TSTP Solution File: ANA023-10 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : ANA023-10 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n003.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 : 600s
% DateTime : Thu Jul 14 19:14:39 EDT 2022
% Result : Unsatisfiable 0.20s 0.40s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 51
% Syntax : Number of clauses : 150 ( 80 unt; 0 nHn; 112 RR)
% Number of literals : 256 ( 255 equ; 107 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 4 con; 0-4 aty)
% Number of variables : 101 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ifeq_axiom,axiom,
ifeq2(A,A,B,C) = B ).
cnf(ifeq_axiom_001,axiom,
ifeq(A,A,B,C) = B ).
cnf(cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0,axiom,
ifeq2(class_OrderedGroup_Ocomm__monoid__add(T_a),true,c_plus(c_0,V_y,T_a),V_y) = V_y ).
cnf(cls_OrderedGroup_Ocompare__rls__9_0,axiom,
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 ).
cnf(cls_OrderedGroup_Ocompare__rls__9_1,axiom,
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 ).
cnf(cls_Orderings_Oorder__class_Oorder__trans_0,axiom,
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 ).
cnf(cls_conjecture_1,negated_conjecture,
c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) = true ).
cnf(cls_conjecture_2,negated_conjecture,
c_lessequals(v_k(v_x),v_f(v_x),t_b) = true ).
cnf(cls_conjecture_3,negated_conjecture,
c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) != true ).
cnf(clsrel_Orderings_Olinorder_4,axiom,
ifeq(class_Orderings_Olinorder(T),true,class_Orderings_Oorder(T),true) = true ).
cnf(clsrel_Ring__and__Field_Oordered__idom_23,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_OrderedGroup_Ocomm__monoid__add(T),true) = true ).
cnf(clsrel_Ring__and__Field_Oordered__idom_33,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Orderings_Olinorder(T),true) = true ).
cnf(clsrel_Ring__and__Field_Oordered__idom_54,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_OrderedGroup_Opordered__ab__group__add(T),true) = true ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b) = true ).
cnf(refute_0_0,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(c_plus(c_0,X_43,t_b),X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true) = true,
inference(subst,[],[cls_OrderedGroup_Ocompare__rls__9_1:[bind(T_a,$fot(t_b)),bind(V_a,$fot(c_0)),bind(V_b,$fot(X_43)),bind(V_c,$fot(X_44))]]) ).
cnf(refute_0_1,plain,
ifeq2(class_OrderedGroup_Ocomm__monoid__add(t_b),true,c_plus(c_0,X_11,t_b),X_11) = X_11,
inference(subst,[],[cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0:[bind(T_a,$fot(t_b)),bind(V_y,$fot(X_11))]]) ).
cnf(refute_0_2,plain,
ifeq(class_Ring__and__Field_Oordered__idom(t_b),true,class_OrderedGroup_Ocomm__monoid__add(t_b),true) = true,
inference(subst,[],[clsrel_Ring__and__Field_Oordered__idom_23:[bind(T,$fot(t_b))]]) ).
cnf(refute_0_3,plain,
( class_Ring__and__Field_Oordered__idom(t_b) != true
| ifeq(class_Ring__and__Field_Oordered__idom(t_b),true,class_OrderedGroup_Ocomm__monoid__add(t_b),true) != true
| ifeq(true,true,class_OrderedGroup_Ocomm__monoid__add(t_b),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(class_Ring__and__Field_Oordered__idom(t_b),true,class_OrderedGroup_Ocomm__monoid__add(t_b),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_4,plain,
( ifeq(class_Ring__and__Field_Oordered__idom(t_b),true,class_OrderedGroup_Ocomm__monoid__add(t_b),true) != true
| ifeq(true,true,class_OrderedGroup_Ocomm__monoid__add(t_b),true) = true ),
inference(resolve,[$cnf( $equal(class_Ring__and__Field_Oordered__idom(t_b),true) )],[tfree_tcs,refute_0_3]) ).
cnf(refute_0_5,plain,
ifeq(true,true,class_OrderedGroup_Ocomm__monoid__add(t_b),true) = true,
inference(resolve,[$cnf( $equal(ifeq(class_Ring__and__Field_Oordered__idom(t_b),true,class_OrderedGroup_Ocomm__monoid__add(t_b),true),true) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
ifeq(true,true,class_OrderedGroup_Ocomm__monoid__add(t_b),true) = class_OrderedGroup_Ocomm__monoid__add(t_b),
inference(subst,[],[ifeq_axiom_001:[bind(A,$fot(true)),bind(B,$fot(class_OrderedGroup_Ocomm__monoid__add(t_b))),bind(C,$fot(true))]]) ).
cnf(refute_0_7,plain,
( ifeq(true,true,class_OrderedGroup_Ocomm__monoid__add(t_b),true) != class_OrderedGroup_Ocomm__monoid__add(t_b)
| ifeq(true,true,class_OrderedGroup_Ocomm__monoid__add(t_b),true) != true
| class_OrderedGroup_Ocomm__monoid__add(t_b) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,class_OrderedGroup_Ocomm__monoid__add(t_b),true),true) ),[0],$fot(class_OrderedGroup_Ocomm__monoid__add(t_b))]]) ).
cnf(refute_0_8,plain,
( ifeq(true,true,class_OrderedGroup_Ocomm__monoid__add(t_b),true) != true
| class_OrderedGroup_Ocomm__monoid__add(t_b) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,class_OrderedGroup_Ocomm__monoid__add(t_b),true),class_OrderedGroup_Ocomm__monoid__add(t_b)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
class_OrderedGroup_Ocomm__monoid__add(t_b) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,class_OrderedGroup_Ocomm__monoid__add(t_b),true),true) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
( class_OrderedGroup_Ocomm__monoid__add(t_b) != true
| ifeq2(class_OrderedGroup_Ocomm__monoid__add(t_b),true,c_plus(c_0,X_11,t_b),X_11) != X_11
| ifeq2(true,true,c_plus(c_0,X_11,t_b),X_11) = X_11 ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(class_OrderedGroup_Ocomm__monoid__add(t_b),true,c_plus(c_0,X_11,t_b),X_11),X_11) ),[0,0],$fot(true)]]) ).
cnf(refute_0_11,plain,
( ifeq2(class_OrderedGroup_Ocomm__monoid__add(t_b),true,c_plus(c_0,X_11,t_b),X_11) != X_11
| ifeq2(true,true,c_plus(c_0,X_11,t_b),X_11) = X_11 ),
inference(resolve,[$cnf( $equal(class_OrderedGroup_Ocomm__monoid__add(t_b),true) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
ifeq2(true,true,c_plus(c_0,X_11,t_b),X_11) = X_11,
inference(resolve,[$cnf( $equal(ifeq2(class_OrderedGroup_Ocomm__monoid__add(t_b),true,c_plus(c_0,X_11,t_b),X_11),X_11) )],[refute_0_1,refute_0_11]) ).
cnf(refute_0_13,plain,
ifeq2(true,true,c_plus(c_0,X_11,t_b),X_11) = c_plus(c_0,X_11,t_b),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(c_plus(c_0,X_11,t_b))),bind(C,$fot(X_11))]]) ).
cnf(refute_0_14,plain,
( ifeq2(true,true,c_plus(c_0,X_11,t_b),X_11) != X_11
| ifeq2(true,true,c_plus(c_0,X_11,t_b),X_11) != c_plus(c_0,X_11,t_b)
| c_plus(c_0,X_11,t_b) = X_11 ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(true,true,c_plus(c_0,X_11,t_b),X_11),X_11) ),[0],$fot(c_plus(c_0,X_11,t_b))]]) ).
cnf(refute_0_15,plain,
( ifeq2(true,true,c_plus(c_0,X_11,t_b),X_11) != X_11
| c_plus(c_0,X_11,t_b) = X_11 ),
inference(resolve,[$cnf( $equal(ifeq2(true,true,c_plus(c_0,X_11,t_b),X_11),c_plus(c_0,X_11,t_b)) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
c_plus(c_0,X_11,t_b) = X_11,
inference(resolve,[$cnf( $equal(ifeq2(true,true,c_plus(c_0,X_11,t_b),X_11),X_11) )],[refute_0_12,refute_0_15]) ).
cnf(refute_0_17,plain,
c_plus(c_0,X_43,t_b) = X_43,
inference(subst,[],[refute_0_16:[bind(X_11,$fot(X_43))]]) ).
cnf(refute_0_18,plain,
( c_plus(c_0,X_43,t_b) != X_43
| ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(c_plus(c_0,X_43,t_b),X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true) != true
| ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(c_plus(c_0,X_43,t_b),X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true),true) ),[0,2,0,0],$fot(X_43)]]) ).
cnf(refute_0_19,plain,
( ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(c_plus(c_0,X_43,t_b),X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true) != true
| ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true) = true ),
inference(resolve,[$cnf( $equal(c_plus(c_0,X_43,t_b),X_43) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(c_plus(c_0,X_43,t_b),X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true),true) )],[refute_0_0,refute_0_19]) ).
cnf(refute_0_21,plain,
ifeq(true,true,ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true) = ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),
inference(subst,[],[ifeq_axiom_001:[bind(A,$fot(true)),bind(B,$fot(ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true))),bind(C,$fot(true))]]) ).
cnf(refute_0_22,plain,
ifeq(class_Ring__and__Field_Oordered__idom(t_b),true,class_OrderedGroup_Opordered__ab__group__add(t_b),true) = true,
inference(subst,[],[clsrel_Ring__and__Field_Oordered__idom_54:[bind(T,$fot(t_b))]]) ).
cnf(refute_0_23,plain,
( class_Ring__and__Field_Oordered__idom(t_b) != true
| ifeq(class_Ring__and__Field_Oordered__idom(t_b),true,class_OrderedGroup_Opordered__ab__group__add(t_b),true) != true
| ifeq(true,true,class_OrderedGroup_Opordered__ab__group__add(t_b),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(class_Ring__and__Field_Oordered__idom(t_b),true,class_OrderedGroup_Opordered__ab__group__add(t_b),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_24,plain,
( ifeq(class_Ring__and__Field_Oordered__idom(t_b),true,class_OrderedGroup_Opordered__ab__group__add(t_b),true) != true
| ifeq(true,true,class_OrderedGroup_Opordered__ab__group__add(t_b),true) = true ),
inference(resolve,[$cnf( $equal(class_Ring__and__Field_Oordered__idom(t_b),true) )],[tfree_tcs,refute_0_23]) ).
cnf(refute_0_25,plain,
ifeq(true,true,class_OrderedGroup_Opordered__ab__group__add(t_b),true) = true,
inference(resolve,[$cnf( $equal(ifeq(class_Ring__and__Field_Oordered__idom(t_b),true,class_OrderedGroup_Opordered__ab__group__add(t_b),true),true) )],[refute_0_22,refute_0_24]) ).
cnf(refute_0_26,plain,
ifeq(true,true,class_OrderedGroup_Opordered__ab__group__add(t_b),true) = class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(subst,[],[ifeq_axiom_001:[bind(A,$fot(true)),bind(B,$fot(class_OrderedGroup_Opordered__ab__group__add(t_b))),bind(C,$fot(true))]]) ).
cnf(refute_0_27,plain,
( ifeq(true,true,class_OrderedGroup_Opordered__ab__group__add(t_b),true) != class_OrderedGroup_Opordered__ab__group__add(t_b)
| ifeq(true,true,class_OrderedGroup_Opordered__ab__group__add(t_b),true) != true
| class_OrderedGroup_Opordered__ab__group__add(t_b) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,class_OrderedGroup_Opordered__ab__group__add(t_b),true),true) ),[0],$fot(class_OrderedGroup_Opordered__ab__group__add(t_b))]]) ).
cnf(refute_0_28,plain,
( ifeq(true,true,class_OrderedGroup_Opordered__ab__group__add(t_b),true) != true
| class_OrderedGroup_Opordered__ab__group__add(t_b) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,class_OrderedGroup_Opordered__ab__group__add(t_b),true),class_OrderedGroup_Opordered__ab__group__add(t_b)) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,class_OrderedGroup_Opordered__ab__group__add(t_b),true),true) )],[refute_0_25,refute_0_28]) ).
cnf(refute_0_30,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true) = ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true),
introduced(tautology,[refl,[$fot(ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true))]]) ).
cnf(refute_0_31,plain,
( class_OrderedGroup_Opordered__ab__group__add(t_b) != true
| ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true) != ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true)
| ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true) = ifeq(true,true,ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true),ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true)) ),[1,0],$fot(true)]]) ).
cnf(refute_0_32,plain,
( class_OrderedGroup_Opordered__ab__group__add(t_b) != true
| ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true) = ifeq(true,true,ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true) ),
inference(resolve,[$cnf( $equal(ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true),ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true)) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true) = ifeq(true,true,ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true),
inference(resolve,[$cnf( $equal(class_OrderedGroup_Opordered__ab__group__add(t_b),true) )],[refute_0_29,refute_0_32]) ).
cnf(refute_0_34,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_35,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_36,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_38,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
( ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true) != ifeq(true,true,ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true)
| ifeq(true,true,ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true) != ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true)
| ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true) = ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true) ),
inference(subst,[],[refute_0_38:[bind(X,$fot(ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true))),bind(Y,$fot(ifeq(true,true,ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true))),bind(Z,$fot(ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true)))]]) ).
cnf(refute_0_40,plain,
( ifeq(true,true,ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true) != ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true)
| ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true) = ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true) ),
inference(resolve,[$cnf( $equal(ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true),ifeq(true,true,ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true)) )],[refute_0_33,refute_0_39]) ).
cnf(refute_0_41,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true) = ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true),ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true)) )],[refute_0_21,refute_0_40]) ).
cnf(refute_0_42,plain,
( ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true) != ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true)
| ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true) != true
| ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true),true) ),[0],$fot(ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true))]]) ).
cnf(refute_0_43,plain,
( ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true) != true
| ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true),ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true)) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true) = true,
inference(resolve,[$cnf( $equal(ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(X_43,X_44,t_b),true,c_lessequals(c_0,c_minus(X_44,X_43,t_b),t_b),true),true),true) )],[refute_0_20,refute_0_43]) ).
cnf(refute_0_45,plain,
ifeq(c_lessequals(v_g(v_x),v_f(v_x),t_b),true,c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),true) = true,
inference(subst,[],[refute_0_44:[bind(X_43,$fot(v_g(v_x))),bind(X_44,$fot(v_f(v_x)))]]) ).
cnf(refute_0_46,plain,
ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(c_lessequals(v_k(v_x),v_f(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true) = true,
inference(subst,[],[cls_Orderings_Oorder__class_Oorder__trans_0:[bind(T_a,$fot(t_b)),bind(V_x,$fot(X_14)),bind(V_y,$fot(v_k(v_x))),bind(V_z,$fot(v_f(v_x)))]]) ).
cnf(refute_0_47,plain,
( c_lessequals(v_k(v_x),v_f(v_x),t_b) != true
| ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(c_lessequals(v_k(v_x),v_f(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true) != true
| ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(c_lessequals(v_k(v_x),v_f(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true),true) ),[0,2,2,0],$fot(true)]]) ).
cnf(refute_0_48,plain,
( ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(c_lessequals(v_k(v_x),v_f(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true) != true
| ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true) = true ),
inference(resolve,[$cnf( $equal(c_lessequals(v_k(v_x),v_f(v_x),t_b),true) )],[cls_conjecture_2,refute_0_47]) ).
cnf(refute_0_49,plain,
ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(c_lessequals(v_k(v_x),v_f(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true),true) )],[refute_0_46,refute_0_48]) ).
cnf(refute_0_50,plain,
ifeq(true,true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true),true) = ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true),
inference(subst,[],[ifeq_axiom_001:[bind(A,$fot(true)),bind(B,$fot(ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true))),bind(C,$fot(true))]]) ).
cnf(refute_0_51,plain,
ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true) = c_lessequals(X_14,v_f(v_x),t_b),
inference(subst,[],[ifeq_axiom_001:[bind(A,$fot(true)),bind(B,$fot(c_lessequals(X_14,v_f(v_x),t_b))),bind(C,$fot(true))]]) ).
cnf(refute_0_52,plain,
ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true) = ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),
introduced(tautology,[refl,[$fot(ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true))]]) ).
cnf(refute_0_53,plain,
( ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true) != ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true)
| ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true) != c_lessequals(X_14,v_f(v_x),t_b)
| ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true) = ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true)) ),[1,2],$fot(c_lessequals(X_14,v_f(v_x),t_b))]]) ).
cnf(refute_0_54,plain,
( ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true) != c_lessequals(X_14,v_f(v_x),t_b)
| ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true) = ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true) ),
inference(resolve,[$cnf( $equal(ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true)) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true) = ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true),
inference(resolve,[$cnf( $equal(ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),c_lessequals(X_14,v_f(v_x),t_b)) )],[refute_0_51,refute_0_54]) ).
cnf(refute_0_56,plain,
ifeq(true,true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true) = ifeq(true,true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true),
introduced(tautology,[refl,[$fot(ifeq(true,true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true))]]) ).
cnf(refute_0_57,plain,
( ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true) != ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true)
| ifeq(true,true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true) != ifeq(true,true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true)
| ifeq(true,true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true) = ifeq(true,true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true),ifeq(true,true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true)) ),[1,2],$fot(ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true))]]) ).
cnf(refute_0_58,plain,
( ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true) != ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true)
| ifeq(true,true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true) = ifeq(true,true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true),true) ),
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true),ifeq(true,true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true)) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
ifeq(true,true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true) = ifeq(true,true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true),true),
inference(resolve,[$cnf( $equal(ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true)) )],[refute_0_55,refute_0_58]) ).
cnf(refute_0_60,plain,
ifeq(class_Orderings_Olinorder(t_b),true,class_Orderings_Oorder(t_b),true) = true,
inference(subst,[],[clsrel_Orderings_Olinorder_4:[bind(T,$fot(t_b))]]) ).
cnf(refute_0_61,plain,
ifeq(class_Ring__and__Field_Oordered__idom(t_b),true,class_Orderings_Olinorder(t_b),true) = true,
inference(subst,[],[clsrel_Ring__and__Field_Oordered__idom_33:[bind(T,$fot(t_b))]]) ).
cnf(refute_0_62,plain,
( class_Ring__and__Field_Oordered__idom(t_b) != true
| ifeq(class_Ring__and__Field_Oordered__idom(t_b),true,class_Orderings_Olinorder(t_b),true) != true
| ifeq(true,true,class_Orderings_Olinorder(t_b),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(class_Ring__and__Field_Oordered__idom(t_b),true,class_Orderings_Olinorder(t_b),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_63,plain,
( ifeq(class_Ring__and__Field_Oordered__idom(t_b),true,class_Orderings_Olinorder(t_b),true) != true
| ifeq(true,true,class_Orderings_Olinorder(t_b),true) = true ),
inference(resolve,[$cnf( $equal(class_Ring__and__Field_Oordered__idom(t_b),true) )],[tfree_tcs,refute_0_62]) ).
cnf(refute_0_64,plain,
ifeq(true,true,class_Orderings_Olinorder(t_b),true) = true,
inference(resolve,[$cnf( $equal(ifeq(class_Ring__and__Field_Oordered__idom(t_b),true,class_Orderings_Olinorder(t_b),true),true) )],[refute_0_61,refute_0_63]) ).
cnf(refute_0_65,plain,
ifeq(true,true,class_Orderings_Olinorder(t_b),true) = class_Orderings_Olinorder(t_b),
inference(subst,[],[ifeq_axiom_001:[bind(A,$fot(true)),bind(B,$fot(class_Orderings_Olinorder(t_b))),bind(C,$fot(true))]]) ).
cnf(refute_0_66,plain,
( ifeq(true,true,class_Orderings_Olinorder(t_b),true) != class_Orderings_Olinorder(t_b)
| ifeq(true,true,class_Orderings_Olinorder(t_b),true) != true
| class_Orderings_Olinorder(t_b) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,class_Orderings_Olinorder(t_b),true),true) ),[0],$fot(class_Orderings_Olinorder(t_b))]]) ).
cnf(refute_0_67,plain,
( ifeq(true,true,class_Orderings_Olinorder(t_b),true) != true
| class_Orderings_Olinorder(t_b) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,class_Orderings_Olinorder(t_b),true),class_Orderings_Olinorder(t_b)) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
class_Orderings_Olinorder(t_b) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,class_Orderings_Olinorder(t_b),true),true) )],[refute_0_64,refute_0_67]) ).
cnf(refute_0_69,plain,
( class_Orderings_Olinorder(t_b) != true
| ifeq(class_Orderings_Olinorder(t_b),true,class_Orderings_Oorder(t_b),true) != true
| ifeq(true,true,class_Orderings_Oorder(t_b),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(class_Orderings_Olinorder(t_b),true,class_Orderings_Oorder(t_b),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_70,plain,
( ifeq(class_Orderings_Olinorder(t_b),true,class_Orderings_Oorder(t_b),true) != true
| ifeq(true,true,class_Orderings_Oorder(t_b),true) = true ),
inference(resolve,[$cnf( $equal(class_Orderings_Olinorder(t_b),true) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
ifeq(true,true,class_Orderings_Oorder(t_b),true) = true,
inference(resolve,[$cnf( $equal(ifeq(class_Orderings_Olinorder(t_b),true,class_Orderings_Oorder(t_b),true),true) )],[refute_0_60,refute_0_70]) ).
cnf(refute_0_72,plain,
ifeq(true,true,class_Orderings_Oorder(t_b),true) = class_Orderings_Oorder(t_b),
inference(subst,[],[ifeq_axiom_001:[bind(A,$fot(true)),bind(B,$fot(class_Orderings_Oorder(t_b))),bind(C,$fot(true))]]) ).
cnf(refute_0_73,plain,
( ifeq(true,true,class_Orderings_Oorder(t_b),true) != class_Orderings_Oorder(t_b)
| ifeq(true,true,class_Orderings_Oorder(t_b),true) != true
| class_Orderings_Oorder(t_b) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,class_Orderings_Oorder(t_b),true),true) ),[0],$fot(class_Orderings_Oorder(t_b))]]) ).
cnf(refute_0_74,plain,
( ifeq(true,true,class_Orderings_Oorder(t_b),true) != true
| class_Orderings_Oorder(t_b) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,class_Orderings_Oorder(t_b),true),class_Orderings_Oorder(t_b)) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
class_Orderings_Oorder(t_b) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,class_Orderings_Oorder(t_b),true),true) )],[refute_0_71,refute_0_74]) ).
cnf(refute_0_76,plain,
ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true) = ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true),
introduced(tautology,[refl,[$fot(ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true))]]) ).
cnf(refute_0_77,plain,
( class_Orderings_Oorder(t_b) != true
| ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true) != ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true)
| ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true) = ifeq(true,true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true),ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true)) ),[1,0],$fot(true)]]) ).
cnf(refute_0_78,plain,
( class_Orderings_Oorder(t_b) != true
| ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true) = ifeq(true,true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true) ),
inference(resolve,[$cnf( $equal(ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true),ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true)) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true) = ifeq(true,true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true),
inference(resolve,[$cnf( $equal(class_Orderings_Oorder(t_b),true) )],[refute_0_75,refute_0_78]) ).
cnf(refute_0_80,plain,
( ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true) != ifeq(true,true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true)
| ifeq(true,true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true) != ifeq(true,true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true),true)
| ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true) = ifeq(true,true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true),true) ),
inference(subst,[],[refute_0_38:[bind(X,$fot(ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true))),bind(Y,$fot(ifeq(true,true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true))),bind(Z,$fot(ifeq(true,true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true),true)))]]) ).
cnf(refute_0_81,plain,
( ifeq(true,true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true) != ifeq(true,true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true),true)
| ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true) = ifeq(true,true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true),true) ),
inference(resolve,[$cnf( $equal(ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true),ifeq(true,true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true)) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true) = ifeq(true,true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true),true),
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true),ifeq(true,true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true),true)) )],[refute_0_59,refute_0_81]) ).
cnf(refute_0_83,plain,
( ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true) != ifeq(true,true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true),true)
| ifeq(true,true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true),true) != ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true)
| ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true) = ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true) ),
inference(subst,[],[refute_0_38:[bind(X,$fot(ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true))),bind(Y,$fot(ifeq(true,true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true),true))),bind(Z,$fot(ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true)))]]) ).
cnf(refute_0_84,plain,
( ifeq(true,true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true),true) != ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true)
| ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true) = ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true) ),
inference(resolve,[$cnf( $equal(ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true),ifeq(true,true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true),true)) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true) = ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true),
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true),true),ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true)) )],[refute_0_50,refute_0_84]) ).
cnf(refute_0_86,plain,
( ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true) != ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true)
| ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true) != true
| ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true),true) ),[0],$fot(ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true))]]) ).
cnf(refute_0_87,plain,
( ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true) != true
| ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true),ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true)) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,c_lessequals(X_14,v_f(v_x),t_b),true) = true,
inference(resolve,[$cnf( $equal(ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(X_14,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X_14,v_f(v_x),t_b),true),true),true),true) )],[refute_0_49,refute_0_87]) ).
cnf(refute_0_89,plain,
ifeq(c_lessequals(v_g(v_x),v_k(v_x),t_b),true,c_lessequals(v_g(v_x),v_f(v_x),t_b),true) = true,
inference(subst,[],[refute_0_88:[bind(X_14,$fot(v_g(v_x)))]]) ).
cnf(refute_0_90,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(subst,[],[cls_OrderedGroup_Ocompare__rls__9_0:[bind(T_a,$fot(t_b)),bind(V_a,$fot(c_0)),bind(V_b,$fot(v_g(v_x))),bind(V_c,$fot(v_k(v_x)))]]) ).
cnf(refute_0_91,plain,
( c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),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) != true
| ifeq(class_OrderedGroup_Opordered__ab__group__add(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),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true),true) ),[0,2,0],$fot(true)]]) ).
cnf(refute_0_92,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
| ifeq(class_OrderedGroup_Opordered__ab__group__add(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),true) = true ),
inference(resolve,[$cnf( $equal(c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),true) )],[cls_conjecture_1,refute_0_91]) ).
cnf(refute_0_93,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true),true) )],[refute_0_90,refute_0_92]) ).
cnf(refute_0_94,plain,
ifeq(true,true,c_lessequals(v_g(v_x),v_k(v_x),t_b),true) = c_lessequals(v_g(v_x),v_k(v_x),t_b),
inference(subst,[],[ifeq_axiom_001:[bind(A,$fot(true)),bind(B,$fot(c_lessequals(v_g(v_x),v_k(v_x),t_b))),bind(C,$fot(true))]]) ).
cnf(refute_0_95,plain,
c_plus(c_0,v_g(v_x),t_b) = v_g(v_x),
inference(subst,[],[refute_0_16:[bind(X_11,$fot(v_g(v_x)))]]) ).
cnf(refute_0_96,plain,
c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b) = c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),
introduced(tautology,[refl,[$fot(c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b))]]) ).
cnf(refute_0_97,plain,
( c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b) != c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b)
| c_plus(c_0,v_g(v_x),t_b) != v_g(v_x)
| c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b) = c_lessequals(v_g(v_x),v_k(v_x),t_b) ),
introduced(tautology,[equality,[$cnf( $equal(c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b)) ),[1,0],$fot(v_g(v_x))]]) ).
cnf(refute_0_98,plain,
( c_plus(c_0,v_g(v_x),t_b) != v_g(v_x)
| c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b) = c_lessequals(v_g(v_x),v_k(v_x),t_b) ),
inference(resolve,[$cnf( $equal(c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b)) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b) = c_lessequals(v_g(v_x),v_k(v_x),t_b),
inference(resolve,[$cnf( $equal(c_plus(c_0,v_g(v_x),t_b),v_g(v_x)) )],[refute_0_95,refute_0_98]) ).
cnf(refute_0_100,plain,
ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true) = c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),
inference(subst,[],[ifeq_axiom_001:[bind(A,$fot(true)),bind(B,$fot(c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b))),bind(C,$fot(true))]]) ).
cnf(refute_0_101,plain,
( c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b) != c_lessequals(v_g(v_x),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) != 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) = c_lessequals(v_g(v_x),v_k(v_x),t_b) ),
inference(subst,[],[refute_0_38:[bind(X,$fot(ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true))),bind(Y,$fot(c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b))),bind(Z,$fot(c_lessequals(v_g(v_x),v_k(v_x),t_b)))]]) ).
cnf(refute_0_102,plain,
( c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b) != c_lessequals(v_g(v_x),v_k(v_x),t_b)
| ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true) = c_lessequals(v_g(v_x),v_k(v_x),t_b) ),
inference(resolve,[$cnf( $equal(ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b)) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true) = c_lessequals(v_g(v_x),v_k(v_x),t_b),
inference(resolve,[$cnf( $equal(c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),c_lessequals(v_g(v_x),v_k(v_x),t_b)) )],[refute_0_99,refute_0_102]) ).
cnf(refute_0_104,plain,
ifeq(true,true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true) = ifeq(true,true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true),
introduced(tautology,[refl,[$fot(ifeq(true,true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true))]]) ).
cnf(refute_0_105,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(v_g(v_x),v_k(v_x),t_b)
| ifeq(true,true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true) != ifeq(true,true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true)
| ifeq(true,true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true) = ifeq(true,true,c_lessequals(v_g(v_x),v_k(v_x),t_b),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true),ifeq(true,true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true)) ),[1,2],$fot(c_lessequals(v_g(v_x),v_k(v_x),t_b))]]) ).
cnf(refute_0_106,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(v_g(v_x),v_k(v_x),t_b)
| ifeq(true,true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true) = ifeq(true,true,c_lessequals(v_g(v_x),v_k(v_x),t_b),true) ),
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true),ifeq(true,true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true)) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
ifeq(true,true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true) = ifeq(true,true,c_lessequals(v_g(v_x),v_k(v_x),t_b),true),
inference(resolve,[$cnf( $equal(ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),c_lessequals(v_g(v_x),v_k(v_x),t_b)) )],[refute_0_103,refute_0_106]) ).
cnf(refute_0_108,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true) = ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true),
introduced(tautology,[refl,[$fot(ifeq(class_OrderedGroup_Opordered__ab__group__add(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),true))]]) ).
cnf(refute_0_109,plain,
( class_OrderedGroup_Opordered__ab__group__add(t_b) != true
| ifeq(class_OrderedGroup_Opordered__ab__group__add(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),true) != ifeq(class_OrderedGroup_Opordered__ab__group__add(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),true)
| ifeq(class_OrderedGroup_Opordered__ab__group__add(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),true) = ifeq(true,true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true),ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true)) ),[1,0],$fot(true)]]) ).
cnf(refute_0_110,plain,
( class_OrderedGroup_Opordered__ab__group__add(t_b) != true
| ifeq(class_OrderedGroup_Opordered__ab__group__add(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),true) = ifeq(true,true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true) ),
inference(resolve,[$cnf( $equal(ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true),ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true)) )],[refute_0_108,refute_0_109]) ).
cnf(refute_0_111,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true) = ifeq(true,true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true),
inference(resolve,[$cnf( $equal(class_OrderedGroup_Opordered__ab__group__add(t_b),true) )],[refute_0_29,refute_0_110]) ).
cnf(refute_0_112,plain,
( ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true) != ifeq(true,true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true)
| ifeq(true,true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true) != ifeq(true,true,c_lessequals(v_g(v_x),v_k(v_x),t_b),true)
| ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true) = ifeq(true,true,c_lessequals(v_g(v_x),v_k(v_x),t_b),true) ),
inference(subst,[],[refute_0_38:[bind(X,$fot(ifeq(class_OrderedGroup_Opordered__ab__group__add(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),true))),bind(Y,$fot(ifeq(true,true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true))),bind(Z,$fot(ifeq(true,true,c_lessequals(v_g(v_x),v_k(v_x),t_b),true)))]]) ).
cnf(refute_0_113,plain,
( ifeq(true,true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true) != ifeq(true,true,c_lessequals(v_g(v_x),v_k(v_x),t_b),true)
| ifeq(class_OrderedGroup_Opordered__ab__group__add(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),true) = ifeq(true,true,c_lessequals(v_g(v_x),v_k(v_x),t_b),true) ),
inference(resolve,[$cnf( $equal(ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true),ifeq(true,true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true)) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true) = ifeq(true,true,c_lessequals(v_g(v_x),v_k(v_x),t_b),true),
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true),ifeq(true,true,c_lessequals(v_g(v_x),v_k(v_x),t_b),true)) )],[refute_0_107,refute_0_113]) ).
cnf(refute_0_115,plain,
( ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true) != ifeq(true,true,c_lessequals(v_g(v_x),v_k(v_x),t_b),true)
| ifeq(true,true,c_lessequals(v_g(v_x),v_k(v_x),t_b),true) != c_lessequals(v_g(v_x),v_k(v_x),t_b)
| ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true) = c_lessequals(v_g(v_x),v_k(v_x),t_b) ),
inference(subst,[],[refute_0_38:[bind(X,$fot(ifeq(class_OrderedGroup_Opordered__ab__group__add(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),true))),bind(Y,$fot(ifeq(true,true,c_lessequals(v_g(v_x),v_k(v_x),t_b),true))),bind(Z,$fot(c_lessequals(v_g(v_x),v_k(v_x),t_b)))]]) ).
cnf(refute_0_116,plain,
( ifeq(true,true,c_lessequals(v_g(v_x),v_k(v_x),t_b),true) != c_lessequals(v_g(v_x),v_k(v_x),t_b)
| ifeq(class_OrderedGroup_Opordered__ab__group__add(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),true) = c_lessequals(v_g(v_x),v_k(v_x),t_b) ),
inference(resolve,[$cnf( $equal(ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true),ifeq(true,true,c_lessequals(v_g(v_x),v_k(v_x),t_b),true)) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true) = c_lessequals(v_g(v_x),v_k(v_x),t_b),
inference(resolve,[$cnf( $equal(ifeq(true,true,c_lessequals(v_g(v_x),v_k(v_x),t_b),true),c_lessequals(v_g(v_x),v_k(v_x),t_b)) )],[refute_0_94,refute_0_116]) ).
cnf(refute_0_118,plain,
( ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true) != c_lessequals(v_g(v_x),v_k(v_x),t_b)
| ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true) != true
| c_lessequals(v_g(v_x),v_k(v_x),t_b) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true),true) ),[0],$fot(c_lessequals(v_g(v_x),v_k(v_x),t_b))]]) ).
cnf(refute_0_119,plain,
( ifeq(class_OrderedGroup_Opordered__ab__group__add(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),true) != true
| c_lessequals(v_g(v_x),v_k(v_x),t_b) = true ),
inference(resolve,[$cnf( $equal(ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true),c_lessequals(v_g(v_x),v_k(v_x),t_b)) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
c_lessequals(v_g(v_x),v_k(v_x),t_b) = true,
inference(resolve,[$cnf( $equal(ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true),true) )],[refute_0_93,refute_0_119]) ).
cnf(refute_0_121,plain,
( c_lessequals(v_g(v_x),v_k(v_x),t_b) != true
| ifeq(c_lessequals(v_g(v_x),v_k(v_x),t_b),true,c_lessequals(v_g(v_x),v_f(v_x),t_b),true) != true
| ifeq(true,true,c_lessequals(v_g(v_x),v_f(v_x),t_b),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(c_lessequals(v_g(v_x),v_k(v_x),t_b),true,c_lessequals(v_g(v_x),v_f(v_x),t_b),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_122,plain,
( ifeq(c_lessequals(v_g(v_x),v_k(v_x),t_b),true,c_lessequals(v_g(v_x),v_f(v_x),t_b),true) != true
| ifeq(true,true,c_lessequals(v_g(v_x),v_f(v_x),t_b),true) = true ),
inference(resolve,[$cnf( $equal(c_lessequals(v_g(v_x),v_k(v_x),t_b),true) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
ifeq(true,true,c_lessequals(v_g(v_x),v_f(v_x),t_b),true) = true,
inference(resolve,[$cnf( $equal(ifeq(c_lessequals(v_g(v_x),v_k(v_x),t_b),true,c_lessequals(v_g(v_x),v_f(v_x),t_b),true),true) )],[refute_0_89,refute_0_122]) ).
cnf(refute_0_124,plain,
ifeq(true,true,c_lessequals(v_g(v_x),v_f(v_x),t_b),true) = c_lessequals(v_g(v_x),v_f(v_x),t_b),
inference(subst,[],[ifeq_axiom_001:[bind(A,$fot(true)),bind(B,$fot(c_lessequals(v_g(v_x),v_f(v_x),t_b))),bind(C,$fot(true))]]) ).
cnf(refute_0_125,plain,
( ifeq(true,true,c_lessequals(v_g(v_x),v_f(v_x),t_b),true) != c_lessequals(v_g(v_x),v_f(v_x),t_b)
| ifeq(true,true,c_lessequals(v_g(v_x),v_f(v_x),t_b),true) != true
| c_lessequals(v_g(v_x),v_f(v_x),t_b) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,c_lessequals(v_g(v_x),v_f(v_x),t_b),true),true) ),[0],$fot(c_lessequals(v_g(v_x),v_f(v_x),t_b))]]) ).
cnf(refute_0_126,plain,
( ifeq(true,true,c_lessequals(v_g(v_x),v_f(v_x),t_b),true) != true
| c_lessequals(v_g(v_x),v_f(v_x),t_b) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,c_lessequals(v_g(v_x),v_f(v_x),t_b),true),c_lessequals(v_g(v_x),v_f(v_x),t_b)) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
c_lessequals(v_g(v_x),v_f(v_x),t_b) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,c_lessequals(v_g(v_x),v_f(v_x),t_b),true),true) )],[refute_0_123,refute_0_126]) ).
cnf(refute_0_128,plain,
( c_lessequals(v_g(v_x),v_f(v_x),t_b) != true
| ifeq(c_lessequals(v_g(v_x),v_f(v_x),t_b),true,c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),true) != true
| ifeq(true,true,c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(c_lessequals(v_g(v_x),v_f(v_x),t_b),true,c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_129,plain,
( ifeq(c_lessequals(v_g(v_x),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(true,true,c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),true) = true ),
inference(resolve,[$cnf( $equal(c_lessequals(v_g(v_x),v_f(v_x),t_b),true) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
ifeq(true,true,c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),true) = true,
inference(resolve,[$cnf( $equal(ifeq(c_lessequals(v_g(v_x),v_f(v_x),t_b),true,c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),true),true) )],[refute_0_45,refute_0_129]) ).
cnf(refute_0_131,plain,
ifeq(true,true,c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),true) = c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
inference(subst,[],[ifeq_axiom_001:[bind(A,$fot(true)),bind(B,$fot(c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b))),bind(C,$fot(true))]]) ).
cnf(refute_0_132,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)
| ifeq(true,true,c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),true) != true
| c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),true),true) ),[0],$fot(c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b))]]) ).
cnf(refute_0_133,plain,
( ifeq(true,true,c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),true) != true
| c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),true),c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b)) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),true),true) )],[refute_0_130,refute_0_133]) ).
cnf(refute_0_135,plain,
$false,
inference(resolve,[$cnf( $equal(c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),true) )],[refute_0_134,cls_conjecture_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ANA023-10 : TPTP v8.1.0. Released v7.5.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jul 8 05:36:42 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.40 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.40
% 0.20/0.40 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.44
%------------------------------------------------------------------------------