%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ANA023-10 : TPTP v9.0.0. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 04:59:11 AM UTC 2025
% Result : Unsatisfiable 0.13s 0.38s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 43
% Syntax : Number of formulae : 129 ( 97 unt; 0 typ; 0 def)
% Number of atoms : 175 ( 167 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 57 ( 18 ~; 14 |; 0 &)
% ( 25 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 7 ( 7 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 : 15 ( 15 usr; 4 con; 0-4 aty)
% Number of variables : 201 ( 183 !; 0 ?; 201 :)
% 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_minus_type,type,
c_minus: ( $i * $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(c_0_type,type,
c_0: $i ).
tff(ifeq_type,type,
ifeq: ( $i * $i * $i * $i ) > $i ).
tff(c_plus_type,type,
c_plus: ( $i * $i * $i ) > $i ).
tff(class_OrderedGroup_Opordered__ab__group__add_type,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $i ).
tff(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $i ).
tff(v_k_type,type,
v_k: $i > $i ).
tff(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $i ).
tff(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $i ).
tff(1,plain,
^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
refl(( ( ifeq(class_OrderedGroup_Opordered__ab__group__add(T_a),true,ifeq(c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a),true,c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a),true),true) = true )
<=> ( ifeq(class_OrderedGroup_Opordered__ab__group__add(T_a),true,ifeq(c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a),true,c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a),true),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] : ( ifeq(class_OrderedGroup_Opordered__ab__group__add(T_a),true,ifeq(c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a),true,c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a),true),true) = true )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] : ( ifeq(class_OrderedGroup_Opordered__ab__group__add(T_a),true,ifeq(c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a),true,c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a),true),true) = true ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] : ( ifeq(class_OrderedGroup_Opordered__ab__group__add(T_a),true,ifeq(c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a),true,c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a),true),true) = true )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] : ( ifeq(class_OrderedGroup_Opordered__ab__group__add(T_a),true,ifeq(c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a),true,c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a),true),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] : ( ifeq(class_OrderedGroup_Opordered__ab__group__add(T_a),true,ifeq(c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a),true,c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a),true),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_1) ).
tff(5,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] : ( ifeq(class_OrderedGroup_Opordered__ab__group__add(T_a),true,ifeq(c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a),true,c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a),true),true) = true ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] : ( ifeq(class_OrderedGroup_Opordered__ab__group__add(T_a),true,ifeq(c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a),true,c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a),true),true) = true ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] : ( ifeq(class_OrderedGroup_Opordered__ab__group__add(T_a),true,ifeq(c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a),true,c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a),true),true) = true ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] : ( ifeq(class_OrderedGroup_Opordered__ab__group__add(T_a),true,ifeq(c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a),true,c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a),true),true) = true )
| ( ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b),true,c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),true),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b),true,c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),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/sandbox2/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,class_OrderedGroup_Opordered__ab__group__add(t_b),true) = class_OrderedGroup_Opordered__ab__group__add(t_b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
ifeq(true,true,class_OrderedGroup_Opordered__ab__group__add(t_b),true) = class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
( ( class_Ring__and__Field_Oordered__idom(t_b) = true )
<=> ( class_Ring__and__Field_Oordered__idom(t_b) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
class_Ring__and__Field_Oordered__idom(t_b) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
tff(21,plain,
class_Ring__and__Field_Oordered__idom(t_b) = true,
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
true = class_Ring__and__Field_Oordered__idom(t_b),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
ifeq(true,true,class_OrderedGroup_Opordered__ab__group__add(t_b),true) = ifeq(class_Ring__and__Field_Oordered__idom(t_b),true,class_OrderedGroup_Opordered__ab__group__add(t_b),true),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
ifeq(class_Ring__and__Field_Oordered__idom(t_b),true,class_OrderedGroup_Opordered__ab__group__add(t_b),true) = ifeq(true,true,class_OrderedGroup_Opordered__ab__group__add(t_b),true),
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
^ [T: $i] :
refl(( ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_OrderedGroup_Opordered__ab__group__add(T),true) = true )
<=> ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_OrderedGroup_Opordered__ab__group__add(T),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(26,plain,
( ! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_OrderedGroup_Opordered__ab__group__add(T),true) = true )
<=> ! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_OrderedGroup_Opordered__ab__group__add(T),true) = true ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
( ! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_OrderedGroup_Opordered__ab__group__add(T),true) = true )
<=> ! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_OrderedGroup_Opordered__ab__group__add(T),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,axiom,
! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_OrderedGroup_Opordered__ab__group__add(T),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
tff(29,plain,
! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_OrderedGroup_Opordered__ab__group__add(T),true) = true ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_OrderedGroup_Opordered__ab__group__add(T),true) = true ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_OrderedGroup_Opordered__ab__group__add(T),true) = true ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
( ~ ! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_OrderedGroup_Opordered__ab__group__add(T),true) = true )
| ( ifeq(class_Ring__and__Field_Oordered__idom(t_b),true,class_OrderedGroup_Opordered__ab__group__add(t_b),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
ifeq(class_Ring__and__Field_Oordered__idom(t_b),true,class_OrderedGroup_Opordered__ab__group__add(t_b),true) = true,
inference(unit_resolution,[status(thm)],[32,31]) ).
tff(34,plain,
true = ifeq(class_Ring__and__Field_Oordered__idom(t_b),true,class_OrderedGroup_Opordered__ab__group__add(t_b),true),
inference(symmetry,[status(thm)],[33]) ).
tff(35,plain,
true = class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(transitivity,[status(thm)],[34,24,18]) ).
tff(36,plain,
ifeq(true,true,ifeq(c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b),true,c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),true),true) = ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b),true,c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),true),true),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,ifeq(c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b),true,c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),true),true) = ifeq(c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b),true,c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),true) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,plain,
ifeq(true,true,ifeq(c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b),true,c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),true),true) = ifeq(c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b),true,c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),true),
inference(unit_resolution,[status(thm)],[37,16]) ).
tff(39,plain,
ifeq(c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b),true,c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),true) = ifeq(true,true,ifeq(c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b),true,c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),true),true),
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b),true) = c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(41,plain,
ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b),true) = c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b),
inference(unit_resolution,[status(thm)],[40,16]) ).
tff(42,plain,
( ( c_lessequals(v_k(v_x),v_f(v_x),t_b) = true )
<=> ( c_lessequals(v_k(v_x),v_f(v_x),t_b) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,axiom,
c_lessequals(v_k(v_x),v_f(v_x),t_b) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(44,plain,
c_lessequals(v_k(v_x),v_f(v_x),t_b) = true,
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
true = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b),true) = ifeq(c_lessequals(v_k(v_x),v_f(v_x),t_b),true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b),true),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
ifeq(c_lessequals(v_k(v_x),v_f(v_x),t_b),true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b),true) = ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b),true),
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,ifeq(c_lessequals(v_k(v_x),v_f(v_x),t_b),true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b),true),true) = ifeq(c_lessequals(v_k(v_x),v_f(v_x),t_b),true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b),true) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
ifeq(true,true,ifeq(c_lessequals(v_k(v_x),v_f(v_x),t_b),true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b),true),true) = ifeq(c_lessequals(v_k(v_x),v_f(v_x),t_b),true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b),true),
inference(unit_resolution,[status(thm)],[48,16]) ).
tff(50,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true) = c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(51,plain,
ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true) = c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),
inference(unit_resolution,[status(thm)],[50,16]) ).
tff(52,plain,
( ( c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) = true )
<=> ( c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,axiom,
c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(54,plain,
c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) = true,
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
true = c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true) = ifeq(c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
ifeq(c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true) = ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b) = ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),
inference(symmetry,[status(thm)],[51]) ).
tff(59,plain,
c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b) = ifeq(c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),
inference(transitivity,[status(thm)],[58,56]) ).
tff(60,plain,
c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) = class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(transitivity,[status(thm)],[54,34,24,18]) ).
tff(61,plain,
ifeq(c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true) = ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true),
inference(monotonicity,[status(thm)],[60,59]) ).
tff(62,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true) = ifeq(c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
refl(( ( ifeq(class_OrderedGroup_Opordered__ab__group__add(T_a),true,ifeq(c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a),true,c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a),true),true) = true )
<=> ( ifeq(class_OrderedGroup_Opordered__ab__group__add(T_a),true,ifeq(c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a),true,c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a),true),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(64,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] : ( ifeq(class_OrderedGroup_Opordered__ab__group__add(T_a),true,ifeq(c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a),true,c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a),true),true) = true )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] : ( ifeq(class_OrderedGroup_Opordered__ab__group__add(T_a),true,ifeq(c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a),true,c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a),true),true) = true ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] : ( ifeq(class_OrderedGroup_Opordered__ab__group__add(T_a),true,ifeq(c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a),true,c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a),true),true) = true )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] : ( ifeq(class_OrderedGroup_Opordered__ab__group__add(T_a),true,ifeq(c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a),true,c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a),true),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,axiom,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] : ( ifeq(class_OrderedGroup_Opordered__ab__group__add(T_a),true,ifeq(c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a),true,c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a),true),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_0) ).
tff(67,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] : ( ifeq(class_OrderedGroup_Opordered__ab__group__add(T_a),true,ifeq(c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a),true,c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a),true),true) = true ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] : ( ifeq(class_OrderedGroup_Opordered__ab__group__add(T_a),true,ifeq(c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a),true,c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a),true),true) = true ),
inference(skolemize,[status(sab)],[67]) ).
tff(69,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] : ( ifeq(class_OrderedGroup_Opordered__ab__group__add(T_a),true,ifeq(c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a),true,c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a),true),true) = true ),
inference(modus_ponens,[status(thm)],[68,64]) ).
tff(70,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] : ( ifeq(class_OrderedGroup_Opordered__ab__group__add(T_a),true,ifeq(c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a),true,c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a),true),true) = true )
| ( ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(71,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true) = true,
inference(unit_resolution,[status(thm)],[70,69]) ).
tff(72,plain,
true = ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true),
inference(symmetry,[status(thm)],[71]) ).
tff(73,plain,
true = c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),
inference(transitivity,[status(thm)],[72,62,57,51]) ).
tff(74,plain,
ifeq(true,true,ifeq(c_lessequals(v_k(v_x),v_f(v_x),t_b),true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b),true),true) = ifeq(c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true,ifeq(c_lessequals(v_k(v_x),v_f(v_x),t_b),true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b),true),true),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
ifeq(c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true,ifeq(c_lessequals(v_k(v_x),v_f(v_x),t_b),true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b),true),true) = ifeq(true,true,ifeq(c_lessequals(v_k(v_x),v_f(v_x),t_b),true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b),true),true),
inference(symmetry,[status(thm)],[74]) ).
tff(76,plain,
ifeq(c_lessequals(v_k(v_x),v_f(v_x),t_b),true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b),true) = ifeq(true,true,ifeq(c_lessequals(v_k(v_x),v_f(v_x),t_b),true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b),true),true),
inference(symmetry,[status(thm)],[49]) ).
tff(77,plain,
ifeq(c_lessequals(v_k(v_x),v_f(v_x),t_b),true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b),true) = ifeq(c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true,ifeq(c_lessequals(v_k(v_x),v_f(v_x),t_b),true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b),true),true),
inference(transitivity,[status(thm)],[76,74]) ).
tff(78,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(79,plain,
ifeq(true,true,class_Orderings_Oorder(t_b),true) = class_Orderings_Oorder(t_b),
inference(unit_resolution,[status(thm)],[78,16]) ).
tff(80,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,class_Orderings_Olinorder(t_b),true) = class_Orderings_Olinorder(t_b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(81,plain,
ifeq(true,true,class_Orderings_Olinorder(t_b),true) = class_Orderings_Olinorder(t_b),
inference(unit_resolution,[status(thm)],[80,16]) ).
tff(82,plain,
ifeq(true,true,class_Orderings_Olinorder(t_b),true) = ifeq(class_Ring__and__Field_Oordered__idom(t_b),true,class_Orderings_Olinorder(t_b),true),
inference(monotonicity,[status(thm)],[22]) ).
tff(83,plain,
ifeq(class_Ring__and__Field_Oordered__idom(t_b),true,class_Orderings_Olinorder(t_b),true) = ifeq(true,true,class_Orderings_Olinorder(t_b),true),
inference(symmetry,[status(thm)],[82]) ).
tff(84,plain,
^ [T: $i] :
refl(( ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Orderings_Olinorder(T),true) = true )
<=> ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Orderings_Olinorder(T),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(85,plain,
( ! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Orderings_Olinorder(T),true) = true )
<=> ! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Orderings_Olinorder(T),true) = true ) ),
inference(quant_intro,[status(thm)],[84]) ).
tff(86,plain,
( ! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Orderings_Olinorder(T),true) = true )
<=> ! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Orderings_Olinorder(T),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,axiom,
! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Orderings_Olinorder(T),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
tff(88,plain,
! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Orderings_Olinorder(T),true) = true ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Orderings_Olinorder(T),true) = true ),
inference(skolemize,[status(sab)],[88]) ).
tff(90,plain,
! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Orderings_Olinorder(T),true) = true ),
inference(modus_ponens,[status(thm)],[89,85]) ).
tff(91,plain,
( ~ ! [T: $i] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Orderings_Olinorder(T),true) = true )
| ( ifeq(class_Ring__and__Field_Oordered__idom(t_b),true,class_Orderings_Olinorder(t_b),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(92,plain,
ifeq(class_Ring__and__Field_Oordered__idom(t_b),true,class_Orderings_Olinorder(t_b),true) = true,
inference(unit_resolution,[status(thm)],[91,90]) ).
tff(93,plain,
true = ifeq(class_Ring__and__Field_Oordered__idom(t_b),true,class_Orderings_Olinorder(t_b),true),
inference(symmetry,[status(thm)],[92]) ).
tff(94,plain,
true = class_Orderings_Olinorder(t_b),
inference(transitivity,[status(thm)],[93,83,81]) ).
tff(95,plain,
ifeq(true,true,class_Orderings_Oorder(t_b),true) = ifeq(class_Orderings_Olinorder(t_b),true,class_Orderings_Oorder(t_b),true),
inference(monotonicity,[status(thm)],[94]) ).
tff(96,plain,
ifeq(class_Orderings_Olinorder(t_b),true,class_Orderings_Oorder(t_b),true) = ifeq(true,true,class_Orderings_Oorder(t_b),true),
inference(symmetry,[status(thm)],[95]) ).
tff(97,plain,
^ [T: $i] :
refl(( ( ifeq(class_Orderings_Olinorder(T),true,class_Orderings_Oorder(T),true) = true )
<=> ( ifeq(class_Orderings_Olinorder(T),true,class_Orderings_Oorder(T),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(98,plain,
( ! [T: $i] : ( ifeq(class_Orderings_Olinorder(T),true,class_Orderings_Oorder(T),true) = true )
<=> ! [T: $i] : ( ifeq(class_Orderings_Olinorder(T),true,class_Orderings_Oorder(T),true) = true ) ),
inference(quant_intro,[status(thm)],[97]) ).
tff(99,plain,
( ! [T: $i] : ( ifeq(class_Orderings_Olinorder(T),true,class_Orderings_Oorder(T),true) = true )
<=> ! [T: $i] : ( ifeq(class_Orderings_Olinorder(T),true,class_Orderings_Oorder(T),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(100,axiom,
! [T: $i] : ( ifeq(class_Orderings_Olinorder(T),true,class_Orderings_Oorder(T),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).
tff(101,plain,
! [T: $i] : ( ifeq(class_Orderings_Olinorder(T),true,class_Orderings_Oorder(T),true) = true ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
! [T: $i] : ( ifeq(class_Orderings_Olinorder(T),true,class_Orderings_Oorder(T),true) = true ),
inference(skolemize,[status(sab)],[101]) ).
tff(103,plain,
! [T: $i] : ( ifeq(class_Orderings_Olinorder(T),true,class_Orderings_Oorder(T),true) = true ),
inference(modus_ponens,[status(thm)],[102,98]) ).
tff(104,plain,
( ~ ! [T: $i] : ( ifeq(class_Orderings_Olinorder(T),true,class_Orderings_Oorder(T),true) = true )
| ( ifeq(class_Orderings_Olinorder(t_b),true,class_Orderings_Oorder(t_b),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(105,plain,
ifeq(class_Orderings_Olinorder(t_b),true,class_Orderings_Oorder(t_b),true) = true,
inference(unit_resolution,[status(thm)],[104,103]) ).
tff(106,plain,
true = ifeq(class_Orderings_Olinorder(t_b),true,class_Orderings_Oorder(t_b),true),
inference(symmetry,[status(thm)],[105]) ).
tff(107,plain,
c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b) = class_Orderings_Oorder(t_b),
inference(transitivity,[status(thm)],[58,56,61,71,106,96,79]) ).
tff(108,plain,
ifeq(c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true,ifeq(c_lessequals(v_k(v_x),v_f(v_x),t_b),true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b),true),true) = ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true,ifeq(c_lessequals(v_k(v_x),v_f(v_x),t_b),true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b),true),true),true),
inference(monotonicity,[status(thm)],[107,77]) ).
tff(109,plain,
ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true,ifeq(c_lessequals(v_k(v_x),v_f(v_x),t_b),true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b),true),true),true) = ifeq(c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true,ifeq(c_lessequals(v_k(v_x),v_f(v_x),t_b),true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b),true),true),
inference(symmetry,[status(thm)],[108]) ).
tff(110,plain,
^ [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
refl(( ( ifeq(class_Orderings_Oorder(T_a),true,ifeq(c_lessequals(V_x,V_y,T_a),true,ifeq(c_lessequals(V_y,V_z,T_a),true,c_lessequals(V_x,V_z,T_a),true),true),true) = true )
<=> ( ifeq(class_Orderings_Oorder(T_a),true,ifeq(c_lessequals(V_x,V_y,T_a),true,ifeq(c_lessequals(V_y,V_z,T_a),true,c_lessequals(V_x,V_z,T_a),true),true),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(111,plain,
( ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] : ( ifeq(class_Orderings_Oorder(T_a),true,ifeq(c_lessequals(V_x,V_y,T_a),true,ifeq(c_lessequals(V_y,V_z,T_a),true,c_lessequals(V_x,V_z,T_a),true),true),true) = true )
<=> ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] : ( ifeq(class_Orderings_Oorder(T_a),true,ifeq(c_lessequals(V_x,V_y,T_a),true,ifeq(c_lessequals(V_y,V_z,T_a),true,c_lessequals(V_x,V_z,T_a),true),true),true) = true ) ),
inference(quant_intro,[status(thm)],[110]) ).
tff(112,plain,
( ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] : ( ifeq(class_Orderings_Oorder(T_a),true,ifeq(c_lessequals(V_x,V_y,T_a),true,ifeq(c_lessequals(V_y,V_z,T_a),true,c_lessequals(V_x,V_z,T_a),true),true),true) = true )
<=> ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] : ( ifeq(class_Orderings_Oorder(T_a),true,ifeq(c_lessequals(V_x,V_y,T_a),true,ifeq(c_lessequals(V_y,V_z,T_a),true,c_lessequals(V_x,V_z,T_a),true),true),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(113,axiom,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] : ( ifeq(class_Orderings_Oorder(T_a),true,ifeq(c_lessequals(V_x,V_y,T_a),true,ifeq(c_lessequals(V_y,V_z,T_a),true,c_lessequals(V_x,V_z,T_a),true),true),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
tff(114,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] : ( ifeq(class_Orderings_Oorder(T_a),true,ifeq(c_lessequals(V_x,V_y,T_a),true,ifeq(c_lessequals(V_y,V_z,T_a),true,c_lessequals(V_x,V_z,T_a),true),true),true) = true ),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] : ( ifeq(class_Orderings_Oorder(T_a),true,ifeq(c_lessequals(V_x,V_y,T_a),true,ifeq(c_lessequals(V_y,V_z,T_a),true,c_lessequals(V_x,V_z,T_a),true),true),true) = true ),
inference(skolemize,[status(sab)],[114]) ).
tff(116,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] : ( ifeq(class_Orderings_Oorder(T_a),true,ifeq(c_lessequals(V_x,V_y,T_a),true,ifeq(c_lessequals(V_y,V_z,T_a),true,c_lessequals(V_x,V_z,T_a),true),true),true) = true ),
inference(modus_ponens,[status(thm)],[115,111]) ).
tff(117,plain,
( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] : ( ifeq(class_Orderings_Oorder(T_a),true,ifeq(c_lessequals(V_x,V_y,T_a),true,ifeq(c_lessequals(V_y,V_z,T_a),true,c_lessequals(V_x,V_z,T_a),true),true),true) = true )
| ( ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true,ifeq(c_lessequals(v_k(v_x),v_f(v_x),t_b),true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b),true),true),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(118,plain,
ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true,ifeq(c_lessequals(v_k(v_x),v_f(v_x),t_b),true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b),true),true),true) = true,
inference(unit_resolution,[status(thm)],[117,116]) ).
tff(119,plain,
true = ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true,ifeq(c_lessequals(v_k(v_x),v_f(v_x),t_b),true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b),true),true),true),
inference(symmetry,[status(thm)],[118]) ).
tff(120,plain,
true = c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b),
inference(transitivity,[status(thm)],[119,109,75,49,47,41]) ).
tff(121,plain,
ifeq(true,true,c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),true) = ifeq(c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b),true,c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),true),
inference(monotonicity,[status(thm)],[120]) ).
tff(122,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),true) = c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(123,plain,
ifeq(true,true,c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),true) = c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
inference(unit_resolution,[status(thm)],[122,16]) ).
tff(124,plain,
c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) = ifeq(true,true,c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),true),
inference(symmetry,[status(thm)],[123]) ).
tff(125,plain,
c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) = true,
inference(transitivity,[status(thm)],[124,121,39,36,9]) ).
tff(126,plain,
( ( c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) != true )
<=> ( c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) != true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(127,axiom,
c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(128,plain,
c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) != true,
inference(modus_ponens,[status(thm)],[127,126]) ).
tff(129,plain,
$false,
inference(unit_resolution,[status(thm)],[128,125]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ANA023-10 : TPTP v9.0.0. Released v7.5.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 11:21:48 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.38 % SZS status Unsatisfiable
% 0.13/0.38 % SZS output start Proof
% See solution above
% 0.21/0.41 % E exiting
%------------------------------------------------------------------------------