @ v_g @ c_HOL_Oabs ) ) )
| ( ( t_b @ ( v_c @ v_x @ v_f @ c_HOL_Oabs ) )
!= ( t_b @ ( v_c @ v_x @ v_b @ c_HOL_Oabs ) ) )
| ( ( A @ v_g )
!= ( A @ v_b ) )
| ( ( t_b @ ( A @ v_b @ c_HOL_Oabs ) )
!= ( t_b @ ( t_b @ ( v_c @ v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( v_c @ v_x @ v_b @ c_HOL_Oabs ) @ c_times ) ) ) ) ),
inference(simp,[status(thm)],[46]) ).
thf(50,plain,
! [A: $i] :
( ( ( t_b @ ( v_c @ v_x @ v_f @ c_HOL_Oabs ) )
!= ( t_b @ ( v_c @ v_x @ v_g @ c_HOL_Oabs ) ) )
| ( t_b != t_b )
| ( ( v_c @ v_x @ v_f )
!= ( v_c @ v_x @ v_b ) )
| ( ( A @ v_g )
!= ( A @ v_b ) )
| ( ( t_b @ ( A @ v_b @ c_HOL_Oabs ) )
!= ( t_b @ ( t_b @ ( v_c @ v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( v_c @ v_x @ v_b @ c_HOL_Oabs ) @ c_times ) ) ) ) ),
inference(simp,[status(thm)],[49]) ).
thf(53,plain,
! [A: $i] :
( ( ( t_b @ ( v_c @ v_x @ v_f @ c_HOL_Oabs ) )
!= ( t_b @ ( v_c @ v_x @ v_g @ c_HOL_Oabs ) ) )
| ( ( v_c @ v_x @ v_f )
!= ( v_c @ v_x @ v_b ) )
| ( ( A @ v_g )
!= ( A @ v_b ) )
| ( ( t_b @ ( A @ v_b @ c_HOL_Oabs ) )
!= ( t_b @ ( t_b @ ( v_c @ v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( v_c @ v_x @ v_b @ c_HOL_Oabs ) @ c_times ) ) ) ) ),
inference(simp,[status(thm)],[50]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_17) ).
thf(26,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(27,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(cnf,[status(esa)],[26]) ).
thf(38,plain,
! [A: $i] :
( ( ( t_b @ class_Ring__and__Field_Oordered__idom )
!= ( A @ class_Ring__and__Field_Oordered__idom ) )
| ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,27]) ).
thf(39,plain,
! [A: $i] :
( ( ( t_b @ class_Ring__and__Field_Oordered__idom )
!= ( A @ class_Ring__and__Field_Oordered__idom ) )
| ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(simp,[status(thm)],[38]) ).
thf(40,plain,
t_b @ class_OrderedGroup_Oab__semigroup__mult,
inference(pattern_uni,[status(thm)],[39:[bind(A,$thf( t_b ))]]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_times ) ) )
= ( A @ ( B @ ( C @ c_times ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omult__ac__2_0) ).
thf(21,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_times ) ) )
= ( A @ ( B @ ( C @ c_times ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(22,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_times ) ) )
= ( A @ ( B @ ( C @ c_times ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(cnf,[status(esa)],[21]) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ( ( A @ ( C @ ( B @ c_times ) ) )
= ( A @ ( B @ ( C @ c_times ) ) ) ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(978,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_b @ class_OrderedGroup_Oab__semigroup__mult )
!= ( A @ class_OrderedGroup_Oab__semigroup__mult ) )
| ~ $true
| ( ( A @ ( C @ ( B @ c_times ) ) )
= ( A @ ( B @ ( C @ c_times ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[40,23]) ).
thf(979,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_b @ class_OrderedGroup_Oab__semigroup__mult )
!= ( A @ class_OrderedGroup_Oab__semigroup__mult ) )
| ( ( A @ ( C @ ( B @ c_times ) ) )
= ( A @ ( B @ ( C @ c_times ) ) ) ) ),
inference(simp,[status(thm)],[978]) ).
thf(980,plain,
! [B: $i,A: $i] :
( ( t_b @ ( B @ ( A @ c_times ) ) )
= ( t_b @ ( A @ ( B @ c_times ) ) ) ),
inference(pattern_uni,[status(thm)],[979:[bind(A,$thf( t_b ))]]) ).
thf(1033,plain,
! [B: $i,A: $i] :
( ( t_b @ ( B @ ( A @ c_times ) ) )
= ( t_b @ ( A @ ( B @ c_times ) ) ) ),
inference(simp,[status(thm)],[980]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_21) ).
thf(28,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(29,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(cnf,[status(esa)],[28]) ).
thf(60,plain,
! [A: $i] :
( ( ( t_b @ class_Ring__and__Field_Oordered__idom )
!= ( A @ class_Ring__and__Field_Oordered__idom ) )
| ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,29]) ).
thf(61,plain,
! [A: $i] :
( ( ( t_b @ class_Ring__and__Field_Oordered__idom )
!= ( A @ class_Ring__and__Field_Oordered__idom ) )
| ( A @ class_OrderedGroup_Osemigroup__mult ) ),
inference(simp,[status(thm)],[60]) ).
thf(62,plain,
t_b @ class_OrderedGroup_Osemigroup__mult,
inference(pattern_uni,[status(thm)],[61:[bind(A,$thf( t_b ))]]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_times ) ) @ c_times ) ) )
= ( A @ ( A @ ( D @ ( C @ c_times ) ) @ ( B @ c_times ) ) ) )
| ~ ( A @ class_OrderedGroup_Osemigroup__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omult__ac__1_0) ).
thf(18,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_times ) ) @ c_times ) ) )
= ( A @ ( A @ ( D @ ( C @ c_times ) ) @ ( B @ c_times ) ) ) )
| ~ ( A @ class_OrderedGroup_Osemigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(19,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_times ) ) @ c_times ) ) )
= ( A @ ( A @ ( D @ ( C @ c_times ) ) @ ( B @ c_times ) ) ) )
| ~ ( A @ class_OrderedGroup_Osemigroup__mult ) ),
inference(cnf,[status(esa)],[18]) ).
thf(20,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ class_OrderedGroup_Osemigroup__mult )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_times ) ) @ c_times ) ) )
= ( A @ ( A @ ( D @ ( C @ c_times ) ) @ ( B @ c_times ) ) ) ) ),
inference(lifteq,[status(thm)],[19]) ).
thf(106,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_b @ class_OrderedGroup_Osemigroup__mult )
!= ( A @ class_OrderedGroup_Osemigroup__mult ) )
| ~ $true
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_times ) ) @ c_times ) ) )
= ( A @ ( A @ ( D @ ( C @ c_times ) ) @ ( B @ c_times ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[62,20]) ).
thf(107,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_b @ class_OrderedGroup_Osemigroup__mult )
!= ( A @ class_OrderedGroup_Osemigroup__mult ) )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_times ) ) @ c_times ) ) )
= ( A @ ( A @ ( D @ ( C @ c_times ) ) @ ( B @ c_times ) ) ) ) ),
inference(simp,[status(thm)],[106]) ).
thf(108,plain,
! [C: $i,B: $i,A: $i] :
( ( t_b @ ( C @ ( t_b @ ( B @ ( A @ c_times ) ) @ c_times ) ) )
= ( t_b @ ( t_b @ ( C @ ( B @ c_times ) ) @ ( A @ c_times ) ) ) ),
inference(pattern_uni,[status(thm)],[107:[bind(A,$thf( t_b ))]]) ).
thf(150,plain,
! [C: $i,B: $i,A: $i] :
( ( t_b @ ( C @ ( t_b @ ( B @ ( A @ c_times ) ) @ c_times ) ) )
= ( t_b @ ( t_b @ ( C @ ( B @ c_times ) ) @ ( A @ c_times ) ) ) ),
inference(simp,[status(thm)],[108]) ).
thf(1065,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( t_b @ ( B @ ( A @ c_times ) ) )
!= ( t_b @ ( E @ ( t_b @ ( D @ ( C @ c_times ) ) @ c_times ) ) ) )
| ( ( t_b @ ( A @ ( B @ c_times ) ) )
= ( t_b @ ( t_b @ ( E @ ( D @ c_times ) ) @ ( C @ c_times ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1033,150]) ).
thf(1066,plain,
! [C: $i,B: $i,A: $i] :
( ( t_b @ ( t_b @ ( C @ ( B @ c_times ) ) @ ( A @ c_times ) ) )
= ( t_b @ ( t_b @ ( A @ ( C @ c_times ) ) @ ( B @ c_times ) ) ) ),
inference(pattern_uni,[status(thm)],[1065:[bind(A,$thf( t_b @ ( G @ ( F @ c_times ) ) )),bind(B,$thf( B )),bind(C,$thf( F )),bind(D,$thf( G )),bind(E,$thf( B ))]]) ).
thf(1224,plain,
! [C: $i,B: $i,A: $i] :
( ( t_b @ ( t_b @ ( C @ ( B @ c_times ) ) @ ( A @ c_times ) ) )
= ( t_b @ ( t_b @ ( A @ ( C @ c_times ) ) @ ( B @ c_times ) ) ) ),
inference(simp,[status(thm)],[1066]) ).
thf(1320,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( t_b @ ( A @ ( B @ c_times ) ) )
!= ( t_b @ ( E @ ( D @ c_times ) ) ) )
| ( ( t_b @ ( t_b @ ( B @ ( A @ c_times ) ) @ ( C @ c_times ) ) )
= ( t_b @ ( t_b @ ( C @ ( E @ c_times ) ) @ ( D @ c_times ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1033,1224]) ).
thf(1321,plain,
! [C: $i,B: $i,A: $i] :
( ( t_b @ ( t_b @ ( B @ ( A @ c_times ) ) @ ( C @ c_times ) ) )
= ( t_b @ ( t_b @ ( C @ ( A @ c_times ) ) @ ( B @ c_times ) ) ) ),
inference(pattern_uni,[status(thm)],[1320:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( A ))]]) ).
thf(188,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_b @ ( C @ ( t_b @ ( B @ ( A @ c_times ) ) @ c_times ) ) )
!= ( t_b @ ( t_b @ ( D @ v_g @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) ) )
| ( t_b @ ( t_b @ ( t_b @ ( C @ ( B @ c_times ) ) @ ( A @ c_times ) ) @ ( t_b @ ( D @ v_b @ c_HOL_Oabs ) @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[150,12]) ).
thf(206,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( t_b != t_b )
| ( C
!= ( t_b @ ( D @ v_g @ c_HOL_Oabs ) ) )
| ( ( t_b @ ( B @ ( A @ c_times ) ) )
!= v_c )
| ( t_b @ ( t_b @ ( t_b @ ( C @ ( B @ c_times ) ) @ ( A @ c_times ) ) @ ( t_b @ ( D @ v_b @ c_HOL_Oabs ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[188]) ).
thf(235,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_b @ ( B @ ( A @ c_times ) ) )
!= v_c )
| ( t_b @ ( t_b @ ( t_b @ ( t_b @ ( C @ v_g @ c_HOL_Oabs ) @ ( B @ c_times ) ) @ ( A @ c_times ) ) @ ( t_b @ ( C @ v_b @ c_HOL_Oabs ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[206]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_times ) ) @ ( A @ ( B @ ( D @ c_times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0) ).
thf(24,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_times ) ) @ ( A @ ( B @ ( D @ c_times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(25,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_times ) ) @ ( A @ ( B @ ( D @ c_times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(cnf,[status(esa)],[24]) ).
thf(171,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( t_b @ ( C @ ( t_b @ ( B @ ( A @ c_times ) ) @ c_times ) ) )
!= ( t_b @ ( E @ ( D @ c_times ) ) ) )
| ( ( t_b @ ( F @ ( t_b @ ( t_b @ ( C @ ( B @ c_times ) ) @ ( A @ c_times ) ) @ c_times ) ) )
= ( t_b @ ( t_b @ ( F @ ( E @ c_times ) ) @ ( D @ c_times ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[150,150]) ).
thf(172,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( t_b @ ( B @ ( t_b @ ( t_b @ ( A @ ( D @ c_times ) ) @ ( C @ c_times ) ) @ c_times ) ) )
= ( t_b @ ( t_b @ ( B @ ( A @ c_times ) ) @ ( t_b @ ( D @ ( C @ c_times ) ) @ c_times ) ) ) ),
inference(pattern_uni,[status(thm)],[171:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( t_b @ ( H @ ( G @ c_times ) ) )),bind(E,$thf( C )),bind(F,$thf( F ))]]) ).
thf(253,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( t_b @ ( B @ ( t_b @ ( t_b @ ( A @ ( D @ c_times ) ) @ ( C @ c_times ) ) @ c_times ) ) )
= ( t_b @ ( t_b @ ( B @ ( A @ c_times ) ) @ ( t_b @ ( D @ ( C @ c_times ) ) @ c_times ) ) ) ),
inference(simp,[status(thm)],[172]) ).
thf(257,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( t_b @ ( t_b @ ( B @ ( t_b @ ( A @ ( D @ c_times ) ) @ c_times ) ) @ ( C @ c_times ) ) )
= ( t_b @ ( t_b @ ( t_b @ ( B @ ( A @ c_times ) ) @ ( D @ c_times ) ) @ ( C @ c_times ) ) ) ),
inference(rewrite,[status(thm)],[253,150]) ).
thf(1067,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( t_b @ ( B @ ( A @ c_times ) ) )
!= ( t_b @ ( D @ ( C @ c_times ) ) ) )
| ( ( t_b @ ( E @ ( t_b @ ( A @ ( B @ c_times ) ) @ c_times ) ) )
= ( t_b @ ( t_b @ ( E @ ( D @ c_times ) ) @ ( C @ c_times ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1033,150]) ).
thf(1068,plain,
! [C: $i,B: $i,A: $i] :
( ( t_b @ ( C @ ( t_b @ ( A @ ( B @ c_times ) ) @ c_times ) ) )
= ( t_b @ ( t_b @ ( C @ ( B @ c_times ) ) @ ( A @ c_times ) ) ) ),
inference(pattern_uni,[status(thm)],[1067:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(1225,plain,
! [C: $i,B: $i,A: $i] :
( ( t_b @ ( C @ ( t_b @ ( A @ ( B @ c_times ) ) @ c_times ) ) )
= ( t_b @ ( t_b @ ( C @ ( B @ c_times ) ) @ ( A @ c_times ) ) ) ),
inference(simp,[status(thm)],[1068]) ).
thf(1703,plain,
! [C: $i,B: $i,A: $i] :
( ( t_b @ ( t_b @ ( C @ ( A @ c_times ) ) @ ( B @ c_times ) ) )
= ( t_b @ ( t_b @ ( C @ ( B @ c_times ) ) @ ( A @ c_times ) ) ) ),
inference(rewrite,[status(thm)],[1225,150]) ).
thf(261,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( t_b @ ( t_b @ ( B @ ( t_b @ ( A @ ( D @ c_times ) ) @ c_times ) ) @ ( C @ c_times ) ) )
!= ( t_b @ ( F @ ( E @ c_times ) ) ) )
| ( ( t_b @ ( G @ ( t_b @ ( t_b @ ( t_b @ ( B @ ( A @ c_times ) ) @ ( D @ c_times ) ) @ ( C @ c_times ) ) @ c_times ) ) )
= ( t_b @ ( t_b @ ( G @ ( F @ c_times ) ) @ ( E @ c_times ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[257,150]) ).
thf(262,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( t_b @ ( B @ ( t_b @ ( t_b @ ( t_b @ ( C @ ( E @ c_times ) ) @ ( D @ c_times ) ) @ ( A @ c_times ) ) @ c_times ) ) )
= ( t_b @ ( t_b @ ( B @ ( t_b @ ( C @ ( t_b @ ( E @ ( D @ c_times ) ) @ c_times ) ) @ c_times ) ) @ ( A @ c_times ) ) ) ),
inference(pattern_uni,[status(thm)],[261:[bind(A,$thf( L )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( K )),bind(E,$thf( C )),bind(F,$thf( t_b @ ( I @ ( t_b @ ( L @ ( K @ c_times ) ) @ c_times ) ) )),bind(G,$thf( G ))]]) ).
thf(335,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( t_b @ ( B @ ( t_b @ ( t_b @ ( t_b @ ( C @ ( E @ c_times ) ) @ ( D @ c_times ) ) @ ( A @ c_times ) ) @ c_times ) ) )
= ( t_b @ ( t_b @ ( B @ ( t_b @ ( C @ ( t_b @ ( E @ ( D @ c_times ) ) @ c_times ) ) @ c_times ) ) @ ( A @ c_times ) ) ) ),
inference(simp,[status(thm)],[262]) ).
thf(372,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( t_b @ ( t_b @ ( B @ ( t_b @ ( t_b @ ( C @ ( E @ c_times ) ) @ ( D @ c_times ) ) @ c_times ) ) @ ( A @ c_times ) ) )
= ( t_b @ ( t_b @ ( t_b @ ( B @ ( C @ c_times ) ) @ ( t_b @ ( E @ ( D @ c_times ) ) @ c_times ) ) @ ( A @ c_times ) ) ) ),
inference(rewrite,[status(thm)],[335,257,150]) ).
thf(1312,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( t_b @ ( B @ ( A @ c_times ) ) )
!= ( t_b @ ( E @ ( D @ c_times ) ) ) )
| ( ( t_b @ ( t_b @ ( A @ ( B @ c_times ) ) @ ( C @ c_times ) ) )
= ( t_b @ ( t_b @ ( C @ ( E @ c_times ) ) @ ( D @ c_times ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1033,1224]) ).
thf(1313,plain,
! [C: $i,B: $i,A: $i] :
( ( t_b @ ( t_b @ ( A @ ( B @ c_times ) ) @ ( C @ c_times ) ) )
= ( t_b @ ( t_b @ ( C @ ( B @ c_times ) ) @ ( A @ c_times ) ) ) ),
inference(pattern_uni,[status(thm)],[1312:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(51,plain,
! [A: $i] :
( ( t_b != t_b )
| ( ( v_c @ v_x @ v_f )
!= ( v_c @ v_x @ v_g ) )
| ( ( t_b @ ( v_c @ v_x @ v_f @ c_HOL_Oabs ) )
!= ( t_b @ ( v_c @ v_x @ v_b @ c_HOL_Oabs ) ) )
| ( ( A @ v_g )
!= ( A @ v_b ) )
| ( ( t_b @ ( A @ v_b @ c_HOL_Oabs ) )
!= ( t_b @ ( t_b @ ( v_c @ v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( v_c @ v_x @ v_b @ c_HOL_Oabs ) @ c_times ) ) ) ) ),
inference(simp,[status(thm)],[49]) ).
thf(54,plain,
! [A: $i] :
( ( ( v_c @ v_x @ v_f )
!= ( v_c @ v_x @ v_g ) )
| ( ( t_b @ ( v_c @ v_x @ v_f @ c_HOL_Oabs ) )
!= ( t_b @ ( v_c @ v_x @ v_b @ c_HOL_Oabs ) ) )
| ( ( A @ v_g )
!= ( A @ v_b ) )
| ( ( t_b @ ( A @ v_b @ c_HOL_Oabs ) )
!= ( t_b @ ( t_b @ ( v_c @ v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( v_c @ v_x @ v_b @ c_HOL_Oabs ) @ c_times ) ) ) ) ),
inference(simp,[status(thm)],[51]) ).
thf(263,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( t_b @ ( C @ ( t_b @ ( B @ ( A @ c_times ) ) @ c_times ) ) )
!= ( t_b @ ( D @ ( G @ c_times ) ) ) )
| ( ( t_b @ ( t_b @ ( E @ ( t_b @ ( t_b @ ( C @ ( B @ c_times ) ) @ ( A @ c_times ) ) @ c_times ) ) @ ( F @ c_times ) ) )
= ( t_b @ ( t_b @ ( t_b @ ( E @ ( D @ c_times ) ) @ ( G @ c_times ) ) @ ( F @ c_times ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[150,257]) ).
thf(264,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( t_b @ ( t_b @ ( B @ ( t_b @ ( t_b @ ( A @ ( E @ c_times ) ) @ ( D @ c_times ) ) @ c_times ) ) @ ( C @ c_times ) ) )
= ( t_b @ ( t_b @ ( t_b @ ( B @ ( A @ c_times ) ) @ ( t_b @ ( E @ ( D @ c_times ) ) @ c_times ) ) @ ( C @ c_times ) ) ) ),
inference(pattern_uni,[status(thm)],[263:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( C )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( t_b @ ( I @ ( H @ c_times ) ) ))]]) ).
thf(338,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( t_b @ ( t_b @ ( B @ ( t_b @ ( t_b @ ( A @ ( E @ c_times ) ) @ ( D @ c_times ) ) @ c_times ) ) @ ( C @ c_times ) ) )
= ( t_b @ ( t_b @ ( t_b @ ( B @ ( A @ c_times ) ) @ ( t_b @ ( E @ ( D @ c_times ) ) @ c_times ) ) @ ( C @ c_times ) ) ) ),
inference(simp,[status(thm)],[264]) ).
thf(611,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( t_b @ ( t_b @ ( t_b @ ( B @ ( t_b @ ( A @ ( E @ c_times ) ) @ c_times ) ) @ ( D @ c_times ) ) @ ( C @ c_times ) ) )
= ( t_b @ ( t_b @ ( t_b @ ( t_b @ ( B @ ( A @ c_times ) ) @ ( E @ c_times ) ) @ ( D @ c_times ) ) @ ( C @ c_times ) ) ) ),
inference(rewrite,[status(thm)],[338,257]) ).
thf(1090,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_b @ ( B @ ( A @ c_times ) ) )
!= ( t_b @ ( t_b @ ( v_c @ v_x @ v_g @ c_HOL_Oabs ) @ ( t_b @ ( v_c @ v_x @ v_f @ c_HOL_Oabs ) @ c_times ) ) ) )
| ( ( t_b @ ( A @ ( B @ c_times ) ) )
!= ( t_b @ ( C @ v_g @ c_HOL_Oabs ) ) )
| ( ( t_b @ ( C @ v_b @ c_HOL_Oabs ) )
!= ( t_b @ ( t_b @ ( v_c @ v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( v_c @ v_x @ v_b @ c_HOL_Oabs ) @ c_times ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1033,42]) ).
thf(1091,plain,
! [A: $i] :
( ( ( t_b @ ( t_b @ ( v_c @ v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( v_c @ v_x @ v_g @ c_HOL_Oabs ) @ c_times ) ) )
!= ( t_b @ ( A @ v_g @ c_HOL_Oabs ) ) )
| ( ( t_b @ ( A @ v_b @ c_HOL_Oabs ) )
!= ( t_b @ ( t_b @ ( v_c @ v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( v_c @ v_x @ v_b @ c_HOL_Oabs ) @ c_times ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1090:[bind(A,$thf( t_b @ ( v_c @ v_x @ v_f @ c_HOL_Oabs ) )),bind(B,$thf( t_b @ ( v_c @ v_x @ v_g @ c_HOL_Oabs ) )),bind(C,$thf( C ))]]) ).
thf(1240,plain,
! [A: $i] :
( ( ( t_b @ ( t_b @ ( v_c @ v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( v_c @ v_x @ v_g @ c_HOL_Oabs ) @ c_times ) ) )
!= ( t_b @ ( A @ v_g @ c_HOL_Oabs ) ) )
| ( ( t_b @ ( A @ v_b @ c_HOL_Oabs ) )
!= ( t_b @ ( t_b @ ( v_c @ v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( v_c @ v_x @ v_b @ c_HOL_Oabs ) @ c_times ) ) ) ) ),
inference(simp,[status(thm)],[1091]) ).
thf(52,plain,
! [A: $i] :
( ( t_b != t_b )
| ( ( v_c @ v_x @ v_f )
!= ( v_c @ v_x @ v_g ) )
| ( t_b != t_b )
| ( ( v_c @ v_x @ v_f )
!= ( v_c @ v_x @ v_b ) )
| ( ( A @ v_g )
!= ( A @ v_b ) )
| ( ( t_b @ ( A @ v_b @ c_HOL_Oabs ) )
!= ( t_b @ ( t_b @ ( v_c @ v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( v_c @ v_x @ v_b @ c_HOL_Oabs ) @ c_times ) ) ) ) ),
inference(simp,[status(thm)],[49]) ).
thf(55,plain,
! [A: $i] :
( ( ( v_c @ v_x @ v_f )
!= ( v_c @ v_x @ v_g ) )
| ( ( v_c @ v_x @ v_f )
!= ( v_c @ v_x @ v_b ) )
| ( ( A @ v_g )
!= ( A @ v_b ) )
| ( ( t_b @ ( A @ v_b @ c_HOL_Oabs ) )
!= ( t_b @ ( t_b @ ( v_c @ v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( v_c @ v_x @ v_b @ c_HOL_Oabs ) @ c_times ) ) ) ) ),
inference(simp,[status(thm)],[52]) ).
thf(44,plain,
! [A: $i] :
( ( ( t_b @ ( t_b @ ( v_c @ v_x @ v_g @ c_HOL_Oabs ) @ ( t_b @ ( v_c @ v_x @ v_f @ c_HOL_Oabs ) @ c_times ) ) )
!= ( t_b @ ( t_b @ ( v_c @ v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( v_c @ v_x @ v_b @ c_HOL_Oabs ) @ c_times ) ) ) )
| ( t_b != t_b )
| ( ( A @ v_g )
!= ( A @ v_b ) )
| ( ( t_b @ ( A @ v_b @ c_HOL_Oabs ) )
!= ( t_b @ ( t_b @ ( v_c @ v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( v_c @ v_x @ v_b @ c_HOL_Oabs ) @ c_times ) ) ) ) ),
inference(simp,[status(thm)],[43]) ).
thf(47,plain,
! [A: $i] :
( ( ( t_b @ ( t_b @ ( v_c @ v_x @ v_g @ c_HOL_Oabs ) @ ( t_b @ ( v_c @ v_x @ v_f @ c_HOL_Oabs ) @ c_times ) ) )
!= ( t_b @ ( t_b @ ( v_c @ v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( v_c @ v_x @ v_b @ c_HOL_Oabs ) @ c_times ) ) ) )
| ( ( A @ v_g )
!= ( A @ v_b ) )
| ( ( t_b @ ( A @ v_b @ c_HOL_Oabs ) )
!= ( t_b @ ( t_b @ ( v_c @ v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( v_c @ v_x @ v_b @ c_HOL_Oabs ) @ c_times ) ) ) ) ),
inference(simp,[status(thm)],[44]) ).
thf(4139,plain,
$false,
inference(e,[status(thm)],[84,65,53,13,27,80,1321,235,30,1033,42,24,25,257,37,1703,14,372,1313,20,29,28,21,33,32,17,12,54,611,49,1224,18,150,16,31,72,1240,40,26,55,23,47,15,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA031-2 : 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
% 0.14/0.41 % Computer : n017.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sat Sep 26 22:03:19 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 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
% 0.88/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.28/1.17 % [INFO] Parsing done (184ms).
% 1.28/1.19 % [INFO] Running in sequential loop mode.
% 1.87/1.58 % [INFO] eprover registered as external prover.
% 1.87/1.59 % [INFO] Scanning for conjecture ...
% 2.06/1.68 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 2.24/1.73 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 2.24/1.74 % [INFO] Problem is propositional (TPTP CNF).
% 2.24/1.75 % [INFO] Type checking passed.
% 2.24/1.75 % [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 ...
% 28.20/7.32 % External prover 'e' found a proof!
% 28.20/7.32 % [INFO] Killing All external provers ...
% 28.20/7.33 % Time passed: 6771ms (effective reasoning time: 6134ms)
% 28.20/7.33 % Axioms used in derivation (8): cls_OrderedGroup_Oabs__ge__zero_0, clsrel_Ring__and__Field_Oordered__idom_17, cls_OrderedGroup_Omult__ac__2_0, clsrel_Ring__and__Field_Oordered__idom_21, clsrel_Ring__and__Field_Oordered__idom_42, cls_OrderedGroup_Omult__ac__1_0, clsrel_Ring__and__Field_Oordered__idom_50, cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0
% 28.20/7.33 % No. of inferences in proof: 108
% 28.20/7.33 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 6771 ms resp. 6134 ms w/o parsing
% 23.53/7.42 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 23.53/7.42 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------