%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ANA034-10 : TPTP v9.0.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 04:59:14 AM UTC 2025
% Result : Unsatisfiable 0.14s 0.40s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 70
% Syntax : Number of formulae : 213 ( 160 unt; 0 typ; 0 def)
% Number of atoms : 288 ( 276 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 93 ( 29 ~; 25 |; 0 &)
% ( 39 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of FOOLs : 11 ( 11 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 6 con; 0-4 aty)
% Number of variables : 301 ( 275 !; 0 ?; 301 :)
% Comments :
%------------------------------------------------------------------------------
tff(true_type,type,
true: $i ).
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $i ).
tff(t_b_type,type,
t_b: $i ).
tff(c_times_type,type,
c_times: ( $i * $i * $i ) > $i ).
tff(c_HOL_Oabs_type,type,
c_HOL_Oabs: ( $i * $i ) > $i ).
tff(v_g_type,type,
v_g: $i > $i ).
tff(v_x_type,type,
v_x: $i ).
tff(v_f_type,type,
v_f: $i > $i ).
tff(v_ca_type,type,
v_ca: $i ).
tff(v_c_type,type,
v_c: $i ).
tff(v_b_type,type,
v_b: $i > $i ).
tff(v_a_type,type,
v_a: $i > $i ).
tff(ifeq_type,type,
ifeq: ( $i * $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Opordered__semiring_type,type,
class_Ring__and__Field_Opordered__semiring: $i > $i ).
tff(c_0_type,type,
c_0: $i ).
tff(class_OrderedGroup_Olordered__ab__group__abs_type,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $i ).
tff(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $i ).
tff(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $i ).
tff(c_less_type,type,
c_less: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Opordered__cancel__semiring_type,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $i ).
tff(ifeq2_type,type,
ifeq2: ( $i * $i * $i * $i ) > $i ).
tff(1,plain,
^ [V_c: $i,V_d: $i,V_b: $i,V_a: $i,T_a: $i] :
refl(( ( ifeq(c_lessequals(c_0,V_b,T_a),true,ifeq(c_lessequals(c_0,V_c,T_a),true,ifeq(c_lessequals(V_a,V_b,T_a),true,ifeq(c_lessequals(V_c,V_d,T_a),true,ifeq(class_Ring__and__Field_Opordered__semiring(T_a),true,c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_d,T_a),T_a),true),true),true),true),true) = true )
<=> ( ifeq(c_lessequals(c_0,V_b,T_a),true,ifeq(c_lessequals(c_0,V_c,T_a),true,ifeq(c_lessequals(V_a,V_b,T_a),true,ifeq(c_lessequals(V_c,V_d,T_a),true,ifeq(class_Ring__and__Field_Opordered__semiring(T_a),true,c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_d,T_a),T_a),true),true),true),true),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V_c: $i,V_d: $i,V_b: $i,V_a: $i,T_a: $i] : ( ifeq(c_lessequals(c_0,V_b,T_a),true,ifeq(c_lessequals(c_0,V_c,T_a),true,ifeq(c_lessequals(V_a,V_b,T_a),true,ifeq(c_lessequals(V_c,V_d,T_a),true,ifeq(class_Ring__and__Field_Opordered__semiring(T_a),true,c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_d,T_a),T_a),true),true),true),true),true) = true )
<=> ! [V_c: $i,V_d: $i,V_b: $i,V_a: $i,T_a: $i] : ( ifeq(c_lessequals(c_0,V_b,T_a),true,ifeq(c_lessequals(c_0,V_c,T_a),true,ifeq(c_lessequals(V_a,V_b,T_a),true,ifeq(c_lessequals(V_c,V_d,T_a),true,ifeq(class_Ring__and__Field_Opordered__semiring(T_a),true,c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_d,T_a),T_a),true),true),true),true),true) = true ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_c: $i,V_d: $i,V_b: $i,V_a: $i,T_a: $i] : ( ifeq(c_lessequals(c_0,V_b,T_a),true,ifeq(c_lessequals(c_0,V_c,T_a),true,ifeq(c_lessequals(V_a,V_b,T_a),true,ifeq(c_lessequals(V_c,V_d,T_a),true,ifeq(class_Ring__and__Field_Opordered__semiring(T_a),true,c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_d,T_a),T_a),true),true),true),true),true) = true )
<=> ! [V_c: $i,V_d: $i,V_b: $i,V_a: $i,T_a: $i] : ( ifeq(c_lessequals(c_0,V_b,T_a),true,ifeq(c_lessequals(c_0,V_c,T_a),true,ifeq(c_lessequals(V_a,V_b,T_a),true,ifeq(c_lessequals(V_c,V_d,T_a),true,ifeq(class_Ring__and__Field_Opordered__semiring(T_a),true,c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_d,T_a),T_a),true),true),true),true),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [V_c: $i,V_d: $i,V_b: $i,V_a: $i,T_a: $i] : ( ifeq(c_lessequals(c_0,V_b,T_a),true,ifeq(c_lessequals(c_0,V_c,T_a),true,ifeq(c_lessequals(V_a,V_b,T_a),true,ifeq(c_lessequals(V_c,V_d,T_a),true,ifeq(class_Ring__and__Field_Opordered__semiring(T_a),true,c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_d,T_a),T_a),true),true),true),true),true) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__mono_0) ).
tff(5,plain,
! [V_c: $i,V_d: $i,V_b: $i,V_a: $i,T_a: $i] : ( ifeq(c_lessequals(c_0,V_b,T_a),true,ifeq(c_lessequals(c_0,V_c,T_a),true,ifeq(c_lessequals(V_a,V_b,T_a),true,ifeq(c_lessequals(V_c,V_d,T_a),true,ifeq(class_Ring__and__Field_Opordered__semiring(T_a),true,c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_d,T_a),T_a),true),true),true),true),true) = true ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V_c: $i,V_d: $i,V_b: $i,V_a: $i,T_a: $i] : ( ifeq(c_lessequals(c_0,V_b,T_a),true,ifeq(c_lessequals(c_0,V_c,T_a),true,ifeq(c_lessequals(V_a,V_b,T_a),true,ifeq(c_lessequals(V_c,V_d,T_a),true,ifeq(class_Ring__and__Field_Opordered__semiring(T_a),true,c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_d,T_a),T_a),true),true),true),true),true) = true ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V_c: $i,V_d: $i,V_b: $i,V_a: $i,T_a: $i] : ( ifeq(c_lessequals(c_0,V_b,T_a),true,ifeq(c_lessequals(c_0,V_c,T_a),true,ifeq(c_lessequals(V_a,V_b,T_a),true,ifeq(c_lessequals(V_c,V_d,T_a),true,ifeq(class_Ring__and__Field_Opordered__semiring(T_a),true,c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_d,T_a),T_a),true),true),true),true),true) = true ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V_c: $i,V_d: $i,V_b: $i,V_a: $i,T_a: $i] : ( ifeq(c_lessequals(c_0,V_b,T_a),true,ifeq(c_lessequals(c_0,V_c,T_a),true,ifeq(c_lessequals(V_a,V_b,T_a),true,ifeq(c_lessequals(V_c,V_d,T_a),true,ifeq(class_Ring__and__Field_Opordered__semiring(T_a),true,c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_d,T_a),T_a),true),true),true),true),true) = true )
| ( ifeq(c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true,ifeq(c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b),true,ifeq(c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true,ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),true,ifeq(class_Ring__and__Field_Opordered__semiring(t_b),true,c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true),true),true),true),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
ifeq(c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true,ifeq(c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b),true,ifeq(c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true,ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),true,ifeq(class_Ring__and__Field_Opordered__semiring(t_b),true,c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true),true),true),true),true) = true,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ifeq(A,A,B,C) = B )
<=> ( ifeq(A,A,B,C) = B ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).
tff(14,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b),true) = c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
ifeq(true,true,c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b),true) = c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,class_OrderedGroup_Olordered__ab__group__abs(t_b),true) = class_OrderedGroup_Olordered__ab__group__abs(t_b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(20,plain,
ifeq(true,true,class_OrderedGroup_Olordered__ab__group__abs(t_b),true) = class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(unit_resolution,[status(thm)],[19,16]) ).
tff(21,plain,
( ( class_Ring__and__Field_Oordered__idom(t_b) = true )
<=> ( class_Ring__and__Field_Oordered__idom(t_b) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
class_Ring__and__Field_Oordered__idom(t_b) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
tff(23,plain,
class_Ring__and__Field_Oordered__idom(t_b) = true,
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
true = class_Ring__and__Field_Oordered__idom(t_b),
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
ifeq(true,true,class_OrderedGroup_Olordered__ab__group__abs(t_b),true) = ifeq(class_Ring__and__Field_Oordered__idom(t_b),true,class_OrderedGroup_Olordered__ab__group__abs(t_b),true),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
ifeq(class_Ring__and__Field_Oordered__idom(t_b),true,class_OrderedGroup_Olordered__ab__group__abs(t_b),true) = ifeq(true,true,class_OrderedGroup_Olordered__ab__group__abs(t_b),true),
inference(symmetry,[status(thm)],[25]) ).
tff(27,plain,
^ [T: $i] :
refl(( ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_OrderedGroup_Olordered__ab__group__abs(T),true) = true )
<=> ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_OrderedGroup_Olordered__ab__group__abs(T),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_OrderedGroup_Olordered__ab__group__abs(T),true) = true )
<=> ! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_OrderedGroup_Olordered__ab__group__abs(T),true) = true ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_OrderedGroup_Olordered__ab__group__abs(T),true) = true )
<=> ! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_OrderedGroup_Olordered__ab__group__abs(T),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_OrderedGroup_Olordered__ab__group__abs(T),true) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
tff(31,plain,
! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_OrderedGroup_Olordered__ab__group__abs(T),true) = true ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_OrderedGroup_Olordered__ab__group__abs(T),true) = true ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_OrderedGroup_Olordered__ab__group__abs(T),true) = true ),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,plain,
( ~ ! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_OrderedGroup_Olordered__ab__group__abs(T),true) = true )
| ( ifeq(class_Ring__and__Field_Oordered__idom(t_b),true,class_OrderedGroup_Olordered__ab__group__abs(t_b),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(35,plain,
ifeq(class_Ring__and__Field_Oordered__idom(t_b),true,class_OrderedGroup_Olordered__ab__group__abs(t_b),true) = true,
inference(unit_resolution,[status(thm)],[34,33]) ).
tff(36,plain,
true = ifeq(class_Ring__and__Field_Oordered__idom(t_b),true,class_OrderedGroup_Olordered__ab__group__abs(t_b),true),
inference(symmetry,[status(thm)],[35]) ).
tff(37,plain,
true = class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(transitivity,[status(thm)],[36,26,20]) ).
tff(38,plain,
ifeq(true,true,c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b),true) = ifeq(class_OrderedGroup_Olordered__ab__group__abs(t_b),true,c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b),true),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(t_b),true,c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b),true) = ifeq(true,true,c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b),true),
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
^ [V_a: $i,T_a: $i] :
refl(( ( ifeq(class_OrderedGroup_Olordered__ab__group__abs(T_a),true,c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a),true) = true )
<=> ( ifeq(class_OrderedGroup_Olordered__ab__group__abs(T_a),true,c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(41,plain,
( ! [V_a: $i,T_a: $i] : ( ifeq(class_OrderedGroup_Olordered__ab__group__abs(T_a),true,c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a),true) = true )
<=> ! [V_a: $i,T_a: $i] : ( ifeq(class_OrderedGroup_Olordered__ab__group__abs(T_a),true,c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a),true) = true ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
( ! [V_a: $i,T_a: $i] : ( ifeq(class_OrderedGroup_Olordered__ab__group__abs(T_a),true,c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a),true) = true )
<=> ! [V_a: $i,T_a: $i] : ( ifeq(class_OrderedGroup_Olordered__ab__group__abs(T_a),true,c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,axiom,
! [V_a: $i,T_a: $i] : ( ifeq(class_OrderedGroup_Olordered__ab__group__abs(T_a),true,c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a),true) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
tff(44,plain,
! [V_a: $i,T_a: $i] : ( ifeq(class_OrderedGroup_Olordered__ab__group__abs(T_a),true,c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a),true) = true ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [V_a: $i,T_a: $i] : ( ifeq(class_OrderedGroup_Olordered__ab__group__abs(T_a),true,c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a),true) = true ),
inference(skolemize,[status(sab)],[44]) ).
tff(46,plain,
! [V_a: $i,T_a: $i] : ( ifeq(class_OrderedGroup_Olordered__ab__group__abs(T_a),true,c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a),true) = true ),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
( ~ ! [V_a: $i,T_a: $i] : ( ifeq(class_OrderedGroup_Olordered__ab__group__abs(T_a),true,c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a),true) = true )
| ( ifeq(class_OrderedGroup_Olordered__ab__group__abs(t_b),true,c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(t_b),true,c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b),true) = true,
inference(unit_resolution,[status(thm)],[47,46]) ).
tff(49,plain,
true = ifeq(class_OrderedGroup_Olordered__ab__group__abs(t_b),true,c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b),true),
inference(symmetry,[status(thm)],[48]) ).
tff(50,plain,
true = c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b),
inference(transitivity,[status(thm)],[49,39,18]) ).
tff(51,plain,
ifeq(true,true,ifeq(c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true,ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),true,ifeq(class_Ring__and__Field_Opordered__semiring(t_b),true,c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true),true),true),true) = ifeq(c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b),true,ifeq(c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true,ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),true,ifeq(class_Ring__and__Field_Opordered__semiring(t_b),true,c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true),true),true),true),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,ifeq(c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true,ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),true,ifeq(class_Ring__and__Field_Opordered__semiring(t_b),true,c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true),true),true),true) = ifeq(c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true,ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),true,ifeq(class_Ring__and__Field_Opordered__semiring(t_b),true,c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true),true),true) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(53,plain,
ifeq(true,true,ifeq(c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true,ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),true,ifeq(class_Ring__and__Field_Opordered__semiring(t_b),true,c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true),true),true),true) = ifeq(c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true,ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),true,ifeq(class_Ring__and__Field_Opordered__semiring(t_b),true,c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true),true),true),
inference(unit_resolution,[status(thm)],[52,16]) ).
tff(54,plain,
ifeq(c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true,ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),true,ifeq(class_Ring__and__Field_Opordered__semiring(t_b),true,c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true),true),true) = ifeq(true,true,ifeq(c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true,ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),true,ifeq(class_Ring__and__Field_Opordered__semiring(t_b),true,c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true),true),true),true),
inference(symmetry,[status(thm)],[53]) ).
tff(55,plain,
ifeq(c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true,ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),true,ifeq(class_Ring__and__Field_Opordered__semiring(t_b),true,c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true),true),true) = ifeq(c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b),true,ifeq(c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true,ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),true,ifeq(class_Ring__and__Field_Opordered__semiring(t_b),true,c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true),true),true),true),
inference(transitivity,[status(thm)],[54,51]) ).
tff(56,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true) = c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(57,plain,
ifeq(true,true,c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true) = c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),
inference(unit_resolution,[status(thm)],[56,16]) ).
tff(58,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,class_Orderings_Oorder(t_b),true) = class_Orderings_Oorder(t_b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(59,plain,
ifeq(true,true,class_Orderings_Oorder(t_b),true) = class_Orderings_Oorder(t_b),
inference(unit_resolution,[status(thm)],[58,16]) ).
tff(60,plain,
ifeq(true,true,class_Orderings_Oorder(t_b),true) = ifeq(class_OrderedGroup_Olordered__ab__group__abs(t_b),true,class_Orderings_Oorder(t_b),true),
inference(monotonicity,[status(thm)],[37]) ).
tff(61,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(t_b),true,class_Orderings_Oorder(t_b),true) = ifeq(true,true,class_Orderings_Oorder(t_b),true),
inference(symmetry,[status(thm)],[60]) ).
tff(62,plain,
^ [T: $i] :
refl(( ( ifeq(class_OrderedGroup_Olordered__ab__group__abs(T),true,class_Orderings_Oorder(T),true) = true )
<=> ( ifeq(class_OrderedGroup_Olordered__ab__group__abs(T),true,class_Orderings_Oorder(T),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(63,plain,
( ! [T: $i] : ( ifeq(class_OrderedGroup_Olordered__ab__group__abs(T),true,class_Orderings_Oorder(T),true) = true )
<=> ! [T: $i] : ( ifeq(class_OrderedGroup_Olordered__ab__group__abs(T),true,class_Orderings_Oorder(T),true) = true ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,plain,
( ! [T: $i] : ( ifeq(class_OrderedGroup_Olordered__ab__group__abs(T),true,class_Orderings_Oorder(T),true) = true )
<=> ! [T: $i] : ( ifeq(class_OrderedGroup_Olordered__ab__group__abs(T),true,class_Orderings_Oorder(T),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,axiom,
! [T: $i] : ( ifeq(class_OrderedGroup_Olordered__ab__group__abs(T),true,class_Orderings_Oorder(T),true) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).
tff(66,plain,
! [T: $i] : ( ifeq(class_OrderedGroup_Olordered__ab__group__abs(T),true,class_Orderings_Oorder(T),true) = true ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
! [T: $i] : ( ifeq(class_OrderedGroup_Olordered__ab__group__abs(T),true,class_Orderings_Oorder(T),true) = true ),
inference(skolemize,[status(sab)],[66]) ).
tff(68,plain,
! [T: $i] : ( ifeq(class_OrderedGroup_Olordered__ab__group__abs(T),true,class_Orderings_Oorder(T),true) = true ),
inference(modus_ponens,[status(thm)],[67,63]) ).
tff(69,plain,
( ~ ! [T: $i] : ( ifeq(class_OrderedGroup_Olordered__ab__group__abs(T),true,class_Orderings_Oorder(T),true) = true )
| ( ifeq(class_OrderedGroup_Olordered__ab__group__abs(t_b),true,class_Orderings_Oorder(t_b),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(70,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(t_b),true,class_Orderings_Oorder(t_b),true) = true,
inference(unit_resolution,[status(thm)],[69,68]) ).
tff(71,plain,
true = ifeq(class_OrderedGroup_Olordered__ab__group__abs(t_b),true,class_Orderings_Oorder(t_b),true),
inference(symmetry,[status(thm)],[70]) ).
tff(72,plain,
true = class_Orderings_Oorder(t_b),
inference(transitivity,[status(thm)],[71,61,59]) ).
tff(73,plain,
ifeq(true,true,c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true) = ifeq(class_Orderings_Oorder(t_b),true,c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true),
inference(monotonicity,[status(thm)],[72]) ).
tff(74,plain,
ifeq(class_Orderings_Oorder(t_b),true,c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true) = ifeq(true,true,c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true),
inference(symmetry,[status(thm)],[73]) ).
tff(75,plain,
( ~ ! [V_a: $i,T_a: $i] : ( ifeq(class_OrderedGroup_Olordered__ab__group__abs(T_a),true,c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a),true) = true )
| ( ifeq(class_OrderedGroup_Olordered__ab__group__abs(t_b),true,c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(76,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(t_b),true,c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b),true) = true,
inference(unit_resolution,[status(thm)],[75,46]) ).
tff(77,plain,
ifeq(true,true,c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b),true) = ifeq(class_OrderedGroup_Olordered__ab__group__abs(t_b),true,c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b),true),
inference(monotonicity,[status(thm)],[37]) ).
tff(78,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b),true) = c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(79,plain,
ifeq(true,true,c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b),true) = c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b),
inference(unit_resolution,[status(thm)],[78,16]) ).
tff(80,plain,
c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b) = ifeq(true,true,c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b),true),
inference(symmetry,[status(thm)],[79]) ).
tff(81,plain,
c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b) = class_Orderings_Oorder(t_b),
inference(transitivity,[status(thm)],[80,77,76,71,61,59]) ).
tff(82,plain,
ifeq(c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b),true,c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true) = ifeq(class_Orderings_Oorder(t_b),true,c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true),
inference(monotonicity,[status(thm)],[81]) ).
tff(83,plain,
ifeq(class_Orderings_Oorder(t_b),true,c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true) = ifeq(c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b),true,c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true),
inference(symmetry,[status(thm)],[82]) ).
tff(84,plain,
c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) = ifeq(true,true,c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true),
inference(symmetry,[status(thm)],[57]) ).
tff(85,plain,
c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) = ifeq(c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b),true,c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true),
inference(transitivity,[status(thm)],[84,73,83]) ).
tff(86,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,c_lessequals(c_0,v_c,t_b),true) = c_lessequals(c_0,v_c,t_b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(87,plain,
ifeq(true,true,c_lessequals(c_0,v_c,t_b),true) = c_lessequals(c_0,v_c,t_b),
inference(unit_resolution,[status(thm)],[86,16]) ).
tff(88,plain,
ifeq(true,true,c_lessequals(c_0,v_c,t_b),true) = ifeq(class_Orderings_Oorder(t_b),true,c_lessequals(c_0,v_c,t_b),true),
inference(monotonicity,[status(thm)],[72]) ).
tff(89,plain,
ifeq(class_Orderings_Oorder(t_b),true,c_lessequals(c_0,v_c,t_b),true) = ifeq(true,true,c_lessequals(c_0,v_c,t_b),true),
inference(symmetry,[status(thm)],[88]) ).
tff(90,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,ifeq(class_Orderings_Oorder(t_b),true,c_lessequals(c_0,v_c,t_b),true),true) = ifeq(class_Orderings_Oorder(t_b),true,c_lessequals(c_0,v_c,t_b),true) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(91,plain,
ifeq(true,true,ifeq(class_Orderings_Oorder(t_b),true,c_lessequals(c_0,v_c,t_b),true),true) = ifeq(class_Orderings_Oorder(t_b),true,c_lessequals(c_0,v_c,t_b),true),
inference(unit_resolution,[status(thm)],[90,16]) ).
tff(92,plain,
( ( c_less(c_0,v_c,t_b) = true )
<=> ( c_less(c_0,v_c,t_b) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(93,axiom,
c_less(c_0,v_c,t_b) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(94,plain,
c_less(c_0,v_c,t_b) = true,
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
true = c_less(c_0,v_c,t_b),
inference(symmetry,[status(thm)],[94]) ).
tff(96,plain,
ifeq(true,true,ifeq(class_Orderings_Oorder(t_b),true,c_lessequals(c_0,v_c,t_b),true),true) = ifeq(c_less(c_0,v_c,t_b),true,ifeq(class_Orderings_Oorder(t_b),true,c_lessequals(c_0,v_c,t_b),true),true),
inference(monotonicity,[status(thm)],[95]) ).
tff(97,plain,
ifeq(c_less(c_0,v_c,t_b),true,ifeq(class_Orderings_Oorder(t_b),true,c_lessequals(c_0,v_c,t_b),true),true) = ifeq(true,true,ifeq(class_Orderings_Oorder(t_b),true,c_lessequals(c_0,v_c,t_b),true),true),
inference(symmetry,[status(thm)],[96]) ).
tff(98,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
refl(( ( ifeq(c_less(V_x,V_y,T_a),true,ifeq(class_Orderings_Oorder(T_a),true,c_lessequals(V_x,V_y,T_a),true),true) = true )
<=> ( ifeq(c_less(V_x,V_y,T_a),true,ifeq(class_Orderings_Oorder(T_a),true,c_lessequals(V_x,V_y,T_a),true),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(99,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] : ( ifeq(c_less(V_x,V_y,T_a),true,ifeq(class_Orderings_Oorder(T_a),true,c_lessequals(V_x,V_y,T_a),true),true) = true )
<=> ! [V_x: $i,T_a: $i,V_y: $i] : ( ifeq(c_less(V_x,V_y,T_a),true,ifeq(class_Orderings_Oorder(T_a),true,c_lessequals(V_x,V_y,T_a),true),true) = true ) ),
inference(quant_intro,[status(thm)],[98]) ).
tff(100,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] : ( ifeq(c_less(V_x,V_y,T_a),true,ifeq(class_Orderings_Oorder(T_a),true,c_lessequals(V_x,V_y,T_a),true),true) = true )
<=> ! [V_x: $i,T_a: $i,V_y: $i] : ( ifeq(c_less(V_x,V_y,T_a),true,ifeq(class_Orderings_Oorder(T_a),true,c_lessequals(V_x,V_y,T_a),true),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(101,axiom,
! [V_x: $i,T_a: $i,V_y: $i] : ( ifeq(c_less(V_x,V_y,T_a),true,ifeq(class_Orderings_Oorder(T_a),true,c_lessequals(V_x,V_y,T_a),true),true) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
tff(102,plain,
! [V_x: $i,T_a: $i,V_y: $i] : ( ifeq(c_less(V_x,V_y,T_a),true,ifeq(class_Orderings_Oorder(T_a),true,c_lessequals(V_x,V_y,T_a),true),true) = true ),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
! [V_x: $i,T_a: $i,V_y: $i] : ( ifeq(c_less(V_x,V_y,T_a),true,ifeq(class_Orderings_Oorder(T_a),true,c_lessequals(V_x,V_y,T_a),true),true) = true ),
inference(skolemize,[status(sab)],[102]) ).
tff(104,plain,
! [V_x: $i,T_a: $i,V_y: $i] : ( ifeq(c_less(V_x,V_y,T_a),true,ifeq(class_Orderings_Oorder(T_a),true,c_lessequals(V_x,V_y,T_a),true),true) = true ),
inference(modus_ponens,[status(thm)],[103,99]) ).
tff(105,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] : ( ifeq(c_less(V_x,V_y,T_a),true,ifeq(class_Orderings_Oorder(T_a),true,c_lessequals(V_x,V_y,T_a),true),true) = true )
| ( ifeq(c_less(c_0,v_c,t_b),true,ifeq(class_Orderings_Oorder(t_b),true,c_lessequals(c_0,v_c,t_b),true),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(106,plain,
ifeq(c_less(c_0,v_c,t_b),true,ifeq(class_Orderings_Oorder(t_b),true,c_lessequals(c_0,v_c,t_b),true),true) = true,
inference(unit_resolution,[status(thm)],[105,104]) ).
tff(107,plain,
true = ifeq(c_less(c_0,v_c,t_b),true,ifeq(class_Orderings_Oorder(t_b),true,c_lessequals(c_0,v_c,t_b),true),true),
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
class_Orderings_Oorder(t_b) = ifeq(true,true,class_Orderings_Oorder(t_b),true),
inference(symmetry,[status(thm)],[59]) ).
tff(109,plain,
class_Orderings_Oorder(t_b) = c_lessequals(c_0,v_c,t_b),
inference(transitivity,[status(thm)],[108,60,70,107,97,91,89,87]) ).
tff(110,plain,
ifeq(class_Orderings_Oorder(t_b),true,c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true) = ifeq(c_lessequals(c_0,v_c,t_b),true,ifeq(c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b),true,c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true),true),
inference(monotonicity,[status(thm)],[109,85]) ).
tff(111,plain,
ifeq(c_lessequals(c_0,v_c,t_b),true,ifeq(c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b),true,c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true),true) = ifeq(class_Orderings_Oorder(t_b),true,c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true),
inference(symmetry,[status(thm)],[110]) ).
tff(112,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,ifeq(c_lessequals(c_0,v_c,t_b),true,ifeq(c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b),true,c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true),true),true) = ifeq(c_lessequals(c_0,v_c,t_b),true,ifeq(c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b),true,c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true),true) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(113,plain,
ifeq(true,true,ifeq(c_lessequals(c_0,v_c,t_b),true,ifeq(c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b),true,c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true),true),true) = ifeq(c_lessequals(c_0,v_c,t_b),true,ifeq(c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b),true,c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true),true),
inference(unit_resolution,[status(thm)],[112,16]) ).
tff(114,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,class_Ring__and__Field_Opordered__cancel__semiring(t_b),true) = class_Ring__and__Field_Opordered__cancel__semiring(t_b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(115,plain,
ifeq(true,true,class_Ring__and__Field_Opordered__cancel__semiring(t_b),true) = class_Ring__and__Field_Opordered__cancel__semiring(t_b),
inference(unit_resolution,[status(thm)],[114,16]) ).
tff(116,plain,
ifeq(true,true,class_Ring__and__Field_Opordered__cancel__semiring(t_b),true) = ifeq(class_Ring__and__Field_Oordered__idom(t_b),true,class_Ring__and__Field_Opordered__cancel__semiring(t_b),true),
inference(monotonicity,[status(thm)],[24]) ).
tff(117,plain,
ifeq(class_Ring__and__Field_Oordered__idom(t_b),true,class_Ring__and__Field_Opordered__cancel__semiring(t_b),true) = ifeq(true,true,class_Ring__and__Field_Opordered__cancel__semiring(t_b),true),
inference(symmetry,[status(thm)],[116]) ).
tff(118,plain,
^ [T: $i] :
refl(( ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Ring__and__Field_Opordered__cancel__semiring(T),true) = true )
<=> ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Ring__and__Field_Opordered__cancel__semiring(T),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(119,plain,
( ! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Ring__and__Field_Opordered__cancel__semiring(T),true) = true )
<=> ! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Ring__and__Field_Opordered__cancel__semiring(T),true) = true ) ),
inference(quant_intro,[status(thm)],[118]) ).
tff(120,plain,
( ! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Ring__and__Field_Opordered__cancel__semiring(T),true) = true )
<=> ! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Ring__and__Field_Opordered__cancel__semiring(T),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(121,axiom,
! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Ring__and__Field_Opordered__cancel__semiring(T),true) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
tff(122,plain,
! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Ring__and__Field_Opordered__cancel__semiring(T),true) = true ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Ring__and__Field_Opordered__cancel__semiring(T),true) = true ),
inference(skolemize,[status(sab)],[122]) ).
tff(124,plain,
! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Ring__and__Field_Opordered__cancel__semiring(T),true) = true ),
inference(modus_ponens,[status(thm)],[123,119]) ).
tff(125,plain,
( ~ ! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Ring__and__Field_Opordered__cancel__semiring(T),true) = true )
| ( ifeq(class_Ring__and__Field_Oordered__idom(t_b),true,class_Ring__and__Field_Opordered__cancel__semiring(t_b),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(126,plain,
ifeq(class_Ring__and__Field_Oordered__idom(t_b),true,class_Ring__and__Field_Opordered__cancel__semiring(t_b),true) = true,
inference(unit_resolution,[status(thm)],[125,124]) ).
tff(127,plain,
true = ifeq(class_Ring__and__Field_Oordered__idom(t_b),true,class_Ring__and__Field_Opordered__cancel__semiring(t_b),true),
inference(symmetry,[status(thm)],[126]) ).
tff(128,plain,
true = class_Ring__and__Field_Opordered__cancel__semiring(t_b),
inference(transitivity,[status(thm)],[127,117,115]) ).
tff(129,plain,
ifeq(true,true,ifeq(c_lessequals(c_0,v_c,t_b),true,ifeq(c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b),true,c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true),true),true) = ifeq(class_Ring__and__Field_Opordered__cancel__semiring(t_b),true,ifeq(c_lessequals(c_0,v_c,t_b),true,ifeq(c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b),true,c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true),true),true),
inference(monotonicity,[status(thm)],[128]) ).
tff(130,plain,
ifeq(class_Ring__and__Field_Opordered__cancel__semiring(t_b),true,ifeq(c_lessequals(c_0,v_c,t_b),true,ifeq(c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b),true,c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true),true),true) = ifeq(true,true,ifeq(c_lessequals(c_0,v_c,t_b),true,ifeq(c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b),true,c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true),true),true),
inference(symmetry,[status(thm)],[129]) ).
tff(131,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
refl(( ( ifeq(class_Ring__and__Field_Opordered__cancel__semiring(T_a),true,ifeq(c_lessequals(c_0,V_a,T_a),true,ifeq(c_lessequals(c_0,V_b,T_a),true,c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a),true),true),true) = true )
<=> ( ifeq(class_Ring__and__Field_Opordered__cancel__semiring(T_a),true,ifeq(c_lessequals(c_0,V_a,T_a),true,ifeq(c_lessequals(c_0,V_b,T_a),true,c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a),true),true),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(132,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] : ( ifeq(class_Ring__and__Field_Opordered__cancel__semiring(T_a),true,ifeq(c_lessequals(c_0,V_a,T_a),true,ifeq(c_lessequals(c_0,V_b,T_a),true,c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a),true),true),true) = true )
<=> ! [V_b: $i,V_a: $i,T_a: $i] : ( ifeq(class_Ring__and__Field_Opordered__cancel__semiring(T_a),true,ifeq(c_lessequals(c_0,V_a,T_a),true,ifeq(c_lessequals(c_0,V_b,T_a),true,c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a),true),true),true) = true ) ),
inference(quant_intro,[status(thm)],[131]) ).
tff(133,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] : ( ifeq(class_Ring__and__Field_Opordered__cancel__semiring(T_a),true,ifeq(c_lessequals(c_0,V_a,T_a),true,ifeq(c_lessequals(c_0,V_b,T_a),true,c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a),true),true),true) = true )
<=> ! [V_b: $i,V_a: $i,T_a: $i] : ( ifeq(class_Ring__and__Field_Opordered__cancel__semiring(T_a),true,ifeq(c_lessequals(c_0,V_a,T_a),true,ifeq(c_lessequals(c_0,V_b,T_a),true,c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a),true),true),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(134,axiom,
! [V_b: $i,V_a: $i,T_a: $i] : ( ifeq(class_Ring__and__Field_Opordered__cancel__semiring(T_a),true,ifeq(c_lessequals(c_0,V_a,T_a),true,ifeq(c_lessequals(c_0,V_b,T_a),true,c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a),true),true),true) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_0) ).
tff(135,plain,
! [V_b: $i,V_a: $i,T_a: $i] : ( ifeq(class_Ring__and__Field_Opordered__cancel__semiring(T_a),true,ifeq(c_lessequals(c_0,V_a,T_a),true,ifeq(c_lessequals(c_0,V_b,T_a),true,c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a),true),true),true) = true ),
inference(modus_ponens,[status(thm)],[134,133]) ).
tff(136,plain,
! [V_b: $i,V_a: $i,T_a: $i] : ( ifeq(class_Ring__and__Field_Opordered__cancel__semiring(T_a),true,ifeq(c_lessequals(c_0,V_a,T_a),true,ifeq(c_lessequals(c_0,V_b,T_a),true,c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a),true),true),true) = true ),
inference(skolemize,[status(sab)],[135]) ).
tff(137,plain,
! [V_b: $i,V_a: $i,T_a: $i] : ( ifeq(class_Ring__and__Field_Opordered__cancel__semiring(T_a),true,ifeq(c_lessequals(c_0,V_a,T_a),true,ifeq(c_lessequals(c_0,V_b,T_a),true,c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a),true),true),true) = true ),
inference(modus_ponens,[status(thm)],[136,132]) ).
tff(138,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] : ( ifeq(class_Ring__and__Field_Opordered__cancel__semiring(T_a),true,ifeq(c_lessequals(c_0,V_a,T_a),true,ifeq(c_lessequals(c_0,V_b,T_a),true,c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a),true),true),true) = true )
| ( ifeq(class_Ring__and__Field_Opordered__cancel__semiring(t_b),true,ifeq(c_lessequals(c_0,v_c,t_b),true,ifeq(c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b),true,c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true),true),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(139,plain,
ifeq(class_Ring__and__Field_Opordered__cancel__semiring(t_b),true,ifeq(c_lessequals(c_0,v_c,t_b),true,ifeq(c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b),true,c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true),true),true) = true,
inference(unit_resolution,[status(thm)],[138,137]) ).
tff(140,plain,
true = ifeq(class_Ring__and__Field_Opordered__cancel__semiring(t_b),true,ifeq(c_lessequals(c_0,v_c,t_b),true,ifeq(c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b),true,c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true),true),true),
inference(symmetry,[status(thm)],[139]) ).
tff(141,plain,
c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b) = ifeq(true,true,c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b),true),
inference(symmetry,[status(thm)],[18]) ).
tff(142,plain,
c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b) = c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),
inference(transitivity,[status(thm)],[141,38,48,140,130,113,111,74,57]) ).
tff(143,plain,
ifeq(c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b),true,ifeq(c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true,ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),true,ifeq(class_Ring__and__Field_Opordered__semiring(t_b),true,c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true),true),true),true) = ifeq(c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true,ifeq(c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b),true,ifeq(c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true,ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),true,ifeq(class_Ring__and__Field_Opordered__semiring(t_b),true,c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true),true),true),true),true),
inference(monotonicity,[status(thm)],[142,55]) ).
tff(144,plain,
( ( c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) = true )
<=> ( c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(145,axiom,
c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(146,plain,
c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) = true,
inference(modus_ponens,[status(thm)],[145,144]) ).
tff(147,plain,
true = c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),
inference(symmetry,[status(thm)],[146]) ).
tff(148,plain,
ifeq(true,true,ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),true,ifeq(class_Ring__and__Field_Opordered__semiring(t_b),true,c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true),true),true) = ifeq(c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true,ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),true,ifeq(class_Ring__and__Field_Opordered__semiring(t_b),true,c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true),true),true),
inference(monotonicity,[status(thm)],[147]) ).
tff(149,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),true,ifeq(class_Ring__and__Field_Opordered__semiring(t_b),true,c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true),true),true) = ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),true,ifeq(class_Ring__and__Field_Opordered__semiring(t_b),true,c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true),true) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(150,plain,
ifeq(true,true,ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),true,ifeq(class_Ring__and__Field_Opordered__semiring(t_b),true,c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true),true),true) = ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),true,ifeq(class_Ring__and__Field_Opordered__semiring(t_b),true,c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true),true),
inference(unit_resolution,[status(thm)],[149,16]) ).
tff(151,plain,
ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),true,ifeq(class_Ring__and__Field_Opordered__semiring(t_b),true,c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true),true) = ifeq(true,true,ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),true,ifeq(class_Ring__and__Field_Opordered__semiring(t_b),true,c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true),true),true),
inference(symmetry,[status(thm)],[150]) ).
tff(152,plain,
( ( c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) = c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) )
<=> ( c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) = c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(153,axiom,
c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) = c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
tff(154,plain,
c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) = c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
inference(modus_ponens,[status(thm)],[153,152]) ).
tff(155,plain,
c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) = c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(symmetry,[status(thm)],[154]) ).
tff(156,plain,
c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b) = c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),
inference(monotonicity,[status(thm)],[155]) ).
tff(157,plain,
c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b) = c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),
inference(symmetry,[status(thm)],[156]) ).
tff(158,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
refl(( ( ifeq2(class_Ring__and__Field_Oordered__idom(T_a),true,c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a),c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a)) = c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) )
<=> ( ifeq2(class_Ring__and__Field_Oordered__idom(T_a),true,c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a),c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a)) = c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(159,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] : ( ifeq2(class_Ring__and__Field_Oordered__idom(T_a),true,c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a),c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a)) = c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] : ( ifeq2(class_Ring__and__Field_Oordered__idom(T_a),true,c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a),c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a)) = c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[158]) ).
tff(160,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] : ( ifeq2(class_Ring__and__Field_Oordered__idom(T_a),true,c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a),c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a)) = c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] : ( ifeq2(class_Ring__and__Field_Oordered__idom(T_a),true,c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a),c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a)) = c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(161,axiom,
! [V_b: $i,V_a: $i,T_a: $i] : ( ifeq2(class_Ring__and__Field_Oordered__idom(T_a),true,c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a),c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a)) = c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__mult_0) ).
tff(162,plain,
! [V_b: $i,V_a: $i,T_a: $i] : ( ifeq2(class_Ring__and__Field_Oordered__idom(T_a),true,c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a),c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a)) = c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[161,160]) ).
tff(163,plain,
! [V_b: $i,V_a: $i,T_a: $i] : ( ifeq2(class_Ring__and__Field_Oordered__idom(T_a),true,c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a),c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a)) = c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) ),
inference(skolemize,[status(sab)],[162]) ).
tff(164,plain,
! [V_b: $i,V_a: $i,T_a: $i] : ( ifeq2(class_Ring__and__Field_Oordered__idom(T_a),true,c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a),c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a)) = c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[163,159]) ).
tff(165,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] : ( ifeq2(class_Ring__and__Field_Oordered__idom(T_a),true,c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a),c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a)) = c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) )
| ( ifeq2(class_Ring__and__Field_Oordered__idom(t_b),true,c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b)) = c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(166,plain,
ifeq2(class_Ring__and__Field_Oordered__idom(t_b),true,c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b)) = c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),
inference(unit_resolution,[status(thm)],[165,164]) ).
tff(167,plain,
ifeq2(true,true,c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b)) = ifeq2(class_Ring__and__Field_Oordered__idom(t_b),true,c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b)),
inference(monotonicity,[status(thm)],[24]) ).
tff(168,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ifeq2(A,A,B,C) = B )
<=> ( ifeq2(A,A,B,C) = B ) )),
inference(bind,[status(th)],[]) ).
tff(169,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ) ),
inference(quant_intro,[status(thm)],[168]) ).
tff(170,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ) ),
inference(rewrite,[status(thm)],[]) ).
tff(171,axiom,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
tff(172,plain,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[171,170]) ).
tff(173,plain,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
inference(skolemize,[status(sab)],[172]) ).
tff(174,plain,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[173,169]) ).
tff(175,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
| ( ifeq2(true,true,c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b)) = c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(176,plain,
ifeq2(true,true,c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b)) = c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),
inference(unit_resolution,[status(thm)],[175,174]) ).
tff(177,plain,
c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b) = ifeq2(true,true,c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b)),
inference(symmetry,[status(thm)],[176]) ).
tff(178,plain,
c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b) = c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),
inference(transitivity,[status(thm)],[177,167,166]) ).
tff(179,plain,
c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b) = c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),
inference(monotonicity,[status(thm)],[178,155]) ).
tff(180,plain,
c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b) = c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),
inference(transitivity,[status(thm)],[179,157]) ).
tff(181,plain,
^ [T: $i] :
refl(( ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Ring__and__Field_Opordered__semiring(T),true) = true )
<=> ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Ring__and__Field_Opordered__semiring(T),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(182,plain,
( ! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Ring__and__Field_Opordered__semiring(T),true) = true )
<=> ! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Ring__and__Field_Opordered__semiring(T),true) = true ) ),
inference(quant_intro,[status(thm)],[181]) ).
tff(183,plain,
( ! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Ring__and__Field_Opordered__semiring(T),true) = true )
<=> ! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Ring__and__Field_Opordered__semiring(T),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(184,axiom,
! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Ring__and__Field_Opordered__semiring(T),true) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
tff(185,plain,
! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Ring__and__Field_Opordered__semiring(T),true) = true ),
inference(modus_ponens,[status(thm)],[184,183]) ).
tff(186,plain,
! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Ring__and__Field_Opordered__semiring(T),true) = true ),
inference(skolemize,[status(sab)],[185]) ).
tff(187,plain,
! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Ring__and__Field_Opordered__semiring(T),true) = true ),
inference(modus_ponens,[status(thm)],[186,182]) ).
tff(188,plain,
( ~ ! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Ring__and__Field_Opordered__semiring(T),true) = true )
| ( ifeq(class_Ring__and__Field_Oordered__idom(t_b),true,class_Ring__and__Field_Opordered__semiring(t_b),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(189,plain,
ifeq(class_Ring__and__Field_Oordered__idom(t_b),true,class_Ring__and__Field_Opordered__semiring(t_b),true) = true,
inference(unit_resolution,[status(thm)],[188,187]) ).
tff(190,plain,
ifeq(true,true,class_Ring__and__Field_Opordered__semiring(t_b),true) = ifeq(class_Ring__and__Field_Oordered__idom(t_b),true,class_Ring__and__Field_Opordered__semiring(t_b),true),
inference(monotonicity,[status(thm)],[24]) ).
tff(191,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,class_Ring__and__Field_Opordered__semiring(t_b),true) = class_Ring__and__Field_Opordered__semiring(t_b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(192,plain,
ifeq(true,true,class_Ring__and__Field_Opordered__semiring(t_b),true) = class_Ring__and__Field_Opordered__semiring(t_b),
inference(unit_resolution,[status(thm)],[191,16]) ).
tff(193,plain,
class_Ring__and__Field_Opordered__semiring(t_b) = ifeq(true,true,class_Ring__and__Field_Opordered__semiring(t_b),true),
inference(symmetry,[status(thm)],[192]) ).
tff(194,plain,
class_Ring__and__Field_Opordered__semiring(t_b) = class_Orderings_Oorder(t_b),
inference(transitivity,[status(thm)],[193,190,189,71,61,59]) ).
tff(195,plain,
ifeq(class_Ring__and__Field_Opordered__semiring(t_b),true,c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true) = ifeq(class_Orderings_Oorder(t_b),true,c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true),
inference(monotonicity,[status(thm)],[194,180]) ).
tff(196,plain,
ifeq(class_Orderings_Oorder(t_b),true,c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true) = ifeq(class_Ring__and__Field_Opordered__semiring(t_b),true,c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true),
inference(symmetry,[status(thm)],[195]) ).
tff(197,plain,
( ( c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) = true )
<=> ( c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(198,axiom,
c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(199,plain,
c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) = true,
inference(modus_ponens,[status(thm)],[198,197]) ).
tff(200,plain,
true = c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
inference(symmetry,[status(thm)],[199]) ).
tff(201,plain,
ifeq(true,true,ifeq(class_Orderings_Oorder(t_b),true,c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true),true) = ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),true,ifeq(class_Ring__and__Field_Opordered__semiring(t_b),true,c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true),true),
inference(monotonicity,[status(thm)],[200,196]) ).
tff(202,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,ifeq(class_Orderings_Oorder(t_b),true,c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true),true) = ifeq(class_Orderings_Oorder(t_b),true,c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(203,plain,
ifeq(true,true,ifeq(class_Orderings_Oorder(t_b),true,c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true),true) = ifeq(class_Orderings_Oorder(t_b),true,c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true),
inference(unit_resolution,[status(thm)],[202,16]) ).
tff(204,plain,
ifeq(class_Orderings_Oorder(t_b),true,c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true) = ifeq(true,true,ifeq(class_Orderings_Oorder(t_b),true,c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true),true),
inference(symmetry,[status(thm)],[203]) ).
tff(205,plain,
ifeq(true,true,c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),true) = ifeq(class_Orderings_Oorder(t_b),true,c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true),
inference(monotonicity,[status(thm)],[72,157]) ).
tff(206,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),true) = c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(207,plain,
ifeq(true,true,c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),true) = c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),
inference(unit_resolution,[status(thm)],[206,16]) ).
tff(208,plain,
c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b) = ifeq(true,true,c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),true),
inference(symmetry,[status(thm)],[207]) ).
tff(209,plain,
c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b) = true,
inference(transitivity,[status(thm)],[208,205,204,201,151,148,54,51,143,9]) ).
tff(210,plain,
( ( c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b) != true )
<=> ( c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b) != true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(211,axiom,
c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
tff(212,plain,
c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b) != true,
inference(modus_ponens,[status(thm)],[211,210]) ).
tff(213,plain,
$false,
inference(unit_resolution,[status(thm)],[212,209]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : ANA034-10 : TPTP v9.0.0. Released v7.3.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n001.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Jun 19 11:26:48 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.14/0.40 % SZS status Unsatisfiable
% 0.14/0.40 % SZS output start Proof
% See solution above
% 0.22/0.47 % E exiting
%------------------------------------------------------------------------------